Time and Fractals: Perspectives in Economics, Entrepreneurship, and Management (Contributions to Management Science) 3031381874, 9783031381874

Table of contents :
Acknowledgements
Contents
Contributors
List of Figures
List of Tables
An Introduction to Time and Fractals: Perspectives in Economics, Entrepreneurship, and Management
References
Part I: Time
Time Series Analysis of Entrepreneurial Orientation: A Machine Learning Approach Using GEM Data
1 Introduction
2 Theoretical Framework
2.1 Entrepreneurial Orientation and Its Dimensions
2.2 Entrepreneurial Orientation and Gender Differences
2.3 An Overview of Entrepreneurial Orientation in Low-Income and High-Income Countries
3 Methodology
3.1 Sample and Data Collection
3.2 Data Analysis and Results
3.2.1 EO´s Temporal Changes Based on Countries´ Income
3.2.2 EO´s Temporal Changes Based on Gender
3.2.3 Correlation
3.2.4 OLS Regression Procedure
3.2.5 Time Series Predictive Models
4 Conclusions and Discussion
5 Contributions, Limitations, and Future Research
References
A Theoretical Research on the Effectiveness of Time Management in Dynamics of Employee-Organization Relationship
1 Introduction
2 Conceptualization of Employee-Organization Relationship
2.1 Employee/Individual
2.2 Employment Relationship
2.3 Organizational Context
3 Theoretical Framework of Employee-Organization Relationship
4 Conceptualization of Time Management
5 Theoretical Framework of Time Management
6 Time Management Approaches
7 A Review of Literature
8 Necessary Skills for the Realization of Organizational Time Management
8.1 Organizational (Manager´s) Skills in Realizing Time Management Process
8.2 Individual Skills in Realizing Time Management Process
9 Time Management Effectiveness in Employee-Organization Relationships Clarifying Commonalities Between TM and EOR
9.1 Manager Clarification and Foresight in Strategic Decision-Making
9.2 Manager´s Futurology Path
9.3 Stress Management
9.4 Creativity and Innovation
9.5 Work-Family Flexibility
9.6 Job Satisfaction
9.7 Organizational Performance Improvement
10 Discussion
11 Conclusion
12 Recommendations for Future Research
13 Operational Guidelines for Organization Managers
References
The Degradation of Goals over Time: How Ambiguity and Managerial Cognition Shape Distributions of Project Time and Cost with E...
1 Information States, Cognitions, and Decisions
1.1 Evidence Linking Information States to Overruns in a Cognitive-Technical System
2 How Overruns Emerge from the Interaction Between Project Structure and Managerial Cognition
2.1 Cognition: The Project Manager-Decision-Maker
2.2 Characteristics of the Project Technical System
2.3 Parent Organizations, Customers, and Subcontractors
3 Improving the Management of a System of Ambiguity and Cognition
3.1 Improved Modeling
3.2 Create a Learning Organization
3.3 Improve Communication and Negotiation Among Project Decision Makers
3.4 Simplify: Reduce Interdependencies and Complexity
3.5 Study Other Projects
3.6 Delay Some Decisions
4 Conclusion
Appendix
References
Time to Respond: Identification, Proximity, and Safety at Work
1 Introduction
2 Safety Models
3 Foundations
4 The Model Elements in More Detail
5 Additional Influences and the Identification-Proximity Relationship
6 Model Summary
7 Conclusion
Appendix
Applying the Model
References
Part II: Fractals
Fractals and Nonlinear Dynamic Modeling in Energy Economics: A Comprehensive Overview
1 Introduction
2 Fractal in Energy Economics: Study of Methodological Developments
2.1 Fractal Methodology and Developments
2.1.1 Fractal Methodology: Basic Techniques
2.1.2 Fractal Methodology: Developments in Energy Economics
2.2 Fractal Methodology in Energy Economics: Research Gap
3 Fractal and Nonlinear Modeling of Energy Economics: A Thematic Analysis of Studies
3.1 Literature Review
3.1.1 Before the 2000s
3.1.2 The 2000s (2000-2009)
3.1.3 The 2010s (2010-2019)
3.1.4 The 2020s (2020-Until Now)
3.2 Fractal in Energy Economic Studies: Thematically Research Gap
4 Conclusion
References
COVID-19 and Fractal Characteristics in Energy Markets: Evidence from US Energy Price Time Series
1 Introduction
2 Literature Review
3 US Energy Markets and COVID-19 Pandemic
4 Methodology
5 Empirical Results
6 Discussion
7 Conclusion and Policy Implications
References
Fractal Organizations and Employee-Organization Relationship Dynamics
1 Introduction
2 Chaos and Evolution in Management Systems: An Example of Human Systems
3 Theoretical Literature of EOR
4 Theoretical Literature of Fractal and Fractal Organization
4.1 Fractal Patterns
5 Commonalities Between EOR and Fractal Organization as the Facilitator of Desirability and Dynamics of Organizational Relatio...
5.1 The Requirement to Have a Pattern of Organizational Behavior
5.2 The Integrity of Goals and the Unity of Individuals´ and Organization´s Interests
5.3 Requirements of Nucor Corporation
5.4 The Importance of the Individual´s Role
5.5 The Structure of Governing Interpersonal and Organizational Relationships
5.6 Dynamics of Information and Background Knowledge of Dynamics of Relationships in Fractal Organizations
5.7 The Importance of Mutual Trust as a Facilitating Factor
6 The Necessity of Fractal Dynamic Behavior in Optimal Management of Employee-Organization Relationships
7 Discussion
8 Conclusion
References
Index

Citation preview

Contributions to Management Science

Nezameddin Faghih   Editor

Time and Fractals

Perspectives in Economics, Entrepreneurship, and Management

Contributions to Management Science

The series Contributions to Management Science contains research publications in all fields of business and management science. These publications are primarily monographs and multiple author works containing new research results, and also feature selected conference-based publications are also considered. The focus of the series lies in presenting the development of latest theoretical and empirical research across different viewpoints. This book series is indexed in Scopus.

Nezameddin Faghih Editor

Time and Fractals Perspectives in Economics, Entrepreneurship, and Management

Editor Nezameddin Faghih UNESCO Chair Professor Emeritus Cambridge, MA, USA

ISSN 1431-1941 ISSN 2197-716X (electronic) Contributions to Management Science ISBN 978-3-031-38187-4 ISBN 978-3-031-38188-1 (eBook) https://doi.org/10.1007/978-3-031-38188-1 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Paper in this product is recyclable.

This book is dedicated to the City of Estahban (Fars, Iran), with amazingly beautiful fractal structures, and to the great people of Estahban, who have been producing wonderful products throughout history: figs, saffron, pomegranates, grapes, walnuts, and almonds, presenting natural fractal beauties.

Acknowledgements

The editor would like to express his sincere gratitude to Lorraine Klimowich for her great efforts in the publication process of this book. He would also like to wholeheartedly thank all chapter authors and reviewers who have devoted their time, effort, and generosity as without their generous support completing this volume would not have been possible: Samaneh Bahrololoum, Selmi Bilel, Ebrahim Bonyadi, Mozhgan Danesh, Parsa Haghighatgoo, David L. McLain, Mehdi Emami-Meybodi, Masoumeh Moterased, Sakine Owjimehr, Fatemeh Rezazadeh, Mina Rezazadeh, Sima Rezazadeh, Ali Hussein Samadi, Leyla Sarfaraz, Lida Sarreshtehdari, Jackson J. Tan, and Jinpei Wu.

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Contents

An Introduction to Time and Fractals: Perspectives in Economics, Entrepreneurship, and Management . . . . . . . . . . . . . . . . Nezameddin Faghih Part I

1

Time

Time Series Analysis of Entrepreneurial Orientation: A Machine Learning Approach Using GEM Data . . . . . . . . . . . . . . . . . Mozhgan Danesh, Nezameddin Faghih, and Masoumeh Moterased

15

A Theoretical Research on the Effectiveness of Time Management in Dynamics of Employee-Organization Relationship . . . . . . . . . . . . . . . Fatemeh Rezazadeh, Sima Rezazadeh, and Mina Rezazadeh

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The Degradation of Goals over Time: How Ambiguity and Managerial Cognition Shape Distributions of Project Time and Cost with Evidence from Actual and Simulated Projects . . . . . . . . . David L. McLain and Jinpei Wu

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Time to Respond: Identification, Proximity, and Safety at Work . . . . . . 101 David L. McLain Part II

Fractals

Fractals and Nonlinear Dynamic Modeling in Energy Economics: A Comprehensive Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Mehdi Emami-Meybodi and Ali Hussein Samadi

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Contents

COVID-19 and Fractal Characteristics in Energy Markets: Evidence from US Energy Price Time Series . . . . . . . . . . . . . . . . . . . . . 161 Mehdi Emami-Meybodi, Sakine Owjimehr, and Ali Hussein Samadi Fractal Organizations and Employee-Organization Relationship Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 Fatemeh Rezazadeh, Sima Rezazadeh, and Mina Rezazadeh Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

Contributors

Mozhgan Danesh Faculty of Entrepreneurship, Department of Entrepreneurship Management, Science and Research Branch, Islamic Azad University, University of Tehran, Tehran, Iran Mehdi Emami-Meybodi Department of Economics, Meybod University, Meybod, Iran Nezameddin Faghih UNESCO Chair Professor Emeritus, Cambridge, MA, USA David L. McLain State University of New York at Oswego, Oswego, NY, USA Sakine Owjimehr Department of Economics, Shiraz University, Shiraz, Iran Fatemeh Rezazadeh Faculty of Management and Accounting, Organizational Behavior, Allameh Tabataba’i University, Tehran, Iran Mina Rezazadeh Faculty of Engineering, Islamic Azad University Shiraz Branch, Shiraz, Iran Sima Rezazadeh Faculty of Management and Accounting, Islamic Azad University Shiraz Branch, Shiraz, Iran Ali Hussein Samadi Department of Economics, Shiraz University, Shiraz, Iran Jinpei Wu State University of New York at Oswego, Oswego, NY, USA

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List of Figures

Time Series Analysis of Entrepreneurial Orientation: A Machine Learning Approach Using GEM Data Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 6 Fig. 7 Fig. 8 Fig. 9 Fig. 10 Fig. 11 Fig. 12 Fig. 13 Fig. 14 Fig. 15 Fig. 16 Fig. 17 Fig. 18 Fig. 19 Fig. 20

EO temporal changes in 2008–2018 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . EO’s temporal changes based on countries’ income . . . . . . . . . . . . . . . EO’s temporal changes based on gender . .. .. . .. . .. . .. . .. .. . .. . .. . .. Correlation . . . .. . . .. . . .. . . . .. . . .. . . .. . . .. . . .. . . .. . . . .. . . .. . . .. . . .. . . .. . . Proactiveness regression . .. . .. . .. . . .. . .. . .. . . .. . .. . .. . .. . . .. . .. . .. . .. . Proactiveness regression in high-income group . . . . . . . . . . . . . . . . . . . . Proactiveness regression in middle-income group . . . . . . . . . . . . . . . . . Proactiveness regression male . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Proactiveness regression female . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Innovativeness regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Innovativeness regression in high-income group . . . .. . . .. . . . .. . . .. . Innovativeness regression in middle-income group . . . . . . . . . . . . . . . . Innovativeness regression male . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Innovativeness regression female . . . . . . .. . . . . . . . .. . . . . . . .. . . . . . . .. . . . Risk-taking regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Risk-taking regression in high-income group . . . . . . . . . . . . . . . . . . . . . . Risk-taking regression in middle-income group .. . . .. . .. . . .. . .. . .. . Risk-taking regression male .. . . .. . . .. . . . .. . . .. . . .. . . . .. . . .. . . .. . . . .. . Risk-taking regression female . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XGBoost model’s evaluation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25 25 27 28 31 31 32 32 33 33 34 34 35 35 36 37 37 38 38 41

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List of Figures

A Theoretical Research on the Effectiveness of Time Management in Dynamics of Employee-Organization Relationship Fig. 1

Proposed conceptual model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

The Degradation of Goals over Time: How Ambiguity and Managerial Cognition Shape Distributions of Project Time and Cost with Evidence from Actual and Simulated Projects Fig. 1

Fig. 2 Fig. 3

(a) Time taken to complete a mechanical engineering doctoral degree program. (b) US Air Force projects, planned and actual durations. (c) US Air Force projects, projected growth in annual expenditures and actual growth in expenditures. (d) Growth in cost estimates on the Big Dig from 1985 to 2000 .. .. . .. . .. .. . .. Simulated distribution of schedule delays in a two-task project with rework and learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hospital project cost data, ratio of planned to actual cost for 147 large projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83 89 94

Time to Respond: Identification, Proximity, and Safety at Work Fig. 1

Identification and proximity compete with cognitive momentum to influence safety engagement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

Fractals and Nonlinear Dynamic Modeling in Energy Economics: A Comprehensive Overview Fig. 1

Measuring Hurst exponent with trend correction (b) and without trend correction (a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

COVID-19 and Fractal Characteristics in Energy Markets: Evidence from US Energy Price Time Series Fig. 1 Fig. 2 Fig. 3

Fig. 4 Fig. 5

Energy prices return trend in selected US energy markets: before and after the COVID-19 pandemic period . . . . . . . . . . . . . . . . . . Moving window of standard deviations of energy prices return versus time scales in selected US energy markets . . . . . . . . . . The generalized Hurst exponent diagram in terms of order q and multifractal spectrum. (a) Crude oil, (b) conventional gasoline, (c) heating oil, (d) natural gas spot, and (e) electricity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The generalized Hurst values in terms of q values in the pre- and post-COVID-19 periods . . . . . . . . . . . . . . . . . . . . . . . . . . . . The trend of changes in the efficiency values of the American energy markets in the pre- and post-COVID-19 periods . . . . . . . . . .

168 171

175 178 180

List of Figures

Fig. 6 Fig. 7

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Energy prices trends in the US crude oil energy markets and petroleum products in the pre- and post-COVID-19 periods . 181 Energy prices trends in the US natural gas and electricity markets in the pre- and post-COVID-19 periods . . . . . . . . . . . . . . . . . . . 182

Fractal Organizations and Employee-Organization Relationship Dynamics Fig. 1

The process of identifying the structure of the complex system . . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . 192

List of Tables

Time Series Analysis of Entrepreneurial Orientation: A Machine Learning Approach Using GEM Data Table 1 Table 2 Table 3 Table 4

Cross-tabulation of country and participants’ gender and age . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Explanatory variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . OLS binary regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Data set size . . . . .. . . . .. . . . .. . . . .. . . . .. . . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . .

23 24 29 40

A Theoretical Research on the Effectiveness of Time Management in Dynamics of Employee-Organization Relationship Table 1

A review of the background of research done in the field of EOR and TM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

Fractals and Nonlinear Dynamic Modeling in Energy Economics: A Comprehensive Overview Table 1 Table 2 Table 3

Methodologies used in energy economic studies in fractal framework . . . . . . .. . . . . .. . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . .. . . 136 Studies in the field of energy economics with fractal approach in terms of subjects . . . . .. . . .. . . . .. . . . .. . . . .. . . .. . . . .. . . . .. . 150 Frequency of journals publishing fractal energy studies: 2021–2015 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

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List of Tables

COVID-19 and Fractal Characteristics in Energy Markets: Evidence from US Energy Price Time Series Table 1 Table 2 Table 3 Table 4 Table 5 Table 6 Table 7 Table 8

Summary of some studies in the field of energy sector efficiency with the fractal approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Selected US energy markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . US energy market analysis time periods . . .. . .. .. . .. . .. .. . .. . .. .. . .. Descriptive statistics of energy price returns time series in selected US energy markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Generalized Hurst exponent in different degrees’ q and width of the multifractal spectrum before COVID-19 . . . . . . . . . . . . . Generalized Hurst exponent in different degrees’ q and width of the multifractal spectrum after COVID-19 . . . . . . . . . . Ranking the inefficiency based on different criteria before COVID-19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ranking the inefficiency based on different criteria after COVID-19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

166 167 167 170 177 178 179 179

Fractal Organizations and Employee-Organization Relationship Dynamics Table 1

Common characteristics of EOR and fractal organization to create fractal organizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

An Introduction to Time and Fractals: Perspectives in Economics, Entrepreneurship, and Management Nezameddin Faghih

At that very hour my spirit was freed from hours (of Time); (I say ‘freed’) because hours make the young old. All changes have arisen form the hours he that is freed from the hours is freed from change When for an hour you escape from the hours, relation abides not: you become familiar with that which is without relation. The hours are not acquainted with timelessness because for him (who is conscious of time) there is no way there except bewilderment (Rumi. 1207–1273, P. 131). The man transcending space, in whom is the Light of God where is the past, the future, or the present? His being past or future is (only) relative to you both are one thing, and you think they are two. One individual is to him father and to us son: the roof is below Zayd and above Amr (two different persons) The relativity of “below” and “above” arises from those two persons: as regards itself, the roof is one thing only (Rumi. 1207–1273, P. 72).

This edited volume draws attention to the phenomena of time and fractals to advance economics, entrepreneurship, and management research by focusing on some aspects of time and fractals. It initiates a deeper conversation on time and

N. Faghih (✉) UNESCO Chair Professor Emeritus, Cambridge, MA, USA © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Faghih (ed.), Time and Fractals, Contributions to Management Science, https://doi.org/10.1007/978-3-031-38188-1_1

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fractals in economics, entrepreneurship, and management and demonstrates the value of time-based and fractal-based lenses for economics, entrepreneurship, and management research through the illustrations of representative chapters. The search for the description of time is faced with the riddle of its logical incoherence. Time can be defined as a nonspatial continuum or a dimension that is measured in terms of events or occurrences which succeed one another, such that they can be ordered from the past through present into future. Thus, it can be considered as the measure for durations of and intervals between events, that is, the period during which an action, condition, or process exists or continues (Welch & Salisbury, 2006; Dictionary, 2002; Lévesque, & Stephan, 2020). In fact, “this moment,” as the leading edge of time, appears to move constantly forward with a past behind it. An event that occurred at any moment occurred when that moment was “this moment.” We try to understand the causes that lie in its (own) past and trace its consequences that followed and occurred in its (own) future. Thus, the future up to “this moment” of any occurrence in the past has already occurred. As scientists and researchers, our relationships to an occurrence in the past and an occurrence at “this moment” are totally and radically different. In principle, the consequences of past occurrences can be known, or assessed, while the future consequences of an extant or present occurrence can be anticipated, predicted, or forecasted, within a degree of accuracy or a range of errors or possibilities. It seems to be a necessary condition for human life, and apparently if the future were known with certainty, life as we experience it would not be possible. “This moment” is influenced by the past but not completely bound. A decision or action in this moment is the result of a previous decision or action and leads to its future consequences and status that cannot yet be recognized or fully known (Robinson, 1980). Time is mostly implicit in economics, entrepreneurship, and management theories. Nonetheless, dedicated time-focused research is relatively new and emerging. Streams of research that have successfully included time and time-based structures and constructs are research on economic theories, time management, change management, process research, entrepreneurship, sustainability, innovation, and wellbeing. The inclusion of time is accompanied by methodological advances, for example, in longitudinal and day-to-day research, which sharpen the understanding and perception of how causal processes reveal and unfold. It is, however, pointed out that in entrepreneurship research, time is to some extent neglected, except for few studies, which also include viewing entrepreneurship as a nonlinear phenomenon and process, related research on family businesses emphasizing the significance of long-term orientations as time perspectives prevalent in such businesses (Lévesque & Stephan, 2020; Ancona et al., 2001; Roe et al., 2009; Langley et al., 2013; Dawson, 2014; Sonnentag, 2012, 2015; Flammer & Bansal, 2017; Slawinski & Bansal, 2015; Nadkarni & Narayanan, 2007; Nadkarni & Chen, 2014; Dormann & Griffin, 2015; McCormick et al., 2018 l; McMullen & Dimov, 2013; Joglekar & Lévesque, 2013; Levie & Lichtenstein, 2010; Lichtenstein et al., 2007; Lumpkin & Brigham, 2011; Sharma et al., 2013). Nonlinear dynamics, as the name suggests, is related to systems whose outputs are not linear functions of their inputs. In fact, nonlinearities are the rule rather than

An Introduction to Time and Fractals: Perspectives in Economics. . .

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the exception in many research fields. The major progress in the study of nonlinear functions and forms has been the introduction and development of the fractals concept by Mandelbrot (fractal: adjective or noun denoting complex forms that have scale-free or self-similar characteristics and properties). Since the appearance of Mandelbrot’s work (The Fractal Geometry of Nature), the idea of self-similarity and fractals (as the new frontiers of research) has played a significant role in many areas of science, engineering, medicine, arts, biology, psychology, economics, entrepreneurship, management, etc., which would provide a hotbed of research activities over the next decades. In fact, fractals have experienced significant success in quantifying the complexities represented by natural and analytical patterns and continue to capture the imagination of many researchers in a variety of fields. Fractal patterns are also noted for their aesthetic appeal, while some believe that fractal-like patterns are inherently pleasing because they resemble natural scenes and patterns. Additionally, various fields of research show that natural forms have positive influences on human emotional states, and the characteristic fractal geometry of natural elements can induce similar responses (Goldberger, & West, 1987; Dewdney, 1985; Peitgen et al., 1992; Faghih, 2005; Joye, 2006; Ebrahimi & Vrscay, 2008; Mandelbrot, 1982; Faghih et al., 2016; Forouharfar, 2020; Faghih & Forouharfar, 2022; Spehar, & Taylor, 2013). Classical geometry considers regular shapes with integer dimensions, while fractals refer to objects with fractional (i.e., non-integer) dimensions. For instance, a line has dimension 1, a rectangle has dimension 2, and a cube has dimension 3. However, natural and analytical structures are usually irregular, for example, the outlines of trees or coastlines on a map. Compared to the classic, smooth geometric forms, the fractal curves appear wrinkly. Moreover, if the wrinkles of a fractal are examined at higher magnification, more wrinkles are revealed and detected. Then if the smaller wrinkles are examined at higher magnifications, still smaller wrinkles (wrinkles upon wrinkles, upon wrinkles) are detected, and levels of irregular structure would appear endlessly. Evidently, for such an irregular curve, length cannot be simply defined (because the smaller the ruler used to measure it, the longer the line would appear to be). Now, a plot of the logarithm of the drawn ruler size versus the logarithm of the measured length of the line gives a linear graph with a negative slope. Consequently, the straight-line plot (logarithm of the drawn ruler size versus the logarithm of the measured length of the line) on log-log graph paper leads to a power-law relationship (mathematically, fractals can be defined by power law distributions). For a negative slope, the plot renders an inverse power-law relationship. The slope determines the fractal (fractional) dimension of the wrinkled line, and as an example, for a fractal line such as the coastline (on maps of increasing resolution), this value lies between 1 and 2. Therefore, a fractal curve of this type will have larger dimensions than a classical line (of dimension equal to 1), but smaller than that of a rectangular surface (of dimension equal to 2), which would be drawn to enclose the wrinkled curve (Takayasu & Takayasu, 2009; Mandelbrot, 1982; Goldberger & West, 1987). It should be pointed out that there are three related features of fractal forms: selfsimilarity, heterogeneity, and lack of a characteristic (well-defined) scale of length.

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That is, fractals are not homogeneous. More details are revealed in closer inspections. In contrast, classical geometrical forms do not yield more details with higher magnification inspections. Furthermore, fractal structures at smaller scales resemble the larger-scale structures: that is, the large-scale and small-scale wrinkles in the fractal curves are self-similar. The multiplicity of these self-similar scales prevents the determination of the fractals’ length independent of the measurement scale. However, the power of fractal calculus derives partly from its capacity to define the variety of irregular but complex forms that predominate in nature, where spheres, straight lines, and circles are the exceptions. The previously considered wrinkle line “case history” is a model for presenting a natural coastline whose length is lengthened as measured from a satellite image, measured by a walking human’s steps, or estimated from a moving course, for example, the track of a perambulating ant (Mandelbrot, 1982; Goldberger & West, 1987; Dewdney, 1985). In economics, entrepreneurship, and management systems and data, the fractal concept may be used not only to analyze complex structures but also to model certain aspects of system dynamics. Consider, as an example, a complex process that cannot be identified or characterized by frequency or a single rate. It is noted that the process may show structure (oscillations) at several temporal orders of magnitude (e.g., minutes, hours, etc.), in the same way that fractal shapes show detail at several spatial orders of magnitude. These time variations will, as a result, have a frequency spectrum with a wide profile of responses; that is broadband frequency spectrum. The term “broadband spectrum” is used when there is a relatively wide range from low to high frequencies. If a process is identified by only a few closely spaced frequency components or a single frequency, the term “narrowband spectrum” is used. For example, if a process shows oscillations in an apparently irregular fashion, a broadband spectrum can be observed. In contrast, if the oscillations are very regular or if the system oscillates in a periodic, for example, sinusoidal manner, a narrowband spectrum is observed (West & Goldberger, 1987, Mandelbrot, 1982; Goldberger & West, 1987; Dewdney, 1985; Montroll & Shlesinger, 1982; Shlesinger, 1987). The frequency spectrum shape (distribution) associated with a fractal process should also be considered. A fractal process, with self-similar variations on various time scales, produces a frequency spectrum of the shape mentioned earlier, that is, an inverse power law distribution. For the inverse power law spectrum, the lower the frequency component, the higher the power. A graph of log frequency versus log power shows a straight-line plot of negative slope. This type of broadband frequency spectrum is also referred to as 1/f-like due to the inverse relationship between power and frequency (f). Therefore, the concept of fractals is applicable not only to complex geometric shapes with self-similar structures and multiple length scales but also to certain dynamic processes that have fluctuations in multiple time scales. Such fractal time processes are represented by wide frequency band, long tail, low amplitude, and high-frequency power spectra (West & Goldberger, 1987, Mandelbrot, 1982; Goldberger & West, 1987; Dewdney, 1985; Montroll & Shlesinger, 1982; Shlesinger, 1987).

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Fractal properties and characteristics generally appear in most big data (or huge data analysis) in economics, entrepreneurship, and management. There are many examples, for example, financial market models (there are more than a million markets worldwide with their interactions), company data (especially, companies’ interaction data), market analysis and equilibrium, price changes and adjustment, demand and supply, money flow data, investment analysis, asset and income relationship, material flow data in manufacturing and consumption processes, material flow networks, sales data analysis, environmental studies, growth models, financial risk management, crisis analysis and prevention, business management decision-making, nonlinear dynamic systems, planning for integral economic development, urban economic modeling, urban management modeling, urban structure modeling, and complex pattern modeling (Takayasu & Takayasu, 2009; Peters, 1994; La Torre et al., 2011; Takayasu et al., 2000; Mosteanu, 2019; Mosteanu et al., 2019; Soliman, 1996; Dyck, 2006; Khalili Golmankhaneh et al., 2021; Cavailhès et al., 2004). This book consists of two parts containing eight chapters (including this introductory chapter). In this chapter is an introduction of the book. It introduces the book and explains that by focusing on some important aspects of time and fractals, this edited volume provides a deeper discussion to demonstrate the significance of time and fractal phenomena in advancing economics, entrepreneurship, and management research. It embraces a wide spectrum of topics such as time series analysis of entrepreneurial orientation with a machine learning approach using GEM data, a theoretical research on the effectiveness of time management in dynamics of employee-organization relationship, the degradation of goals over time and how ambiguity and managerial cognition shape distributions of project time and cost (with evidence from actual and simulated projects), and understanding and proximity when facing threat (toward an information processing theory of safety engagement), as well as fractals and nonlinear dynamic modeling in energy economics with a comprehensive overview, COVID-19 and fractal characteristics in energy markets with evidence from US energy price time series, and fractal organizations and employee-organization relationship dynamics. In each chapter of the book, authors with expertise in the theme they picked have tried to reveal some emerging aspects of time and fractals in economics, entrepreneurship, and management that can be useful not only for academics and researchers but also for policy makers. Part I, in chapters “Time Series Analysis of Entrepreneurial Orientation: A Machine Learning Approach Using GEM Data”, “A Theoretical Research on the Effectiveness of Time Management in Dynamics of Employee-Organization Relationship”, “The Degradation of Goals Over Time: How Ambiguity and Managerial Cognition Shape Distributions of project Time and Cost with Evidence from Actual and Simulated Projects”, and “Time to Respond: Identification, Proximity, and Safety at Work”, presents some perspectives of time in economics, entrepreneurship, and management. Chapter “Time Series Analysis of Entrepreneurial Orientation: A Machine Learning Approach Using GEM Data” presents time-series analysis of entrepreneurial

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orientation, using a machine learning approach and GEM (Global Entrepreneurship Monitor) data. This research examines whether and how the dimensions of entrepreneurial orientation (EO) have changed over time among male and female entrepreneurs in countries with different incomes and how it will be predicted. This study relies primarily on secondary data, and the research data is collected from the annual individual data set of the Global Entrepreneurship Monitor (GEM). Twenty countries continuously present in the GEM research from 2008 to 2018 were selected from each year’s collection, and the data were analyzed using the XGboost regression algorithm. The findings show that the gap between women’s and men’s risktaking has decreased and is moving toward equality (the slope of women’s risk tolerance is less than men’s). Proactiveness is more in middle-income countries. These two factors have a positive correlation, and the regression shows an increase. Women’s proactiveness has gone up and improved over time. However, in men, there is a constant trend. Chapter A Theoretical Research on the Effectiveness of Time Management in Dynamics of Employee-Organization Relationship undertakes theoretical research on the effectiveness of time management in dynamics of employee-organization relationship. The main concern in management of organizational behavior and human resources is to improve the individuals’ performance working in the organization with aim of increasing their efficiency. Time dimension of the work has become more important due to expansion of global competition and increasing of demand for urgent access to products and services because in desired time management, determination of the goals and priorities as well as monitoring the use of time can provide the effectiveness of occupational processes, maintenance of occupational balance, and success in employee-organization relationships through facilitating productivity, reducing stress. This chapter presents theoretical research to identify the effectiveness of time management in employee-organization relationship dynamics using a descriptive-analytical approach through the method of literature review and analysis. The findings lead to explanation and identification of commonalities between time management and employee-organization relationship, such as manager clarification and foresight in strategic decision-making, manager futurology path, stress management, creativity and innovation, work-family flexibility, job satisfaction, and organizational performance improvement. These commonalities somehow integrate the two areas of employee-organization relationship and time management, and the realization of each of them can indicate its synergistic effect in the improvement and dynamics of organizational relationships and the stability of time management. Chapter “The Degradation of Goals Over Time: How Ambiguity and Managerial Cognition Shape Distributions of Project Time and Cost with Evidence from Actual and Simulated Projects” studies the degradation of goals over time and how ambiguity and managerial cognition shape distributions of project time and cost with evidence from actual and simulated projects. Overruns are arguably the most pernicious and persistent plague on project management. Despite decades of scrutiny and extensive advances in management, technical remedies for overruns remain insufficient. We argue that managerial cognition in reaction to project information,

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not technological shortcomings, harbors critical explanations for overruns. The information that managers have when planning and executing a project is often ambiguous, that is, complex, confusing, and incomplete. This ambiguity provides an opening for the natural psychological biases of project managers to systematically affect project outcomes. The result, across a wide variety of projects, is a predictable “fat-tailed” effect on the distribution of a project’s total duration and cost; moreover, this effect is highly resistant to traditional planning techniques and management controls. This chapter draws on concepts from both engineering and psychology to suggest how, under conditions of ambiguity, a paradoxical combination of cognitive and system factors predictably shapes the distributions of project outcomes. Several diverse examples of project outcome distributions are presented, and a simulation is used to illustrate how the effects of one factor in project ambiguity, complexity in project tasks, and task interactions lead to decisions that systematically bias project duration. Chapter “Time to Respond: Identification, Proximity, and Safety at Work” investigates time to respond (identification, proximity, and safety at work). Recent events affecting occupational safety, and our understanding of how individuals process threat information, encourage a renewed examination of safety psychology. This chapter proposes two information-processing systems as key influences on the prioritization of safety when safety competes with other demands for attention and effort. Derived from cognitive theory and neuroscientific research, these systems are (1) identification, which represents the understanding of threats and responses, recognizing form and magnitude, and (2) proximity, which is the closeness of threats, recognizing both time and distance. Identification arises from the systematic and analytical processing of safety information and relies on the individual’s established identifications, classifications, descriptions, and understandings of threats and safety. Proximity is the temporal and spatial closeness of a threat; it induces a sense of personal exposure, responsibility, urgency, fear, and presence and is dominated by the processing of information specific to the current situation. Identification and proximity lead to safety engagement, and control over the situation plays an important role in determining the actions that follow from engagement. Two examples of applications are also provided. Part II, in chapters “Fractals and Nonlinear Dynamics Modeling in Energy Economics: A Comprehensive Overview”, “COVID-19 and Fractal Characteristics in Energy Markets: Evidence from U.S. Energy Price Time Series”, “Fractal Organizations and Employee-Organization Relationship Dynamics”, focuses on some perspectives of fractals in economics, entrepreneurship, and management. Chapter “Fractals and Nonlinear Dynamics Modeling in Energy Economics: A Comprehensive Overview” presents a comprehensive overview of fractals and nonlinear dynamic modeling in energy economics. With increasing attention to nonlinear approaches in market analysis from the 1980s onward, the fractal structures are the most important of these approaches, especially in energy markets. Several studies have emphasized the existence of complex and nonlinear structures in energy markets, and due to this feature, the researcher’s interest has moved toward the fractal techniques and structures. After more than two decades of fractal studies in energy markets, this chapter attempts to provide a comprehensive overview of

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previous studies in the energy markets to provide clear insights from existing analyses in this field. By identifying research gaps in energy market issues and challenges and methodologies, a clear path can be drawn for future studies. One of the important points confirmed by the results of previous studies is the high ability of fractal modeling to analyze nonlinear dynamics in the time series of energy prices. Various developments that were made in these tools paved the way for the study of energy economic studies from mono-fractal to multifractal. However, methodological gaps in energy studies are still visible. MF-DCCA (multifractal Detrended crosscorrelation analysis) model, lagged DFA (dynamic factor analysis) technique, V’s statistic technique, and finally the combination of the ARIMA (autoregressive integrated moving average) econometric model with the fractal dimension are techniques that have been somewhat neglected in energy studies. Finally, most of the fractal tools introduced in financial market studies have been developed after a time delay in energy economic studies. Therefore, in filling the research gap of nonlinear time series analysis of prices in energy markets, it will be interesting to follow the developments of fractal methodology tools in future studies of financial markets. Chapter “COVID-19 and Fractal Characteristics in Energy Markets: Evidence from U.S. Energy Price Time Series” explores the COVID-19 and fractal characteristics in energy markets with evidence from the US energy price time series. The efficient market hypothesis (EMH) introduced by Fama (1970) has been employed in energy market studies since the 2000s. Using the multifractal detrended fluctuation analysis (MF-DFA) approach, which allows for nonlinear analysis in the time series of energy prices, the deviation of EMH in energy markets can be measured especially in the aftermath of an event or a crisis. Given the outbreak of the COVID19 pandemic, in late 2019 as the most consequential event influencing the global economy, it is attempted to examine the efficiency of the most significant US energy markets in the pre-and post-pandemic era using the fractal approach in this chapter. Results of the MF-DFA technique unveil that, firstly, the multifractal spectrum in all US energy markets has increased significantly post-pandemic, which in turn indicates the complexity and multi-scaling behaviors in such markets. Secondly, the electricity market always exhibits deviations from the efficiency present in the two previous periods due to the nature of the impossible storage. Finally, the results of the present study signify that COVID-19 has transformed the fractal structure pattern of all US selected energy markets. Moreover, the MF-DFA technique yields good power to analyze the time series of energy prices. Chapter “Fractal Organizations and Employee-Organization Relationship Dynamics” studies fractal organizations and examines the employee-organization relationship dynamics. Most organizations increasingly function as living systems in nature. This process reflects the growth of human awareness of mutual relationships between employee and organization. The variety of distinct elements and also the multiplicity of relationships in the structure of dynamic management systems can be very complicated. In explaining the commonalties between employee-organization relationship (EOR) and fractal organization, it can be said that development and growth of organizational and interpersonal relationships are facilitated through alignment of employees’ and organization’s goals and interests and both parties of

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relationship whether the individual or the organization believes that they contribute to desirability and stability of relationship; so they are required to meet the expectations of the other party. Aligning the members with a shared goal and also the main values in line with a set of requirements of manager’s competency is accomplished by leaders who are devoted to inspiring, guiding, monitoring, and empowering the process owners. Individuals in an organization, as the most valuable strategic human resources, observe managerial behavior like an active magnifier. Therefore, the dynamics and mutual nature of EOR depends on the sustainability of organizational capitals. Fractal organization is a new and different way to visualize the networks of relationships and the method of information flow in different situations. In EOR, the enabling or restrictive structure of governing relationship is influenced by mutual trust which determines the level of unity of individual’s and organization’s goals and interests as the starting and central point of the process of employee-organization relationship. Parts of fractal systems make decisions independently but necessarily consider the shared goals and interests of all fractals, in such a way that the structure of relationships in these organizations becomes an enabler and facilitator in the path of achieving growth, development, and dynamics of human systems. So the organizational fractal includes a dynamic behavior of all that exists in an individual and manifests itself at the level of the team, at the level of the organization itself, and again at the level of the system in which the organization exists. Characteristics of mutual dynamics of EOR based on human capitals, strategic and optimal decisionmaking of EOR, and also characteristics like mutual dynamics (based on diversity of options), open information flows, process owners’ participation, and governance of open, generous, and committed relationships facilitate the movement toward fractal organizations and are of special importance. It is hoped that this book will be of interest to a wide range of global audiences and academics and can be a useful reference in the development of economics, entrepreneurship, and management research. Scholars and researchers in these fields have presented chapters and discussed the latest aspects of time and fractals in these fields. Furthermore, it is hoped that this book can add insights, provide creative discussions, and align with scholarly and intellectual interests in understanding current trends and mainstream research on time and fractals. It should also be noted that the facts, opinions, information, views, conclusions, findings, comments, strategies, and positions expressed by the contributors and authors of the chapters are theirs alone and do not necessarily reflect the opinions, views, strategies, or positions of the editors of this edited volume and do not constitute approval or endorsement by the editors. The contributors and authors are responsible for their citation of sources and the accuracy of their bibliographies and references. The editors of this volume cannot be held responsible for any errors or consequences arising from the use of the information contained in the chapters or for any lacks or possible violations of the rights of third parties. While every effort is made by the editors to see that no misleading or inaccurate data, statements, or opinions appear in this volume, the data, their use, interpretations, and the opinions appearing in the chapters are the sole responsibilities of the contributors and authors concerned. The editors accept no liability whatsoever for the consequences of any such misleading or inaccurate data, opinion, information, or statements.

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McCormick, B. W., Reeves, C. J., Downes, P. E., Li, N., & Ilies, R. (2018). Scientific contributions of within-person research in management: Making the juice worth the squeeze. Journal of Management. https://doi.org/10.1177/0149206318788435 McMullen, J. S., & Dimov, D. (2013). Time and the entrepreneurial journey: The problems and promise of studying entrepreneurship as a process. Journal of Management Studies, 50(8), 1481–1512. Montroll, E. W., & Shlesinger, M. F. (1982). On 1/f noise and other distributions with long tails. Proceedings of the National Academy of Sciences of the United States of America, 79, 3380–3383. Mosteanu, N. R. (2019). Intelligent tool to prevent Economic Crisis–Fractals. A possible solution to assess the Management of Financial Risk. Calitatea, 20(172), 13–17. Mosteanu, N. R., Facia, A., Torrebruno, G., & Torrebruno, F. (2019). Fractals–A smart financial tool to assess business management decisions. Journal of Information Systems & Operations Management, 13, 45–56. Nadkarni, S., & Chen, J. (2014). Bridging yesterday, today, and tomorrow: CEO temporal focus, environmental dynamism, and rate of new product introduction. Academy of Management Journal, 57(6), 1810–1833. Nadkarni, S., & Narayanan, V. K. (2007). Strategic schemas, strategic flexibility, and firm performance: The moderating role of industry clock speed. Strategic Management Journal, 28(3), 243–270. Peitgen, H. O., Jürgens, H., Saupe, D., & Feigenbaum, M. J. (1992). Chaos and fractals: new frontiers of science (Vol. 7). Springer. Peters, E. E. (1994). Fractal market analysis: Applying chaos theory to investment and economics (Vol. 24). Wiley. Robinson, J. (1980). Time in economic theory. Kyklos, 33(2), 219–229. Roe, R. A., Waller, M. J., & Clegg, S. R. (Eds.). (2009). Time in Organizational Research. Routledge. Rumi. (1207–1273). (1926). The Mathnawí of Jalaluddín Rumi (Translation and Commentary, Nicholson, Reynold A, Volume III). Messrs Luzac & Co. Ltd. Sharma, P., Salvato, C., & Reay, T. (2013). Temporal dimensions of family enterprise research. Family Business Review, 27(1), 10–19. Shlesinger, M. F. (1987). Fractal time and 1/f noise in complex systems. Annals of the New York Academy of Sciences, 504, 214–228. Slawinski, N., & Bansal, P. (2015). Short on time: Intertemporal tensions in business sustainability. Organization Science, 26(2), 531–549. Soliman, A. S. (1996). Fractals in nonlinear economic dynamic systems. Chaos, Solitons & Fractals, 7(2), 247–256. Sonnentag, S. (2012). Time in organizational research: Catching up on a long-neglected topic in order to improve theory. Organizational Psychology Review, 2(4), 361–368. Sonnentag, S. (2015). Dynamics of well-being. Annual Review of Organizational Psychology and Organizational Behavior, 2, 261–293. Spehar, B., & Taylor, R. P. (2013, March). Fractals in art and nature: Why do we like them? In Human vision and electronic imaging XVIII (Vol. 8651, pp. 298–309). SPIE. Takayasu, M., & Takayasu, H. (2009). Fractals and economics. In Complex systems in finance and econometrics (pp. 444–463). Springer. Takayasu, H., Takayasu, M., Okazaki, M. P., Marumo, K., & Shimizu, T. (2000). Fractal properties in economics. arXiv preprint cond-mat/0008057. Welch, K., & Salisbury, D. D. (2006). The Physics of Time. Physics_of_Time-libre.pdf (d1wqtxts1 xzle7.cloudfront.net) West, B. J., & Goldberger, A. L. (1987). Physiology in fractal dimensions. American Scientist, 75, 354–365.

Part I

Time

Time Series Analysis of Entrepreneurial Orientation: A Machine Learning Approach Using GEM Data Mozhgan Danesh, Nezameddin Faghih, and Masoumeh Moterased

1 Introduction Various definitions of EO have been proposed in the literature (Abbas et al., 2022). Miller (1983) defines EO as a strategic position toward entrepreneurship that is first used to develop a new business in a company. Entrepreneurial-oriented companies are looking for new opportunities (Drucker, 1964) and serve as agencies of change in presenting new products or services to the market and at the top of their competitors (Zacca et al., 2015). Also, Avlonitis and Salavou (2007) emphasize that EO is an organizational phenomenon that demonstrates the organization of their management skills because firms start to take the initiative and alter their competitive action to the advantage of the business in which they operate. Entrepreneurial orientation belongs to individuals who are innovative and have creative thinking (Erista et al., 2020). Researchers have identified that as a strategic position, EO reflects strategy techniques, management principles, and firm-level behaviors that are entrepreneurial (Anderson et al., 2009; Covin & Slevin, 1991; Ferreras-Méndez et al., 2022; Wales, 2016). Although dimensions of EO, as defined by Miller (1983), are critical to understanding the entrepreneurial process, the current entrepreneurial study has identified the necessity to expand a contextualized knowledge of entrepreneurship. Growing observations suggest that economic behavior can be better understood in its historical, temporal, institutional, spatial, and social contexts (Jennings et al., 2013; M. Danesh (✉) Faculty of Entrepreneurship, Department of Entrepreneurship Management, Science and Research Branch, Islamic Azad University, University of Tehran, Tehran, Iran e-mail: [email protected] N. Faghih UNESCO Chair Professor Emeritus, Cambridge, MA, USA M. Moterased Department of Entrepreneurship, Science, and Research Branch, IAU, Tehran, Iran © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Faghih (ed.), Time and Fractals, Contributions to Management Science, https://doi.org/10.1007/978-3-031-38188-1_2

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Lang et al., 2014; Welter & Smallbone, 2011). These contexts prepare opportunities for organizations and individuals and fix limitations for their activities. Although this context helps comprehend why, how, and when entrepreneurship occurs and who gets involved, it is often taken for granted most of the time (Welter, 2011); alternatively, it is noticed as something that entrepreneurs can form according to their requirements and ambitions (Eijdenberg, 2016; Mozumdar et al., 2022). EO is not an uncomplicated phenomenon at unidirectional domain. It is a hybrid construct consisting of three dimensions, innovativeness, proactiveness, and risk-taking (Covin & Wales, 2019), which predicts access to finance in SMEs. Over time, EO has evolved into five dimensions (Lumpkin & Pidduck, 2021). Even though some scholars have suggested that each EO dimension can be treated separately (e.g., Kreiser et al. (2002), we are committed to this view that the defining feature of EO is specifically the consideration of the three components together as a unique construct of EO (Covin et al., 2006). Some research has been conducted to investigate the effect of EO on firm performance, and the results show a positive and significant impact on performance (Cho & Lee, 2018; Covin & Miller, 2014; Cui et al., 2018; Dayan et al., 2016). Most of these studies have not considered the role of gender on the performance and flexibility of SMEs (Expósito et al., 2022; Lim & Envick, 2013; Okello, 2020). Some authors claim that distinct personal factors impact men’s and women’s entrepreneurial propensity (Goktan & Gupta, 2015; Lim & Envick, 2013). The differences in entrepreneurial activity between men and women can be investigated from two different views. The feminist theory describes men and women as “inherently different.” At the same time, the social constructionist view focuses on masculine and feminine characteristics rather than the biological distinction of being male or female (Ahl, 2006). On the other hand, the social constructionist perspective concentrates on masculinity and femininity (Goktan & Gupta, 2015). The positive shift in entrepreneurs’ attributes, manners, and thinking as a consequence of the EO is distinct between men and women entrepreneurs (Hughes & Yang, 2020). Entrepreneurial orientation has several dimensions (innovativeness, risk-taking, and proactiveness). Each may be adopted differently by men and women conducting to differences in performance and flexibility levels based on gender. Thus, the impact of each needs to be evaluated separately (Zeebaree & Siron, 2017). The inconsonance in the conclusions needs a study on a multigroup examination of EO between males and females, which this study pursues to address (Okello, 2020). Findings of gender distinctions in dimensions of EO are not uniform (Zeb & Ihsan, 2020). The areas in which SMEs operate play an essential role in the EO of SMEs. Audretsch et al. (2015) believe that entrepreneurial activities differ in area. Fernández-Serrano and Romero (2013) and Dvouletý (2017) also support the fact that firms located in high-income areas carry out more innovative and proactive activities than SMEs in low-income regions (Kljucnikov et al., 2020). According to contemporary surveys, SMEs generate more than 55% of the GDP and 65% of total employment in high-income countries, more than 60% of the GDP and 70% of total employment in low-income countries, and more than 95% of total employment and about 70% of the GDP in middle-income countries (Diabate et al., 2019). This research aims to investigate the changes in different dimensions of EO with moderators (gender and income of the country) and to predict them using the time

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series approach. For this purpose, the data of this research is from the 2008–2018 GEM survey, which is analyzed using the XGBoost regression algorithm. The contribution of this research to the current literature is manifold. First, this research spreads the emerging work on entrepreneurship as a gendered process (Lewis, 2006; Mirchandani, 1999). Second, new empirical results add to the scant literature that compares female- and male-run businesses concerning their willingness to participate in business activities and, therefore, raise knowledge about the role of entrepreneurial gender in SMEs (Expósito et al., 2022; Okello, 2020). Third, because several countries with different incomes are examined in this research, conducting studies in a cross-cultural setting helps researchers understand entrepreneurial phenomena and develop robust theories (Goktan & Gupta, 2015; Liñán & Chen, 2009). The intercountry analysis explains the environmental and institutional context in different areas, economies, and markets, along with its impact on managerial behaviors and organizational consequences (Butkouskaya et al., 2020). Fourth, as far as we know, this chapter is the first study that examines the temporal changes of the three dimensions of EO in countries with different income levels, taking into account the role of gender, and also predicts the changes in these dimensions. Finally, this study confirmed the value of the predictive model based on machine learning technology concerning the prediction of EO by comparing it with the existing analysis method. The remnant of the chapter is arranged as follows. After the introduction, Sect. 2 presents the theoretical framework of the research that examines and clarifies the concept of EO and its dimensions, EO and gender, and finally EO and low-income and high-income countries. Section 3 describes the methodology we use. Section 4 explains the conclusions and discussion. Section 5 is dedicated to this research’s contributions, limitations, and future research.

2 Theoretical Framework 2.1

Entrepreneurial Orientation and Its Dimensions

While there is no accurate and universal definition of EO (Lechner & Gudmundsson, 2014), a three-dimensional model is utilized to represent EO. Elements of EO contain innovativeness, risk-taking, and proactiveness (Covin & Slevin, 1989). Most scholars support the three-dimensional model, although Lumpkin and Dess (1996) suggested two other dimensions – competitive aggression and autonomy (Shirokova et al., 2016; Su et al., 2011; Zahra & Garvis, 2000). A more specific look at the three structural dimensions of EO shows that EO is directly or indirectly connected to a firm’s performance (Anwar et al., 2022). Innovativeness reflects the capacity to get involved with new ideas and techniques to present new products and services to markets (Damanpour, 1991; Hurley & Hult, 1998; Zahra & Garvis, 2000). According to its influential role in gaining competitive advantage (Atalay et al., 2013), innovativeness is a dimension that has been studied more in the literature. Investigations have shown that the relationship

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between innovation and firm performance has been further confirmed in studies in developed countries. According to research, innovation leads to profitability due to new products or technical processes (Kyrgidou & Spyropoulou, 2013). Risk-taking means the capability to identify and bear strategic (economic) risks for new products, services, and markets (Willebrands et al., 2012). Entrepreneurs can make improvements in their firm performance (Lumpkin & Dess, 1996) by exploiting new opportunities via scheduled and manageable risks (Begley & Boyd, 1987) with a brave decision (Mozumdar et al., 2019). Risk-averting entrepreneurs remain inactive and cannot recognize and exploit new business opportunities in dynamic markets, so their business performance does not improve (Miller & Friesen, 1982). Proactiveness gives entrepreneurs the ability to anticipate customer needs and necessary market changes (Lumpkin & Dess, 2001). Proactive entrepreneurs can bring new products or services to market before competitors (Lumpkin & Dess, 1996; Rauch et al., 2009). This ability enables entrepreneurs to take advantage of new business opportunities and increases the benefits of the first driver, such as high returns, brand awareness, and customer acquisition, consequently enhancing their business performance (Lumpkin & Dess, 2001; Wiklund & Shepherd, 2005). Proactiveness, innovativeness, and risk-taking reflect sub-dimensions of an EO at the same level, while they have unique contributions to the EO scale (Kreiser et al., 2002). Therefore, some researchers claim that these three dimensions should be considered as related but separate constructs rather than as a unifying gestalt (Kreiser & Davis, 2010; Luu & Ngo, 2019). Current research has distinguished the dimensions of EO from the aspect of their nominal meanings (Covin & Wales, 2012), theoretical importance (Pearce et al., 2010), and subtle features (Lumpkin & Dess, 1996). Several studies have examined the distinct effects of different dimensions of EO on firm-level consequences, such as international scope and performance (Dai et al., 2014; Luu & Ngo, 2019). Although these examinations often examine the implications of the EO dimension, they are yet an excellent starting point for comparing and differentiating the EO dimension. Therefore, three inherent and quiet distinctions between the dimensions of EO are discussed (Xiao et al., 2022). First, the strategic goals of the three EO dimensions are contradictory. When innovativeness reflects the firm’s willingness to innovate, proactivity leads the firm’s position to develop the existing market or join a new market ahead of competitors, both of which imply visible and specific entrepreneurial directions for the firm (Miller, 1983; Wales et al., 2020). In contrast, risk-taking leads the company to courageous projects with uncertain consequences, which is an uncertain entrepreneurial direction (Lumpkin & Dess, 1996; Miller, 1983). Second, firms must dominate varying grades of difficulty to adopt specific entrepreneurial directions determined by innovation and proactivity. Innovativeness is the most considerable difficulty because pursuing new products, services, or processes necessarily requires deviating from current practices/technologies and accepting “creative destruction” (Dess & Lumpkin, 2005; Kollmann & Stöckmann, 2014). Proactiveness leads to demand creation in emerging markets or responding to unsatisfied demand in current intact markets; however, this need stays consistent with existing procedures. Firms can operate tried-and-true products/services or innovative products to reach this

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goal; therefore, proactivity requires less difficulty than innovativeness (Lumpkin & Dess, 1996). Third, although all dimensions of EO need resources (Hughes et al., 2021; Luu & Ngo, 2019; Sirén et al., 2017), the kind and quantity of resources are various in EO dimensions. In particular, resources are invested in proactive firms in scanning market signs, similar demand trends, industrial policies, and consumer preferences (Dess & Lumpkin, 2005; Miller, 2011; Tang et al., 2014). Because proactiveness requires a quick response or short-term adaptation (Pearce et al., 2010), this is very shocker when companies obtain optimistic market signals for new opportunities. Innovativeness requires a significant initial investment, such as financial resources, knowledge, and technology capacities (Kreiser et al., 2013; Wang et al., 2017). Innovativeness, in general, needs strong motivation (McDermott & O’Connor, 2002) because firms have to invest a lot of time and resources to conduct a risky and long-term innovation project (Deb & Wiklund, 2017). Like proactiveness (and unlike innovativeness), risk-taking requires market examination in search of potential opportunities (Miller, 2011). In addition, risk-taking firms commonly require considerable and ongoing resources (Rauch et al., 2009; Wiklund & Shepherd, 2003) such as budgets for adventuresome projects, laxity to absorb potential losses, and legality to activate some debts (Saeed et al., 2014). Del FuentesFuentes et al. (2015) stated that even if the level of one dimension is not as significant as other dimensions, the impact of EO on business performance can still be positive. As Lumpkin and Dess (1996) demonstrated, the prosperity of EO does not rely on the existence of all its dimensions (Mozumdar et al., 2022).

2.2

Entrepreneurial Orientation and Gender Differences

As a probable characteristic, gender differences showed a significantly more substantial effect on the higher range of EO levels. Social constructionist and poststructuralist feminist theories form the third strand of literature. It is assumed that upbringing and social interactions demonstrate the inequality between men and women (Ahl, 2006; Fischer et al., 1993). Gender is structural in nature and specified by the social structure, consequently creating stereotypes about differences in attitudes, capabilities, and manner patterns between men and women (Fischer et al., 1993). Suppose society believes that women’s role is primarily related to the family and female managers internalize these principles; in that case, the active pursuit of market opportunities may differ from that of men (Brush et al., 2009). Some research has shown that there are distinguishing personal factors that affect men’s and women’s propensity toward entrepreneurship differentially. These differences can be classified into three categories. First, women are less likely to consider themselves entrepreneurs and see the entrepreneurial environment as less favorable than men (Heilman & Chen, 2003). The belief that the environment for initiating a business is hostile and complicated for women reduces women’s tendency toward entrepreneurship (Kolvereid et al., 1991). Second, human capital literature signifies that knowledge, skillfulness, competencies, and other features related to

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entrepreneurship are unequally distributed between men and women (Cetindamar et al., 2012). As a result, although women have as much human capital as men, they do not obtain the knowledge, capacities, and skills that contribute to entrepreneurship (Marlow, 2002). Third, men and women vary in the degree of expansion of their social contacts (referred to as social capital), which affects the probability that their efforts will be supported by others whose help for the enterprising individual may require (Manolova et al., 2007). The reason is that the social network in which entrepreneurs are embedded affects their capacity to access rare resources required to utilize and discover new business opportunities (Cetindamar et al., 2012). Although several studies have continually shown gender differences in EO (e.g., Hansen et al. (2011), Lim and Envick (2013)), there is a requirement for examinations that “explore the aggregate effects innovativeness, proactiveness, and risktaking behaviors have on overall EO across multiple countries” (Hansen et al., 2011, p: 76). Buratti et al. (2018) state that female managers are inclined to take a more conservative approach to business than men and are less likely to invest in innovative actions. The success of entrepreneurs relies on their risk-taking capacities, which may vary by gender. According to studies, higher-risk orientation leads to higher risk-taking behavior and, as a result, increases the performance of entrepreneurs (Fatoki, 2014). Lim and Envick (2013) and Goktan and Gupta (2015) showed higher levels of entrepreneurial proactiveness in male students compared to their female partners, while Runyan et al. (2006) found no document of gender differences in the proactiveness of small business owner engagement.

2.3

An Overview of Entrepreneurial Orientation in Low-Income and High-Income Countries

The increasing globalization of business and the expansion of entrepreneurship around the world encourages research on the impact of EO on business performance in various countries than the ones where the EO theory has been extended. A strand of literature demonstrates the disparities between the EO of SMEs in an international context. The degree to which EO, particularly the dimensionality of EO (Miller, 2011; Wales, 2016), effect business performance is relevant to the impact of the environment in different countries on business performance (Mozumdar et al., 2022). Likewise, Abrhám et al. (2015) explained that SMEs in high-income areas have more EO than SMEs in low-income areas. As low-income areas lack sufficient resources to carry out innovative activities, they have more barriers to competing with other firms (Fernández-Serrano & Romero, 2013). Considering the economic situations in different countries, Filser et al. (2014) investigated businesses in Austria and Hungary and verified that businesses with more financial resources perform better on EO dimensions. Regarding political risk and its effects on SMEs’ EO, political risk influences the risk-taking and proactive behaviors of SMEs from different countries (Kreiser & Davis, 2010).

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Also, acting in a hostile environment causes businesses to behave more innovatively and proactively and drives them to take risky activities, while operating in a benign environment makes firms behave more conservatively concerning EO (Covin & Slevin, 1989; Laukkanen et al., 2013). Furthermore, Mueller and Thomas (2001) emphasize that entrepreneurs from a country with lower uncertainty avoidance are more likely to be proactive than those from a country with higher uncertainty avoidance. Kreiser et al. (2010) also verify the negative relationship between the level of uncertainty avoidance in a country and the EO of SMEs. In this sense, the global competitiveness index is a crucial index that needs concentration. It estimates the competitiveness of countries, the quality of their public institutions, and the rules of state to demonstrate how countries are productive and efficient. Kreiser et al. (2010) likewise declare that GDP per capita has important and different influences on the risk-taking and proactive behaviors of SMEs from different countries (Kljucnikov et al., 2020). For example, Covin and Slevin (1991) and Kreiser et al. (2010) show that the legislative environment and competition in the market affect risk-taking and proactive and innovative attitudes. Semrau et al. (2016) note that SMEs in countries that have gained institutional growth are likely to function better than in other countries that are less institutionally developed.

3 Methodology The data for this study are drawn from the GEM survey conducted between 2008 and 2018. Based on a basic conceptual framework, the GEM survey examines three variables influencing entrepreneurial behavior: individual characteristics, social interests, and national framework conditions. Several factors influence entrepreneurship at the national level, including social, cultural, political, and economic factors. Individual factors include demographics, entrepreneurial proactiveness and innovation, and perceptions and motivations, such as fear of failure. The GEM framework considers multiple types of entrepreneurship, encompassing startups and established businesses (Bosma et al., 2019). This study aims to examine changes and predict all dimensions of EO over time through the time series approach. In time series analysis, algorithms are applied to learn patterns from data; the algorithms employed in the analysis are primarily based on advanced regressions. The current study uses the OLS (ordinary least squares) binary regression and the XGBoost regression algorithm to understand and predict data. The coded algorithm was implemented in Jupyter Notebook, an interactive extension of the Python console, to simplify the analysis and processing of the data presented in this study. The following libraries were used: Sklearn, Matplotlib, NumPy, Seaborn, and Pandas. During runtime, Python allows for the detection of errors, the exclusion of biases, and assessing the credibility of variables. Furthermore, some individuals did not answer all the items, so their responses were recorded as “NaN” (not a number) or -2 (refused).

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In light of this, the first step focused on data refinement and removing missing data from the database used to perform the algorithm. Since the data were nonparametric, the Spearman method was used to examine the correlation between proactiveness, innovativeness, and risk-taking after pre-processing. The work steps include the following: Selecting data and features Dividing the data, training, and testing the model Checking the obtained results and interpreting the output We discuss these stages in more detail below.

3.1

Sample and Data Collection

The data used in this study are mainly secondary data published by the Global Entrepreneurship Monitor between 2008 and 2018. The hypotheses were tested using GEM data, a famous global survey of entrepreneurial activities. Several studies have used the GEM database in academic research to a broader extent than previously reported (Liñán et al., 2011; Ramos-Rodríguez et al., 2015; Tsai et al., 2016). The purpose of this chapter is to complete the current findings related to temporal changes in EO. Innovation, risk-taking, and proactiveness are the three main dimensions of EO, which have been examined with moderating variables (country income and gender group). The research data were collected from the annual individual data set of the Global Entrepreneurship Monitor (GEM). A total of 20 countries have been continuously included in GEM research from 2008 to 2018. The next step is to merge the data from each year according to the desired variables. An overview of the data distribution among the countries can be found in Table 1. Over the past 11 years, 949,492 people have participated in GEM research in these countries. Spain has the most respondents, while South Korea has the least. Over 51% of the population is female, and 48% is male. Generally, there are more women than men in most countries, like Germany and South Korea, almost equal numbers, but only in Iran are there more men than women. There are also 16 countries with high incomes, as opposed to only four countries with middle incomes. Americans (49.6) and the Netherlands (49.7) have a higher average age than other countries, while Iran has a younger average age (35.3). Since GEM data are collected annually through questionnaires in member countries, their validity and reliability are well established and do not require further investigation. It should be noted, however, that the variables we examined in GEM data were determined based on the type of entrepreneurship (start-up and established). Therefore, new variables had to be created and integrated. Additionally, in GEM data, fear of failure was mentioned instead of risk-taking, creating a risktaking variable by reversing the fear of failure. Using GEM’s income classification, a new variable is defined to examine the difference between countries’ incomes, and

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Table 1 Cross-tabulation of country and participants’ gender and age Countries Argentina (n = 23,792) Brazil (n = 46,084) Chile (n = 70,304) Colombia (n = 48,918) Croatia (n = 21,996) France (n = 22,076) Germany (n = 51,688) Greece (n = 22,000) Iran (n = 36,171) Ireland (n = 20,017) Netherlands (n = 31,310) Peru (n = 22,733) Slovenia (n = 25,101) South Africa (n = 32,392) South Korea (n = 20,002) Spain (n = 268,020) Switzerland (n = 23,451) UK (n = 95,435) USA (n = 45,639) Uruguay (n = 22,363)

Gender (%) Male 45.6 Female 54.4 Male 48 Female 52 Male 47.5 Female 52.5 Male 47.8 Female 52.2 Male 45.5 Female 54.5 Male 47.2 Female 52.7 Male 50.1 Female 49.8 Male 49.5 Female 50.4 Male 53.5 Female 46.4 Male 46.2 Female 53.7 Male 46.1 Female 53.8 Male 49.8 Female 50.2 Male 48 Female 52 Male 49.3 Female 50.6 Male 50.7 Female 49.2 Male 50 Female 49.9 Male 47.8 Female 52.1 Male 44.3 Female 55.6 Male 48 Female 51.9 Male 45.2 Female 54.7

Income (GEM) High income

Age average 43.4

High income

37.8

High income

43.7

Middle income

37.9

High income

43.6

High income

48.4

High income

43

High income

40.6

Middle income

35.3

High income

42

High income

49.7

Middle income

36.7

High income

43.2

Middle income

41.6

High income

40.3

High income

42.5

High income

48.7

High income

48.5

High income

49.6

High income

45.9

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Table 2 Explanatory variables Variable Age

Description Aged 18–64

Gender

Gender of the respondent

Years of survey Country

2008–2018

Country income Innovativeness Proactiveness Risk-taking (reverse FEARFAIL)

Argentina, Brazil, Chile, Colombia, Croatia, France, Germany, Greece, Iran, Ireland, Netherlands, Peru, Slovenia, South Africa, South Korea, Spain, Switzerland, UK, USA, and Uruguay

New technology + new product market combination (early stage + establish) Manages and owns a business (establish + early stage) Qi4. Would fear of failure would prevent you from starting a business?

Values From 18 to 64 of age Male = 1, female = 2 Year of survey Country codes

High-income and middle-income 0 = no indication 1 = indication 0 = no 1 = yes 0 = no 1 = yes

the countries under review are divided into high-income and middle-income groups. The next step involves converting the country income and gender variables into dummy variables to differentiate the correlation between these variables and the target variables. The operational definitions of the investigated variables are shown in Table 2.

3.2

Data Analysis and Results

Data Visualization and Analysis Figure 1 shows the number of changes in each orientation (proactiveness, innovativeness, and risk-taking) from 2008 to 2018. Risk-taking decreased from 2014 to 2018, and it has been almost constant (60% per year), except for 2009, which had a high growth (71.3%). In 2012, this index reached its lowest point (58%). Before 2011, entrepreneurial proactiveness was minor (less than 8%), but since 2011, there has been a jump in entrepreneurial proactiveness (18.5%), and the tendency toward entrepreneurial proactiveness has more than doubled. This trend continued until 2014 (18.8%) but again decreased and reached 17.3% in 2018. Innovativeness in businesses (new technology or a new product in the market) is less than in other EO. This index, like proactiveness, has had a small amount since 2008 and reached its peak in 2011 (6%). After that, it decreased again, and although it had a significant effect in 2016 and 2017 (5%), it decreased in 2018 (4.8%). The use of innovativeness in businesses has mostly stayed the same since 2012.

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Fig. 1 EO temporal changes in 2008–2018

Fig. 2 EO’s temporal changes based on countries’ income

3.2.1

EO’s Temporal Changes Based on Countries’ Income

Figure 2 shows the effect of moderator variables on dependent variables separately over time. Entrepreneurs in middle-income countries have higher risk-taking than in high-income countries. The highest level of risk-taking in the countries in 2009 is recognized for middle-income (78.5%) and high-income (70.5%). After this time, risk-taking in high-income countries began a downward tendency and reached its lowest value (56.5%) in 2012, although it has had a steady trend (59.9%) since 2015. These results differ for middle-income countries. After 2009, risk-taking decreased, but in 2014 it increased again (69%) but fell in 2015 (63.7%); this year, both income

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groups approached each other in this index. After that, it had a steady desire that drove upward from 2018 (64.5%). Entrepreneurial proactiveness is also higher in middle-income than in highincome countries. An upward trend was for both income groups in 2008–2011 (14.5%, 2008, to 22.5%, 2011, for middle-income and 6.8%, 2008, to 17.2%, 2011, for high-income countries). After that, high-income countries continued their proactiveness steady and slightly downward. In contrast to the middle-income group, it rose and reached its peak in 2015 (22.9%) and then conquered a higher summit in 2018 (23 0.7%). The innovativeness index is also lower in both groups than in the other orientations. The distinction in the middle-income group is that the higher rate of using innovativeness in entrepreneurship was initially higher than the other group and reached its peak in 2011 (8.7%). After this time, it went down in 2016 until it was lower than the other group (4.4% middle income and 5.1% high income). Over several years, innovativeness by the high-income group ranged from 4% to 5.2%, but it bottomed out in 2012 (3.5%) and has remained roughly constant since then.

3.2.2

EO’s Temporal Changes Based on Gender

In comparing the behavior of different genders, the peak and descent of the acceptance of EO in different years are similar to the income groups. Men are more risktaking than women. However, both have the same pattern – the highest number of risk-takers in 2009 (72.5% of men and 70.3% of women). The closest distance between both genders is also at this time. After this, risk-taking decreased and reached its lowest level in 2012 (61.8% of men and 54.6% of women). Until 2018, they had a constant value with the same distance. Men are more likely to accept proactiveness than women. The proactiveness of both groups reached its lowest amount in 2009 (7.9% of men and 4.5% of women), but its growth occurred earlier in men; 2011 data shows the highest proactiveness of men (23.5%). While for women, the maximum proactiveness happened in 2014 (15.6%). In Fig. 3, both groups show constant movement since 2014, but women’s upward movement began in 2018 (13.9%). Men and women used innovativeness at the lowest rates in 2009 (4.5% and 2.5%, respectively). Innovativeness use peaked two years later in both gender groups (men 7.3% and women 4.9%). Like other trends, innovativeness has continued its steady downward trend after peaking.

3.2.3

Correlation

As shown in the following figure, there is a binary correlation between the variables in the study. Darker points are more likely to be correlated, while lighter points are less likely to be correlated. Calculate the correlation using the Spearman method because the data is nonparametric. For a better understanding of the correlation between dependent variables and moderator variables, countries’ income, and

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Fig. 3 EO’s temporal changes based on gender

gender into dummy variables, it is recommended that income and gender groups be examined separately with EO. Risk-taking is positively correlated with middleincome countries and men; on the other hand, it is less correlated with high-income countries and women. In addition, entrepreneurial proactiveness is positively correlated between men and middle-income countries, whereas high-income countries and women are negatively correlated. A positive correlation has been found between innovativeness and middle-income countries and the male gender, and a negative correlation has been found between innovativeness and the female gender. There is a negative correlation between risk-taking and the year but a positive correlation between innovativeness and proactiveness. High-income countries and males also show a positive correlation with the year, whereas women and middle-income countries show a negative correlation (Fig. 4).

3.2.4

OLS Regression Procedure

A regression model allows researchers to examine the specific effects that variables have on one another without considering the impact of other variables. In entrepreneurship research, logistic regression techniques (e.g., binary logistic regression, ordinal logistic regression, and multinomial logistic regression) and ordinary least squares (OLS) regression are the most commonly used regression frameworks (Burton, 2021). This chapter focuses on the latter, OLS. OLS regression uses the least squares method, which is relatively straightforward. For illustration purposes, consider a scatter plot of data points that illustrates a linear trend. In OLS regression analysis, a regression plane is fitted onto a “cloud” of data, the direction of which is assumed to be linear. Even though the regression plane does not cover every point in the data cloud, it models the partial relationships between each slope (i.e., each regression coefficient “b”) and the outcome variable while holding the effects of the

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Fig. 4 Correlation

remaining variables constant (Fox, 2016). The OLS linear regression procedure builds a line of best fit. This line would be the most accurate way of depicting the data points spread using a single line. In this research, an OLS regression model has been investigated for each of the independent variables of entrepreneurial tendency (proactiveness, innovation, and risk-taking) compared to the dependent variable (time), and its results are shown in Table 3. Typically, the sum of squares of the differences between the fitted and observed values in the data is minimized to estimate the OLS regression coefficients. An OLS linear regression procedure constructs a line of maximum fit to make the spread of data points as accurate as possible. The least-squares method will result in the lowest sum of squared deviations for all data points (Burton, 2021). Our first step was to construct a binary OLS regression model for the dependent variables (proactiveness, innovativeness, and risk-taking) separately on the

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Table 3 OLS binary regression Models Total

High-income

Middleincome

Male

Female

R2 Adj. R2 Coefficient T DurbinWatson R2 Adj. R2 Coefficient T DurbinWatson R2 Adj. R2 Coefficient T DurbinWatson R2 Adj. R2 Coefficient T DurbinWatson R2 Adj. R2 Coefficient T DurbinWatson

Proactiveness 0.145 0.145 2013.5711 400.742 0.260

Innovativeness 0.046 0.046 2013.0126 214.538 0.087

Risktaking 0.624 0.624 2012.6958 1253.963 1.161

No. of observation 949,492

0.135 0.135 2013.7427 356.078 0.246

0.042 0.042 2013.2525 189.484 0.081

0.613 0.613 2012.7488 1132.24 1.153

809,278

0.198 0.198 2012.9185 186.000 0.353

0.068 0.068 2012.1108 101.065 0.127

0.684 0.684 2012.4218 551.331 1.221

140,214

0.178 0.178 2013.5792 315.873 0.318

0.057 0.057 2013.0261 165.891 0.106

0.653 0.653 2012.8054 930.512 1.224

459,528

0.113 0.113 2013.5716 249.889 0.205

0.037 0.037 2012.9930 135.434 0.069

0.596 0.596 2012.5831 849.5831 1.100

489,964

Note: P>|t| = 0.000

independent variable of the year. Next, we ran regression models based on each moderator variable (income groups and gender). Table 3 presents the results of the OLS regression model fitting. Here are the indicators examined: a determination coefficient of R2 (correlation coefficient square) close to 1 indicates a better fit and a more significant contribution to the expression of changes in the dependent variable by OLS linear least squares. Based on the analysis results, the modified or adjusted coefficient of determination is equal to the coefficient of determination in all regression models. Based on the proximity of these two values, the variables used in the model were effectively used and provided an accurate fit to the data. DurbinWatson’s index is also used to detect correlations in the regression model analyses’

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residuals. This index is used in the time series analysis with the autocorrelation model since our research aims to investigate the time series of entrepreneurial orientation. This statistic always has a value between 0 and 4. As data changes over time and follows a specific pattern, the Durbin-Watson algorithm is applied to detect this pattern. If the results are closer to zero, it indicates a positive correlation, while if the results are more immediate to 4, it means a negative correlation (Dufour & Dagenais, 1985; Rutledge & Barros, 2002). Different results have been obtained based on the independent variables in the models used. The three variables of entrepreneurial orientation (proactiveness, innovation, and risk-taking) were examined separately over time in each data group, and 15 OLS regression models were run, with the results presented in Table 3. The model with total data proactiveness yielded a score of 0.145, which is higher than the scores of the high-income group (0.135) and the female (0.113). Conversely, proactiveness is higher in the middle-income group (0.198) and men (0.178). According to the results of the investigation of proactiveness over time, middle-income countries and males have a more robust entrepreneurial orientation, and proactiveness in these two groups will be more prevalent. Graphs 6–10 illustrate the OLS regression results for the proactiveness variable over time for each model evaluated. Each model, however, has a different mean starting point and end point for the proactiveness regression line, but all graphs show a positive slope of the regression line and an increase in entrepreneurial proactiveness over time. Males have responded positively to proactiveness on average by 12.5% since 2008, while middle-income countries have responded positively by 16%. The rate reached 25% for men and 24% for middle-income countries in 2018. Women chose proactiveness at an average rate of 7% in 2008, which increased to 16% in 2018. Entrepreneurs in high-income countries responded positively to this option on average by 8% in 2008 and 20% on average in 2018. A positive correlation is also observed between proactiveness and time in Durbin-Watson’s OLS regression analysis. These two models show a less positive correlation between independent and dependent variables for the middle-income group (0.353) and men (0.318). Females have the strongest correlation between proactiveness and time (Figs. 5, 6, 7, 8, and 9). Innovativeness has fluctuated slightly over time in all models and groups examined. However, some models showed more results than others. According to the total data, the coefficient of determination (0.046) indicates a relatively low level of acceptance of innovativeness over time. For high-income groups, this index has produced disappointing results (0.042). Due to the negative correlation, the middleincome group (0.068) has experienced a decline in innovation. Furthermore, men tend to be more innovative (0.057) than female (0.037). The Durbin-Watson test also shows a positive correlation between innovativeness and time in the total data (0.087), the high-income group (0.081), and females (0.069). However, the middle-income group (0.127) and men (0.106) demonstrate less autocorrelation between their variables. The autocorrelation between innovativeness and time has been observed more frequently among females than among other groups (Fig. 10). A comparison of OLS regression results for each of the innovativeness models over time is presented in Figs. 11, 12, 13, 14, and 15. All graphs have a positive slope

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Fig. 5 Proactiveness regression

Fig. 6 Proactiveness regression in high-income group

except for graph 13, which shows a decrease in innovativeness in the middle-income group. As described in the previous section, the innovation process was almost constant from the beginning to the end of the study period. In 2011, it only slightly increased but returned to its previous position in the following years. Based on the

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Fig. 7 Proactiveness regression in middle-income group

Fig. 8 Proactiveness regression male

graph, high-income entrepreneurs benefited from innovation in their businesses by an average of 3.5% in 2008 and 5% in 2018. Middle-income countries experience different situations. According to innovation surveys in 2008, 9% of respondents responded, but the number was less than 5% in 2018. The middle-income group has

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Fig. 9 Proactiveness regression female

Fig. 10 Innovativeness regression

been trending downward, even though both income groups were in the same position in 2018. Entrepreneurship has decreased in these countries due to the use of innovation in entrepreneurship. In 2008, 5.4% of men and 3.4% of women responded positively, which increased to 6% for men and 4% for women in 2018.

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Fig. 11 Innovativeness regression in high-income group

Fig. 12 Innovativeness regression in middle-income group

Table 3 presents the OLS regression results of risk-taking over time in the investigated models, indicating a better fit for this variable than for the other two independent variables (proactiveness and innovativeness). There has been a change in risk-taking over time (0.624) in the total data. It can be seen in graphs 16–20 that

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Fig. 13 Innovativeness regression male

Fig. 14 Innovativeness regression female

the regression results of risk-taking over time demonstrate that this index has decreased over time. The negative slope of the regression indicates an inability to accept risk. However, the reduced slope is not the same in all models, and some have moved more steeply toward fear of failure. High-income groups’ risk-taking

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Fig. 15 Risk-taking regression

decreased from 66% in 2008 to 57% in 2018. The middle-income index reached an average of 75% in 2008 and declined to 64% in 2018. Men’s risk-taking in the first year of the research was 69%, which decreased to 62% in 2018, while women’s risktaking fell from 65% to 55% in the final year. Middle-income entrepreneurs (0.684) have experienced a reduction in risk-taking more than high-income entrepreneurs (0.613). It is also relevant to note that men (0.653) have lost their ability to accept risks over time more than women (0.596). As a result, females and high-income groups have experienced a slower reduction in risk-taking than other groups. According to Durbin-Watson’s statistics, all risk models show a value above 1. This resulted in a lower autocorrelation for these models than for other variables, resulting in the highest Durbin-Watson scores for middle-income groups (1.221) and men (1.224) among risk-taking models, which indicates a negative slope to reducing risk-taking among these two groups. The statistics are based on females (1.100) and high-income groups (1.153) (Figs. 16, 17, 18, and 19).

3.2.5

Time Series Predictive Models

XGBoost This study constructs a machine learning-based model by utilizing the XGBoost algorithm. Creating estimates and hyper-parameter settings is one of the preliminary steps in machine learning (Gu et al., 2018). As part of the XGBoost algorithm, the function “XGB-regressor” is implemented. There is a maximum depth of 6 in the

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Fig. 16 Risk-taking regression in high-income group

Fig. 17 Risk-taking regression in middle-income group

model, an eta of 0.5, and a linear regression objective such as “reg: linear” that is chosen to predict the result. In the model, these hyperparameters were obtained through the greedy search function. Extreme gradient boosting (XGBoost) is a machine learning algorithm investigating the importance of all input features for

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Fig. 18 Risk-taking regression male

Fig. 19 Risk-taking regression female

tree boosting. In terms of machine learning problem-solving, it has proven to be a reliable and impressive tool (Chen & Guestrin, 2016). XGBoost can produce a robust classifier from weak classifiers compared to other gradient boosting algorithms. An extreme gradient boosting algorithm (XGBoost) is a scalable machine

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learning system that investigates the importance of all input features. It has been demonstrated to be a trustworthy and impressive machine learning problem-solver (Chen & Guestrin, 2016). XGBoost has the following advantages: (1) handling missing values effectively, (2) preventing overfitting, and (3) reducing running time for parallel and distributed calculations. It uses gradient descent optimization and ideal differentiable loss functions to optimize an objective function by adding weak learners, which minimizes the loss function. The regularized objective is minimized by XGBoost as follows: objðθÞ =

i Lð y i , y i Þ þ

k ΩðfkÞ, fk 2 F

L represents the training loss function that accounts for the deviation between the value yi predicted by our model and the actual value yi. Ω is a regularization function used to determine the model’s complexity, which helps prevent overfitting. A regression tree is defined by F, and a function in F is defined by f. In XGBoost, the greedy search algorithm finds the optimal tree structure by minimizing the objective function using parameters. Using time series forecasting, it is possible to predict the future trends of historical data sets with temporal characteristics. To obtain the highest-quality time series forecast, we applied the XGBoost algorithm, which gives us the most accurate forecast results based on several dependent variables. The algorithm was first run once for the entire data set with dependent and independent variables, and then predictions were made for each control variable separately. This section uses income group and gender as moderator variables to predict EO over time. In time series analysis, historical data is used to create models, which are then applied to predict future outcomes. The first step is to create a “target” variable from the sum of the dependent variables (proactiveness, innovativeness, and risk-taking). Attributes of the target variable include the following: A minimum of one dependent variable must be selected (54.7%). A total of two dependent variables (0.6%) were selected. There was a positive response to all three dependent variables (3.1%). A score of 0 indicates no positive response to any of the dependent variables (33.5%). In order to run the prediction model, we first divided each dataset into training and testing data. The training and test data were selected nonrandomly and based on time since the algorithm is a time series analysis. The training set included 0.75 of the data, while the test set contained 0.25. Due to the difference in the size of the data sets (based on the control variables), Table 4 shows the total number and division of training and test data. Each data set requires the following steps: Establish the target variable for X and the year variable for Y. Use the train test split function (shown in Table 4) to split the data and

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Table 4 Data set size

EO full dataset EO High-income EO Middle-income EO Female EO Male

Data set size 949492

Train size X train (712119, 1)

Y train (712119,)

Test size X test (237373, 1)

Y test (237373,)

809278

(606958, 1)

(606958,)

(202320, 1)

(202320,)

140214

(105160, 1)

(105160,)

(35054, 1)

(35054,)

489964

(367473, 1)

(367473,)

(122491, 1)

(122491,)

459528

(344646, 1)

(344646,)

(114882, 1)

(114882,)

XGBoost model training. Calculate RMSE (root mean square error) and MAE (mean absolute error) for the training dataset. Test the model with a test set of data. Determine the RMSE and MAE of the test dataset. Calculate the mean RMSE and MAE for both data sets and compare them. Evaluation Method In this research, RMSE and MAE are used as evaluation criteria to evaluate the performance of the EO prediction model. As a measure of prediction accuracy, RMSE is the root of the difference between the actual and predicted values of the model divided by the total data. An indicator of forecasting models is MAE, which is the mean of the absolute values of the predicted and actual values. It is often used in conjunction with RMSE to measure the accuracy of forecasting models (Botchkarev, 2018). This analytical framework has been shown in Fig. 20. The MAE and RMSE of XGBoost models are almost identical in training and testing, suggesting that the models are not overfitting. There is a significant difference between the MAE of a middle-income group (0.481) and the MAE of a highincome group (0.538). Compared to the other models, the RMSE is higher for middle-income individuals (0.741) and men (0.731). A summary of the MAE and RMSE for the five prediction models can be found in Fig. 20. A comparison of the five evaluation parameters of XGBoost models shows that EO middle-income model that has the lowest MAE is the most accurate. Regarding forecasting, the machine learning model outperforms simple and conventional linear regression and statistical analysis methods.

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EO FULL DATA

EO HIGH INCOME

Train RMSE min

EO MIDDLE INCOME

Test RMSE min

EO FEMALE

Train MAE min

0.524

0.731 0.524

0.731 0.538

0.671 0.538

0.481

0.481

0.671

0.741

0.727 0.52

0.672 0.516

0.517

0.664

0.704 0.514

0.704

XG B O O S T MO DE L S E VAL UAT I O N RE S AULT S

EO MALE

Test MAE min

Fig. 20 XGBoost model’s evaluation results

4 Conclusions and Discussion This empirical note examines changes over time in the dimensions of EO among men and women in countries with different incomes. This study uses a time series approach to examine changes in each EO dimension over time and predict future changes. Additionally, it utilizes the XGboost regression algorithm to learn and forecast data. The findings of this study provide deep insights into the three dimensions of EO. Researchers have claimed that applying the EO construct (Lumpkin & Dess, 1996; Miller, 1983) at the organizational and individual levels could provide valuable insights into the functioning of entrepreneurs and their respective organizations (Covin & Lumpkin, 2011; Davis et al., 2010). The regression results indicated that gender has a significant impact on EO. Compared to women, men adopt more aggressive and innovative strategies that lead to new ventures, products, and services and research into new markets and customers. There is a positive correlation between innovativeness and men. It is more prevalent in men over time than in women. Entrepreneurs or companies with a high-risk tolerance develop new innovative products and services to reach new markets (Miller, 1983; Morris & Kuratko, 2002). As with innovativeness and proactiveness, risk-taking is positively correlated with men; on the other hand, all three EOs are inversely correlated with women. It is consistent with previous research findings. It has been observed that men are more innovative than women, and with a higher tolerance for risk, they are more likely to engage in entrepreneurial activities, develop new products, and explore new markets. Because of their positive correlation, men were more innovative than women during the studied period. According to past studies, women have lower risk preferences than men (Powell

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& Ansic, 1997) because their risk perception differs (Gustafson, 1998). Since women are more likely to take care of their families and face unemployment and economic difficulties than men, they are less likely to consider entrepreneurship. As a result, women have fewer entrepreneurial options than men (Gustafson, 1998). According to our research, risk-taking reduction has been recorded in all modulating variables, but the rate of reduction in women over time is lower than that of other groups. In other words, over time, women’s risk-taking will decrease less than men’s, and it is predicted that risk-taking will be equal for both genders if this procedure continues. Women’s access to work facilities and the right to invest in productive assets in developing countries can stimulate their risk-taking ability (Okello, 2020). Contrary to previous studies (Ayub et al., 2013; Lim & Envick, 2013; Pérez-Quintana, 2013), it gave higher scores to men’s risk-taking. Not because of the cognitive characteristics and perceptions of women but because of the culture and income of societies that, with access to resources, the risk-taking and flexibility of female entrepreneurs can be accelerated (Hundera et al., 2019). Proactiveness is further in men than women, and like other EO, it positively correlates with men. In recent years, women’s proactiveness has been moving toward evolution, but men’s proactiveness has almost driven through a steady process. Women are more willing to participate in social empowerment programs where they learn how to enter a new economic activity (Hughes & Yang, 2020). It means more women’s access to information sources that improve women’s risk-taking ability and proactiveness (Okello, 2020). The target variable in the XGBoost model is the sum of independent research variables that includes all three dimensions of EO. EO changes over time have yielded acceptable results in both men and women. According to XGBoost time series prediction results, females have a lower RMSE than males. In both genders, the MAE of the test and train models is average and can be trusted for prediction results. Income was another moderating variable we examined in the temporal changes of EO. According to the researchers, EO varies by region (Audretsch et al., 2015) and country’s income. Businesses in high-income regions perform more innovative and dynamic activities than those in middle-income areas (Dvouletý, 2017; Fernández-Serrano & Romero, 2013). Also, since middle-income countries do not have enough resources to carry out innovative activities, they have more obstacles to competing with other countries (Fernández-Serrano & Romero, 2013), so SMEs in high-income regions have more EO than those in middle-income regions (Abrhám et al., 2015; Filser et al., 2014). The growth of innovativeness generally coincides with the regional ecosystem, and local clusters are known as places where tacit knowledge spreads quickly and at a low cost (Gilbert et al., 2008). This issue is more critical in developing countries that often have limited resources (Desouza & Awazu, 2006). The benefits of being part of a geographically localized cluster can be overshadowed by the need to establish connections beyond the local community (Bathelt et al., 2004; Mesquita & Lazzarini, 2008). Countries with lower incomes lose the possibility of communicating with other societies to obtain innovativeness due to fewer financial resources, which causes less innovation in these societies. This research shows that innovativeness changed significantly between 2008 and 2018. Entrepreneurs in

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middle-income countries have been more innovativeness, but in recent years, high-income people have used more innovation in their businesses. On the other hand, middle-income entrepreneurs have moved toward imitation. Studies on the role of creative and innovativeness clusters in the development of the regional ecosystem indicate an increase in the flow of knowledge between companies and the acceleration of their innovativeness capabilities, which helps regional economic growth by increasing the productivity of companies (Caniëls & Romijn, 2003; Schoales, 2006). The results of previous research also confirm that innovativeness is higher in individualistic countries developed with significant financial resources, fewer financial problems, and low risk (Hofstede & Minkov, 2010; Kreiser et al., 2010; Semrau et al. 2016). Risk-taking decreases over time, but the slope of its decline is different in each moderator variable. In some decreasing, faster, and the fear of failure increases. High-income countries negatively correlate with risk-taking, and this group’s reduction is slower than in the middle-income group. Since the middle-income group positively correlates with risk-taking, reducing in these countries leads fewer entrepreneurs to undertake entrepreneurial proactiveness. Risk-taking behavior in different countries is based on cultural values (Hofstede & Minkov, 2010; Kreiser & Davis, 2010; Ruiz-Ortega et al., 2013). Entrepreneurial proactiveness is improving over time, but proactiveness has a negative correlation with high-income and a positive correlation with middle-income countries. The expansion velocity of proactiveness in middle-income countries is higher than that of high-income countries, demonstrating an increase in middleincome proactiveness. These findings contrast with the results of pioneering research. In the previous contention, entrepreneurial proactiveness is higher in countries with low economic, political, and legal risks than in countries with political, legal, and financial risks (Filser & Eggers, 2014). The evaluation of the time series prediction model shows that RSME is higher in middle-income countries and MAE is lower than all other models. The model results in middle-income countries are more reliable than high-income countries, but both models provide suitable predictive power in training and testing data.

5 Contributions, Limitations, and Future Research This study makes the following contributions. First, this study confirmed the value of the predictive model based on machine learning technology concerning the prediction of EO by comparing it with the existing analysis method. However, machine learning has not been actively applied to entrepreneurship research, despite its high performance in forecasting. Researchers can use more complex analysis in entrepreneurship to solve the methodological limitations of this study’s predictive model, which covers proactiveness, innovativeness, and risk-taking as key EO variables. These results help expand the visual field in terms of predictive research methodology. It is expected that the prediction model presented in this study will be helpful

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for investors and government agencies that evaluate the performance of entrepreneurial activities and their changes over time or analyze the value of startups. Second, this study examined the performance of EOs over time using linear regression OLS based on moderator variables. As a result of the findings, EO should be prioritized among middle-income and female groups to slow down this downward trend. The government can design and implement business strategies to minimize the gap between subsets of two groups (country income and gender). More funding options for innovative businesses in middle-income countries and women-led companies are needed. As a result of this financial support, these two groups can participate in exhibitions and workshops, access new information technology, and improve their innovative activities. To improve the business environment, governments, universities, development agencies, and national and international organizations can cooperate on educational programs on EO. Countries can apply the policies to increase SMEs’ income, credit, and profitability and strengthen and improve entrepreneurs’ risk-taking, innovativeness, and proactiveness. Third, this research spreads the emerging work on entrepreneurship as a gendered process (Lewis, 2006; Mirchandani, 1999). Fourth, new empirical results add to the scant literature that compares female- and male-run businesses concerning their willingness to participate in business activities and, therefore, raise knowledge about the role of entrepreneurial gender in SMEs (Expósito et al., 2022; Okello, 2020). Fifth, because several countries with different incomes are examined in this research, conducting studies in a cross-cultural setting helps researchers understand entrepreneurial phenomena and develop robust theories (Goktan & Gupta, 2015; Liñán & Chen, 2009). The intercountry analysis explains the environmental and institutional context in different areas, economies, and markets, along with its impact on managerial behaviors and organizational consequences (Butkouskaya et al., 2020). Sixth, as far as we know, this chapter is the first study that examines the temporal changes of the three dimensions of EO in countries with different income levels, taking into account the role of gender, and also predicts the differences in these dimensions. Limitations also exist in this study – EO is measured by self-assessment. An objective measurement method may be necessary because the assessment is subjective. Additional analysis can provide more accurate concepts when objective measurements are used. This study presented a prediction model for EO using machine learning algorithms as an inductive method. Although machine learning models provide predictive information about the dependent variable, it has the disadvantage that it does not provide sufficient information about the relationship between variables. Machine learning models such as XGBoost use linear regression to use time series and prediction models. Nevertheless, their prediction accuracy and performance are better and higher than the old statistical models. We hope that the new method as a machine learning approach in this study will help to expand the horizon of the critical topic of EO, and this study will help to broaden the interest in predictive data science research in entrepreneurship.

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A Theoretical Research on the Effectiveness of Time Management in Dynamics of Employee-Organization Relationship Fatemeh Rezazadeh

, Sima Rezazadeh

, and Mina Rezazadeh

1 Introduction Time management (TM) and the dynamic nature of the relationship in employeeorganization relationship (EOR) over time requires much more focused attention than in the past because it is clear that EOR, like any other social relationship, does not remain constant over a while and is changing rapidly (Shore et al., 2015). In other words, the dynamic nature of EOR is formed, upgraded, and sustained under the umbrella of TM. The need to manage EORs is one of the essential requirements for an organization’s managers (Stasková & Tóthová, 2015). An initial understanding of the exchange agreement in EOR can serve as a solid foundation to manage the relationship over time and allow the managers to partially predict the employee behaviors during the period of his management in the organization. The realization of concepts, such as organizational citizenship and employee performance improvement, to be guaranteed leads to the promotion and sustainability of EOR quality (Sherman & Morley, 2015). EOR solves the manager’s concerns, optimally managing limited resources amidst countless organizational constraints (Yoon, 2017). Considering that time is the most valuable resource available to humans, other resources gain value only when there is time (Nasrullah & Khan, 2015). Therefore, the need to adapt to the acceleration of changes and optimal use of time has been raised as a topic of TM because time is a nonstop process (Baker et al., 2019). On the F. Rezazadeh (✉) Faculty of Management and Accounting, Organizational Behavior, Allameh Tabataba’i University, Tehran, Iran e-mail: [email protected] S. Rezazadeh Faculty of Management and Accounting, Islamic Azad University Shiraz Branch, Shiraz, Iran M. Rezazadeh Faculty of Engineering, Islamic Azad University Shiraz Branch, Shiraz, Iran © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Faghih (ed.), Time and Fractals, Contributions to Management Science, https://doi.org/10.1007/978-3-031-38188-1_3

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other hand, according to previous materials over the past three decades, the importance of time in the literature on organizational behavior and relationships has become increasingly known. Thus, based on the literature on organizational behavior and relationships, TM is defined as “behaviors whose purpose is to achieve effective use of time during specific and purposeful activities.” This definition suggests that using time is not a goal in but focuses on some targeted activities that cannot be simply followed, such as doing a task requiring effective use of time (Claessens et al., 2007). Generally, people need more time to do all their tasks, primarily due to TM inefficiency. Hence, emphasis on TM in the organization and also at all management levels should be considered because we see many organizational plans, programs, and functions that have not been implemented or exploited at the appropriate time due to the lack of TM and proper planning and have caused economic and social losses to a large extent (Hamzah et al., 2014). Managers’ neglect of this unique resource causes stress in them and indirectly causes waste time and even stress and performance reduction in employees (Sarafraz, 2022). Understanding the limitation of time and the benefits of TM helps us work with time, not face it. Environmental factors affecting organizations’ efficiency and rapid and profound changes in individuals’ demands and needs on the one hand and the need to enhance the performance within the organizations through increasing efficiency, productivity, innovation, and creativity on the other hand have led to successful organizations’ managers to pay more attention to TM techniques (Zampetakisa, 2008). It is challenging for employees to promote their performance as long as they are not well aware of their performance and their strengths and weaknesses. Accordingly, expert knowledge-based management of organizational and interpersonal relationships is still an essential secret to the success of organizations (Che et al., 2022). Notably, the researchers should direct their research toward meaningful concepts so that by integrating their results with previous research findings, they can play an influential and significant role in the formation, maintenance, and completion of EOR (Shore et al., 2012). On the other hand, in most research in the field of TM, more attention should be paid to occupational and organizational factors. Therefore, there is a need for more detailed research on TM mechanisms and also practical factors in its effectiveness (Claessens et al., 2007). Therefore, through the promotion and development of TM concepts in EORs, positive outcomes can be guaranteed because the theoretical and practical gaps in this particular field, as intellectual stimuli, can lead to providing a strategy or a model to regulate EOR mechanisms. In this regard, the results of this chapter appear in the format of the theoretical model suggested; it is possible to open the way for managers and employees to reduce exchange tensions, improve performance, and upgrade the quality of relationships by focusing on TM effectively. This study aims to investigate the TM effectiveness in the dynamics of the relationship between the individual and the organization, focusing on identifying the standard features of these two areas. On the one hand, those common aspects are the consequences of the successful implementation of TM from two perspectives of

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individual-organizational skills and provide the basis for realizing the dynamics and stability of the relationship between the individual and the organization. In other words, while explaining the individual-organizational skills in the field of TM, this study identifies the consequences of the implementation of TM that can provide stability and dynamics of the relationship between the individual and the organization. Therefore, the main focus of this study is to find the answer to this central question: How can the effectiveness of TM be explained in the dynamics of EOR? Therefore, this study reviews the literature and concepts of the communication field of TM and EOR to find the answer to the main question. Realization and accessibility of organizational goals can be facilitated by providing a better understanding and developing basic knowledge in the subject area of the chapter. From the theoretical point of view, the findings of this chapter can be used to expand the research area of EOR by focusing on the effectiveness of TM in the optimal implementation of the strategies of EOR management and the providence of the organizational relationship dynamics and stability. Therefore, different parts of the chapter have been designed and linked together to achieve the primary goal. In such a way, it begins with the conceptualization of the EOR and the description of the main concepts of this field (individual, employment relationship (ER), organizational context) and the theoretical framework of the EOR. In the continuation of the conceptualization of TM, the theoretical framework of TM and TM approaches are presented. Then, the literature review of the two fields of EOR and TM is presented. The following explains the necessary skills to realize organizational TM from two organizational and individual perspectives. Furthermore, to explain the effectiveness of TM in EOR, this chapter focuses on identifying the seven common features of the two mentioned areas. The following proposed conceptual model is presented in the discussion section. Finally, the chapter ends with Conclusion sections, Recommendations for Future Research, and Operational Guidelines for Organization Managers.

2 Conceptualization of Employee-Organization Relationship EOR is the relationship between an organization and its employees that indicates frequent relationships. It is like an umbrella used to evaluate the domain of employees’ interaction and interpersonal dynamics with each other on the one hand and with the organization on the other (Meijerink, 2014). EOR is a multilevel phenomenon that cannot be understood without regarding the interactions between the organization and the employees (Shore et al., 2012). Hence, in this section, a brief explanation of the three main parts of EOR, including individual, organization, and ER, seems desirable.

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Employee/Individual

Globalization in today’s world of rapid changes and evolutions, followed by the evolution of organizations in the form of intelligent systems, has not been able to replace the work through human resources and the relationship between employees and organizations (Bel et al., 2018). Successful integration of individuals in their organization is one of the prerequisites for management success and the organization’s prosperity. The desired mechanism for realizing this prosperity involves creating a balance between the employees’ needs and expectations and their organization’s needs and expectations, and organization management must create coordination and proportion between them (Bardarova & Ivana, 2019). Since individuals are the most strategic resources and organization performances, achievement of organizational goals passes through the channel of individual performances with positive and negative outsourcing (Dutta & Khatri, 2017). They are considered one of the essential elements of the organization, and meeting their organizational and individual needs leads to a feeling of satisfaction and, as a result, increases the organization’s performance (Stasková & Tóthová, 2015). In other words, if the expected contributions of the individual and the organization are aligned, employees will be more satisfied with their jobs (Audenaert et al., 2018).

2.2

Employment Relationship

Organizations are increasingly looking for effective ways to interact and maintain long-term and mutually beneficial relationships with their employees (Kang & Sung, 2017). The highest level of abstraction and basic foundation of EOR is the ER, which generally describes EOR as a contract that includes the terms of an exchange agreement between individuals and employees (Rousseau, 1995). This exchange includes employees who contribute to realizing the organization’s goals (using time and knowledge), and the organization provides incentive exchanges (salary, benefits, job security, and career advancement opportunities) as compensation for the services and motivation of the employee’s desired contributions (Lepak & Snell, 1999). As a context of expectations and perceptions, ER refers to the relationship between an employee and employee’s organization. This relationship may seem very simple, but it is actually a complex social relationship placed in an organizational context and dynamic over time. So ER defines the nature of interactions (Matthijs et al., 2015). The level of persuasive involvement of the individual in the organization plays an essential role in the central phenomenon. Because the feeling of duality, alienation, and separation of the individual from the organization will hinder the social identity, organizational excellence, trans-equilibrium system, and continuous commitment, this level includes the adequacy of providing the employee from the point of view of social, psychological, and financial status. Failure to pay attention to the alignment of the goals and interests of the individual and the organization will lead to

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consequences such as duality, alienation, and mutual forgetting of the goals (Rezazadeh, 2022). The degree of organizational involvement of employees is a continuum where the opposite point of employee commitment is alienation. Employee alienation is considered a mental and psychological experience, a feeling of helplessness, meaninglessness, isolation, and separation. The feeling of helplessness, isolation, and loss of identity caused by alienation should not be ignored. The sense of identity in a person is necessary to realize his/her desired performance and effectiveness because the degree of internalization of organizational goals, norms, and values in employees determines the level of dynamism and sustainability of EOR. Therefore, employees’ alienation levels can be reduced or controlled by persuading employees’ expectations, social needs, and the unit’s assumptions about their goals and interests (Tonks & Nelson, 2008).

2.3

Organizational Context

Context, or what surrounds it, is the place of commitment and includes the terms and standards of the relationship. Organizational context affects the communication links between individuals and organizations (Shore et al., 2015). Organizations are the practical contexts in which behavior occurs. It is believed that organizations are now competing in the world of temporary benefits. Cycle time is reduced for almost everything. The time for business processes is reduced. In the same way, the life span of the competitive advantage is also reduced. Such competitive challenges and pressures related to environmental monitoring and management mean that organizational leaders cannot either recognize the time necessary to manage the crucial elements of the relationship between the individual and the organization or do not have the time necessary to recognize and evaluate it. Thus, paying attention to the practical factors in EOR stability and dynamics will greatly help managers and their management (Shore et al., 2012). Therefore, since the organizational context is dynamic and changing, increasing employee’s engagement through personal and organizational tools continues to attract the attention of organizations and human resource professionals (Malaeb et al., 2022). Variables such as culture/atmosphere, goals, processes, conditions, structure, and time are considered the factors affecting the leader’s behavior and effectiveness in EOR (Sharma, 2017).

3 Theoretical Framework of Employee-Organization Relationship In general, the theoretical framework of the research area of the relationship between the individual and the organization is based on theories such as resources exchanged and the concept of exchange of utilities (Barnard, 1938), social exchange theory

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(Blau, 1964), the norm of reciprocity (Goldner, 1960), and inducementscontributions model (March & Simon, 1958; Tsui et al., 1997; Shore et al., 2012; Gillis, 2017; Kang & Sung, 2017) that has been accepted. The concept of the psychological contract perceived organizational support (the micro-levels) and ERs (the macro-level) makes the three primary levels to understand EOR (Bardarova & Ivana, 2019). According to the systematic review of studies and the theoretical background of the EOR research field, the basic foundation of EOR is the relationship because it is the employment relationship that connects individuals to the organization. ER refers to the level of employee’s participation toward the incentives provided by the organization. As a macro part of EOR, ER is based on two foundations: interaction and organizational context. Interaction based on the norm of opposition appears as the basis of organizational performance in work relationships and is strengthened or weakened based on the level of trust between the parties. The organizational context is the platform where exchanges and interactive behavior of people occur. Therefore, neglecting different micro- and macro-levels of the organizational context in research is considered an essential factor in the weakness of organizational behavior. On the other hand, people are the most important strategic resource that the performance of organizations and the achievement of organizational goals pass through the channel of people’s performance and its various forms with positive and negative outputs (Rezazadeh, 2022). That core category phenomenon in EOR is the coordination and unity of individual’s and organization’s goals and interests. In interpreting this definition, the path of improvement and growth of organizational relationships and interpersonal relationships is leveled through aligning the employees’ goals and interests with the organization’s goals and interests, and both parties to the relationship, whether individual or organization, believe that they have a contribution to the utility and sustainability of this relationship. Besides, they should meet the expectations of the other party. Therefore the extent of the organization’s success in determining the goals as a guide can put the organization and individuals on the path of improvement, and its weakness can undermine the path of organizational improvement (Rezazadeh, 2022).

4 Conceptualization of Time Management Most definitions of TM refer to Lakein (1973): TM includes the process of determining needs, determining and clarifying goals to achieve these needs, and prioritizing and planning tasks needed to achieve these goals (Claessens et al., 2007; Ngowo, 2011; Offei Larbi, 2015; Yaşar & Sağsan, 2020). In other words, TM includes behaviors that require effective use of time while performing specific and purposeful activities. These behaviors are the following:

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• Assessment behaviors: with the aim of awareness of the past, present, and future and an individual’s self-awareness that helps to accept responsibilities within the scope of his/her abilities • Planning behaviors: determining goals, planning tasks, prioritizing, preparing a list of works, and grouping tasks • Supervisory behaviors: aiming to monitor time during activities and create a feedback loop (Claessens et al., 2007) TM means that a person dominates his time and performance and does not allow affairs and events to guide him/her (Zeinuddinez, 2018). It is the optimal use of time as a limited resource that cannot be transferred to other people and is available to each person in a certain amount. It is a program in which the amount of time spent on each activity is identified and planned. One of the necessary conditions and the key to self-direction and the effectiveness of management and managers is the application of TM (Sarafraz, 2022). In other words, TM is a set of teachable habits and behaviors that may be acquired through increasing knowledge and training or performance improvement (Kulkarni, 2020). TM refers to a wide range of skills, instruments, and practical techniques for specific tasks, special projects, and goals to become influential person in the profession, education, and life (Harford et al., 2018). TM is used to increase effectiveness, efficiency, or productivity. In other words, TM includes planning and informed control over the amount of time spent on specific activities (Nor Lela et al., 2012).

5 Theoretical Framework of Time Management The concept of TM in business was first introduced in Taylor’s “Principles of Scientific Management” (1911), which dealt with the optimal method of training and distributing rewards to employees (Vaida & Brinze, 2021). Next, the problem of managing time was discussed in the 1950s and 1960s (Offei Larbi, 2015). In addition to the known frameworks in this field, the research of Rezazadeh (2022), done with foundation data theorizing methodology based on the theoretical framework of Blau (1964) and Meijerink (2014), shows that TM was identified as one of the practical concepts of managers’ empowerment and skill enhancement strategies in order to improve the employee-organization relationship. In other words, TM facilitates the transformation of the structure of hindering relationships into enabling relationships, TM is the factor that creates organizational identity, and TM is an influential factor in the optimal management of interpersonal and organizational relationships.

6 Time Management Approaches Two managerial conceptions that have emerged with different natures of time are utility time and sense time, leading to fundamental approaches of TM (Reinecke & Ansari, 2015). Utility time considers time to be linear and controllable. It is an

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externally measured version of clock time that is strategically used as a resource. Utility time adheres to time (obey the clock). Real TM is achieved at the individual level by avoiding rush and stress, and success can be achieved through balancing abilities and challenges in work processes (Rydén & Sawy, 2018). Nevertheless, according to Roe et al. (2009), sense time runs away from the clock (ignore the clock). It is a subjective time experience sensed by the inner clock. It is realized by being, not by doing, and seeks to create a space for the present moment or psychological state of mind. It is an optimal success measure that can occur during a complex operation or the conclusion of a contract. The perception of both categories is influenced by individual factors (manager) and collective factors (organization). In other words, according to Mead (1932), real TM depends on managers’ interpretation of clock time and requires a conscious and collective effort. The best strategy in this direction is to develop two-way capabilities in managers to simultaneously bridge and focus (individually-organizationally) through the fast and flow method. These capabilities enable organizations to build a culture that can turn opposing views into a strategic advantage. Two-way leadership (leadership based on utility and sense/internal and external/quantitative and qualitative time) capabilities include a high degree of cognitive agility to rapidly integrate and manage paradoxes (Rydén & Sawy, 2018). People have different approaches to TM: • Objectivist approach: This approach has a quantitative and statistical view of time. It considers laws as absolutist and objective, affairs as fixed and motionless, and the working environment and conditions as changing. People with this approach cannot make optimal use of time. • Imaginative approach: This approach believes that some people fantasize that they can do all the expected things in the future. They consider time a reality that will be realized in the future, and failure to understand time leads to missed opportunities that cannot be repeated. • Productivity approach: This approach believes that the best result and work performance should be obtained with the least time and cost because people try to minimize the time required to do one task to get the opportunity to do other tasks (Azhdari et al., 2022).

7 A Review of Literature In line with the analysis of the knowledge structure in previous research, a selection of the research related to the fields of EOR and TM is presented in Table 1.

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Table 1 A review of the background of research done in the field of EOR and TM Researchers Men: Kang and Sung

Year 2015 and 2017

Rezazadeh et al.

2022

Bandiera et al.

2011

What Do CEOs Do? CEPR Discussion

Boles and Davenport

2016

Introduction of Educational Leadership and Time Management

Mazaheri and Avazzadeh; Dokhtbagher and Askariya Born

2017 2016

The Effect of Individual Skills on Time Management on Managers’ Organizational Skills

2018

Piva

2018

The Extent of Applying Time Management Principles to Professional Secretaries Time Allocation Behaviours of Entrepreneurs: The Impact of Individual Entrepreneurial Orientation

(Strategic Internal Communication: Transformational Leadership, Communication Channels, and Employee Satisfaction); (How symmetrical Employee Communication Leads to Employee Engagement and Positive Employee Communication Behaviors: The Mediation of Employee- organization relationships) Analysis and forecasting of the future employee-organization relationship: A systematic literature review

Title Employee’s engagement increases their positive communication behaviors and reduces the organization’s costs

In the field of EOR, from 1990 to 2020, four major theoretical gaps were identified in current research: weakness of theorizing in the field of EOR, lack of sufficient attention and research about the organizational context, lack of research on combined relationships of micro-macro-level, lack of multidimensional research considering the level of individual behavior, organizational context, and employment relationships There is a meaningful and positive relationship between TM and performance. Time devoted to activities that benefit the company has a stronger correlation with productivity and organizational profit than the time devoted to activities that bring personal benefit Most managers need help to clearly understand how to spend their time There is a meaningful relationship between individual skills of TM and organizational skills and its sextet dimensions Managers spend a considerable amount of their time on things that do not benefit their organization Some dimensions of individual entrepreneurial orientation affect the TM behavior of entrepreneurs (continued)

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Table 1 (continued) Researchers Rydén and Sawy

Year 2018

Sarafraz

2022

Senior Managers’ Measures That Hinder Profitability and Time Management Implementation

Li et al.

2021

Are Proactive Employees More Creative? The Roles of Multisource Information Exchange and Social Exchange-Based EmployeeOrganization Relationships

How Managers Perceive RealTime Management: Thinking Fast and Slow

Title Most managers need to recognize clock time from real time. They use clock time as a reference to determine real time. They define real time as the duration in seconds, minutes, hours, or days or evaluate real time as a description of events occurring at a fixed moment Accurate management and optimal use of time by an organization’s employees can increase the employee’s knowledge and performance and the targeted use of time to do better and more organizational affairs In social exchange-based EORs, employees are more engaged in multisource information exchange activities with internal and external stakeholders and subsequently generate more creative ideas

8 Necessary Skills for the Realization of Organizational Time Management TM is a skill that everyone should not only know but also practice. TM skills strengthen efficiency and effectiveness and increase employee’s productivity (Jamaladini et al., 2018). TM oversees a set of skills for better control and use of time. These skills are tools and methods that help an individual effectively use the time to spend his/her time on purposeful activities (Bozbayindir, 2019). The skills of TM can be divided into two general categories: individual (general) and organizational (specific) skills. The general skill of TM in personal life contributes to the specific skill in organizational life, especially communication with employees. An individual generalizes the skill that he/she has acquired in his/her personal life in a new organizational situation (Sarafraz, 2022). In the following, these two categories will be explained.

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Organizational (Manager’s) Skills in Realizing Time Management Process

The organizational skill of TM means the skills that an organization’s management should have. These skills are the sextet skills that a manager applies in the effective use of time in the organizational environment to achieve organizational goals and concerning the implementation of his/her professional duties, including targeting, prioritizing goals and activities, operational planning, and delegation of authority and relationship management (Sarafraz, 2022). The existence of human relationship skills in managers can improve TM and make it effective in the organization, such as the ability to communicate effectively with individuals at different levels; listening and understanding verbal and nonverbal messages; the ability to understand the employees’ verbal and behavioral feedback, foresight, flexibility in relationships, and positive and expressive speech; and understanding the employee’s behavioral values, humility, reverence, positive thoughts, and the like (Jamaladini et al., 2018). Manager’s success in the future depends on skills and competencies that differ from previous managers’ skills and competencies. This requires systems and procedures that align individual and organizational goals and develop them effectively while communicating with managers and specialists (Udall & Hiltrop, 2007). Given that the managers relate the organization to the employees and their competence level is very effective in directing the organizational relationships, they include a broader domain of a manager because playing the optimal multiple roles is in line with the manager’s competence requirements. Managers’ competencies pass through the path of characteristics such as foresight and transparent decision-making, futurology, TM, and stress management. Creation and institutionalization of these characteristics in managers can determine, develop, or improve the level of unity of individual’s and organization’s goals. These characteristics put the organization and the employees in the direction of improvement and achievement as a guide (Rezazadeh, 2022).

8.2

Individual Skills in Realizing Time Management Process

Evidently, different kinds of employees have different opportunities to manage their work time and improve efficiency (Stuken et al., 2021). Using individual skills in optimal use of time is the most critical skill needed for any individual to succeed in all work-life stages. These skills include some general behavior patterns that most individuals use in their personal and family lives to use time and manage it. Successful individuals in the organization are those who value time and constantly strive to command themselves to be better and more efficient. It can be said that TM is a skill and necessity for individuals.

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This belief is in line with the researchers’ opinion, as Miqdadi et al. (2014) also believe that most employees begin to delay when they encounter uncertainty because these individuals lack organizational skills and, therefore, cannot organize the tasks according to their priorities so that they are easily distracted and face functional weakness. According to Zekioglu et al. (2015), TM is crucial for employees because it increases their efficiency, effectiveness, and productivity (Ismail & Khalid, 2020; Jamaladini et al., 2018; Hamzah et al., 2014). Self-regulation skills lead to better performance, and individual skills lead to organizational effectiveness (Sarafraz, 2022). Therefore, organizations need to pay attention to individual needs and skill enhancement in various fields, especially TM (Che et al., 2022).

9 Time Management Effectiveness in Employee-Organization Relationships Clarifying Commonalities Between TM and EOR In this section, the basis of the literature review and generality of the communication field of TM and EOR and the subscription aspects of the two areas can be answered as the main question of the present study. As mentioned in the introduction, we seek to identify and explain the consequences of the successful implementation of TM, which itself is the basis for the realization of the stability and dynamics of the relationship between the individual and the organization, that is, clarifying a particular form of the effectiveness of TM in the individual and organization relationship. In short, the successful implementation of TM significantly benefits individuals and organizations. Benefits include doing more work on time, prioritizing activities, doing and completing activities on time, stopping unnecessary activities, and improving the organization’s performance (Sarafraz, 2022). With this explanation, a part of the workload can be reduced or managed optimally through a scientific strategy of TM because it ultimately helps the employees feel good about being and staying in the organization. It also changes the employee’s perspective and attitudes toward the organizational context. In other words, employees believe that governing relationships in the organization facilitates and empowers relationships (Rezazadeh, 2022). The role of TM is efficient and essential not only in personal affairs but also in organizations, and ignoring it causes time and energy waste. TM in organizations means allocating specific time frames to each task based on the organization’s priorities and values. Therefore, notably, in addition to managers, employees are practical in realizing this process. TM only achieves the implementation of a specific and stable program in the organization, and the organization’s success depends on individual success. In fact, if employees use coherent and valid planning and perform their tasks at a specific time, they will move toward success; otherwise, the organization’s efficiency will decrease and sometimes even face irreparable failures and losses. So determining a time frame is one of the essential principles

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that every organization needs to survive. Optimal use of time and doing tasks at certain times includes personal and organizational productivity. Undoubtedly, TM knowledge not only contributes to the organization’s growth and development but also is very effective in increasing the occupational and individual satisfaction of the organization’s employees (Hamzah et al., 2014; Offei Larbi, 2015; Rovelli, 2020; Vaida & Brinze, 2021). In general, the existence of TM can improve the quantity and quality of services, cost-cutting, prevention of resource losses, reduction of bureaucracy, accretion of competition, efficiency, productivity, and also motivation of the employees. TM can be considered one of the critical components in improving organizational relationships and realizing productivity and, ultimately, the organization success (Moradi & Soleimani, 2019). Manager and employee attention to the TM issue can significantly impact individual-organizational progress and success and, ultimately, the productivity caused by improved interpersonal and organizational relationships (Rezai Soufi et al., 2016). Generally, the effectiveness of TM (the sum of individual and organizational skills) is realized in EOR dynamics and stability. Based on research conducted in the subject area of the chapter, we find out that the successful realization of TM has consequences in the individual-organizational areas. On the one hand, these consequences are an introduction to EOR dynamics; on the other hand, they are considered the commonalities between TM and EOR. In the following section, the effectiveness of these concepts is explained.

9.1

Manager Clarification and Foresight in Strategic Decision-Making

TM is a crucial source for managers because they need enough time to work and think alone, meet with internal and external stakeholders, and define the organization’s strategy and strategic decision-making. However, since management life is short, managers usually have limited time (Rovelli, 2020). Strategic decisions are one of the managers’ essential tasks that significantly impact the organization’s performance (Lafley, 2009). On the other hand, decision-making is one of the skills of TM, and if managers do not have this skill, they will experience adverse effects at every moment of interpersonal and organizational relationships. It is a necessity that managers understand how to manage time and consider its consequences and make correct strategic decisions (Sarafraz, 2022). Manager’s clarification and foresight in decision-making are interpreted through the concepts such as manager’s management and foresight, manager’s decision-making for organization missions, manager’s decision-making to maintain the organization’s interests, participation of process owners in the organization’s decision-making, and decision-making based on realism (Rezazadeh, 2022).

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Manager’s Futurology Path

In an era where constant change and uncertainty are critical features, and businesses face new and unknown issues of the future every day, how can we plan for the future? Indeed, various techniques such as providence, foresight, and futurology have been developed to know what is called the future. Therefore, the current age is the age of futurology, and future management is considered one of the basic strategies for EOR management in the best time frame. Paying attention to cognitive skills and their development is one of the ways to achieve this vital factor (Kalatesefari et al., 2016). Futurology is considered the manager’s thinking and foresight to meet the organization’s future needs. Foresight and futurology by the managers lead to the necessary measures and strategic decisions to achieve the factors of the organization’s future success and prosperity (Ribeiro-Soriano & Urbano, 2010). The critical importance of time is one of the principles of futurology because the focus of futurology is on a systematic and scientific activity in understanding the future time and trying to build and shape it, enabling the human not to be indifferent to the occurrence of inevitable futures and try to build his desirable future (Hamidizadeh, 2011). According to Hoover (2009), futurology seeks to prepare a human for unexpected events in the future. This knowledge attempts to increase control and TM of the future by providing possibilities for increased awareness. Foresight and futurology by the managers lead to the necessary measures to achieve the factors of the organization’s future success. Competent managers facilitate futurology through far-sighted and transparent decisions, and in line with protecting the organization’s interests, they involve the employees in decisions based on needs and realism. This involvement makes the employees feel more belonged and loyal to the organization. Individuals’ closeness to an organization aligns with their goals and causes the unity of individual and organizational goals. This can be the basis for the dynamism of EORs (Rezazadeh, 2022).

9.3

Stress Management

One of the factors affecting the individuals’ life and physical and mental health is stress. Since working conditions are constantly changing, this discussion always exists to a certain degree about work-related issues in managing organizational behavior, especially in the last few decades, when the movement of life has accelerated, and the evolutions in the world of work have become more serious (Odigie, 2016). Most researchers believe that stress disturbs mental health in the current conditions of organizations. Stress has become one of the managers’ problems, dramatically reducing efficiency and productivity and causing behavioral problems (Magtibay et al., 2017). Thus, stress management skills to solve individual problems should be organized according to individual needs. Planning in the organization

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requires a detailed evaluation of employees’ attitudes, views, and activities and opportunities of managers and the organization (Roland et al., 2016). TM is a cluster of behavior that facilitates productivity and reduces stress (Claessens et al., 2007). In other words, TM is an effective technique to reduce stress because it can control an individual using time and planning future activities. It means that TM is one of the factors that can help increase efficiency and productivity (Ismail & Khalid, 2020). So it is necessary for individuals to actively adapt themselves to stressful situations at work by using different techniques and acquiring the skills of stress management methods to deal with problems step by step. Factors such as discrimination, perceived injustice, and employees’ occupational tension and stress have led to weakness and reduction of tolerance threshold and thus weakness in organizational relationships and interactions. Therefore, this problem can be solved and managed by managing stress through the concept of decliner and management of employees’ tension through increasing the tolerance threshold (Rezazadeh, 2022).

9.4

Creativity and Innovation

According to Rezai Soufi et al. (2016), new ideas and thoughts are out of reach and created apart from fundamental issues and beliefs. These far-out processes need time; moving from one thought to another thought and finding far associations and bonds is time-consuming. Therefore, people need to have enough time to do creative work, and one of the essential features of successful individuals and one factor that distinguishes them from others is their dominance over different techniques of TM. Unquestionably, the ability to properly manage time by excellent managers and the ability to create the necessary motivation in employees to use their maximum abilities in creative actions are two factors that guarantee the success of relationships in state and private organizations to a great extent. Zampetakisa et al. (2010) believe that the amount of individual creativity in presenting creative ideas is closely related to organizational culture and climate, and TM is a factor affecting organizational creativity. Creativity and innovation in organizational relationships will be the factor of productions and services, increasing the quality of services, cost-cutting, wastage, material, and human resource dissipation and increasing the work motivation in the employees of the organization, and employee’s occupational satisfaction and reduction of sedentary jobs (Zampetakisa, 2008). This depends on the quality of EOR, the amount of facilitation, and the guidance of creativity by the manager’s and employees’ characteristics because facilitating the path of employees’ creativity through the structure of dominant organizational relationships will have optimal consequences, such as organizational development and mutual satisfaction of individuals and the organization. If the structure of EOR is a deterrent, it will have adverse consequences like duality and separation of individual and organizational goals (Rezazadeh, 2022). Therefore, employees can become both a factor of innovation and a severe breaking to organizational innovation (Stuken et al., 2021).

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Work-Family Flexibility

TM includes work, social, family, personal life, and other interests and duties. If time is used effectively, all types of work can be done on time (Das & Bera, 2021). According to research by Dimou et al. (2016) and Dyrbye et al. (2011), which has been done by integrating the literature on two areas of TM and work-family flexibility, most of them demonstrate the importance of determining the goals and strategies of TM. Integration of work and life means coordinating and combining the elements of life into a whole unit in which work, family, friends, and self are valued and time is allocated to each of them properly (Gade & Yeo, 2019). Therefore, the loss of the boundary between the workplace and the place of residence and the boundaries between work time and leisure time enables the employers to fully monitor their employees’ performance and other behaviors. So using effective methods of TM significantly impacts creating a balance between personal and professional lives (Parli, 2021). Hence, the common point of the literature on both EOR and work-family flexibility is a paradigm change with the tendency to reduce the limitation, and this change is progressing from formal and closed organizational roles to less formal and open systems (Van Dyne & Ellis, 2004). If flexibility is attractive to the employee, its access or use by the individual will motivate the individual to reciprocate rewards to the organization. In this way, greater job satisfaction increases loyalty, and employees’ organizational citizenship behavior is considered a real advantage for the organization. Generally, work-family flexibility significantly improves and strengthens EOR and includes consequences such as organizational support and reduced work pressure on families. In other words, the best response of employees to social exchange is their loyalty, which will lead to the dynamics of social exchange (EOR theoretical foundation) (Shore et al., 2012).

9.6

Job Satisfaction

Job satisfaction means evaluating the efficiency of the organization’s salary (external/internal). The perception of satisfaction, as a perceived motivational and attitudinal aspect, is simultaneously practical (Ramalho et al., 2018). The critical factors in increasing the overall level of job satisfaction are the combination of external factors (monetary rewards and benefits) and internal factors (professional development and relationship desirability) (Davidescu et al., 2020). Macan’s model (1994) indicates that training programs of TM lead to the formation of three types of TM behavior: determining the goals and priorities, TM mechanisms, and organizational priorities. These behaviors lead to the perceived control of time or a sense of control over own time. This feeling, in turn, has a positive impact on job satisfaction and a negative impact on job-induced and somatic tension (Claessens et al., 2007). Based on research (Malekara, 2009; Dehshiri, 2004; Born, 2018; Charles, 2007), knowing

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how to manage time is not only beneficial for the organization but also gives employees higher job satisfaction and thus a greater sense of satisfaction (Sarafraz, 2022). Satisfactory relationships between employees and the organization not only lead to an increase in their level of interaction but also the desired cognitive evaluation of the organization by the employees. Employee’s relationship satisfaction with the organization is a crucial indicator of EOR quality (Men et al., 2020). EOR is a dynamic relationship that is evaluated according to both parties of exchange (individual and organization). Because EOR presents the levels of relationship based on which an organization and its employees trust each other, these levels include trust, mutual control, mutual satisfaction, and mutual commitment (Jiang, 2012; Men et al., 2020; Men & Robinson, 2018; Staab, 2019). So since job satisfaction is the main dimension of EOR, its successful realization guarantees EOR improvement, promotion, and dynamics.

9.7

Organizational Performance Improvement

Based on an extensive review of past literature, researchers believe that TM has a more significant effect on individuals’ performance than other concepts, so it is considered a fundamental issue for job performance (Hamzah et al., 2014; Ngowo, 2011; Offei Larbi, 2015). Generally, by observing the three binding principles in TM, that is, considering every minute, eliminating unnecessary tasks, and dealing with the original nature of the work, we can do more work at the same time, prioritize the activities, do the activities on time, stop doing useless activities, promote the organization’ performance, and prove our value and abilities (Fouladvand Mansoori et al., 2015). TM techniques and strategies are the best way to manage performance successfully. These techniques include group discussion, exchange of views, and sharing comments on key points. So the relationship between TM and resulting performance can be defined as an individual’s ability to achieve desired goals in the short or long term by effectively allocating time (Hamzah et al., 2014). Managers who plan activities in advance meet and interact with many people simultaneously, and this effect is related to a high level of organizational performance (Rovelli, 2020). Therefore, adequate TM skills play a vital role in improving individuals’ performance, including determining goals and priorities, TM mechanism (to-do list), and proper organization of time use (Kaushar, 2013). TM requires a goal-oriented performance through a pragmatic approach (Vaida & Brinze, 2021). In order to explain the relationship between the micro- and macro-levels of the relationship between the individual and the organization, it can be said that EOR is a broad term to describe the relationship between the employee and the organization and the helper of organizations in improving and developing things to achieve a sustainable competitive advantage through effective organizational performance and the organization’s health and cohesion. Thus, understanding how managers and supervisors meet employee’s expectations is vital for organizations to maintain

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long-term commitment and employee’s performance (Shore et al., 2015; Rynes et al., 2012). The research on the relationship between EOR and individual performance shows that psychological contract violation has a negative relationship with individual performance (Coyle-Shapiro & Conway, 2004), and organizational support has a positive relationship with job performance (Armeli et al., 1998). Also, among the quadruple approaches of ER,1 the effect of the two approaches of mutual investment and high investment has more power, and their relationship with job performance is positive (Tsui et al., 1997).

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Discussion

Therefore, in order to answer the interpretation of the question of the present research, it can be said that TM is a skill that every employee should not only know but also do, because the attention of managers and employees to the issue of TM, which is the optimal use of the time available for every individual, can significantly impact an individual-organizational success and development. This ultimately leads to productivity caused by improved interpersonal and organizational relationships. TM is a type of self-management in which three general principles contribute: targeting, listing the priorities, and observing the priorities. Good TM enables individuals to work smarter, not harder. So more work can be done even with limited time and high work pressure. The inability in TM damages individual effectiveness and causes stress. Notably, time is one of the most valuable assets for any human being, and every individual uses it inevitably to improve work and life. So it is better to consider the role of TM seriously and have a specific plan and purpose to avoid wasting it. TM gives the individual the opportunity to increase personal progress in the direction of improvement of the organizational relationships and realization of the organizational productivity and have a faster performance in their affairs. These results are according to the study conducted by Mortazavikiasari et al. (2017), in which it was found that interpersonal and organizational relationship skills have a positive and meaningful relationship with the organizational TM. Improvement increased performance, and reduced stress and anxiety are the consequences of TM skills. Employees who are familiar with practical and unique TM skills, because of their effective use of time and compensating for its lack, are less stressed and consequently feel satisfied with their jobs. As a result, the realization of job satisfaction as one of the main dimensions of EOR guarantees the EOR dynamics. So it is necessary to familiarize employees with life skills and TM skills to reduce stress and

1 Tsui et al. (1997) believe that the four approaches to the employment relationship from the perspective of the incentives provided to employees by the organization/employer include approaches such as mutual funds investment, overinvestment, quasi-equity or monetary investment, and underinvestment.

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factors affecting job satisfaction. Furthermore, favorable to research results by Forbus et al. (2011) and Sarafraz (2022), job satisfaction, organizational efficiency, and effectiveness can reflect EOR dynamics and sustainability. Based on the research conducted by Boniwell and Zimbardo (2015), taking even small steps toward creating a more balanced time perspective (TP) is a valuable goal. Techniques such as TP structure help reduce and ideally prevent occupational stress. They can be valuable and effective in solving the old problem of work-family balance and job burnout because as long as the continuous movement of the lifetime clock toward the final ticktack for each person is the same, this technique is considered the key to personal happiness and finding more meanings in individuals’ personal and work lives. Successful integration of personal and professional goals in line with optimal TM requires self-evaluation, identification, prioritization of short-term and long-term goals, and having a realistic and timely executive plan (Gade & Yeo, 2019). On the other hand, the improvement and sustainability of EOR require the unity and coordination of individual and organizational goals and interests. This coordination depends on the amount of clarification of the goals and awareness of managers and employees of mutual goals and convincing employee’s dependency on the organization. The competent manager facilitates the path of futurology by making farsighted and clear decisions, involves the process owners in decisions to preserve the organization’s interests, and makes decisions based on needs and realism. This involvement makes the employees feel more belonged and loyal to the organization. The closeness of employee’s goals and interests to the organization’s goals and interests can align the employee’s goals with the organization’s goals and cause the reconciliation of the individual and organizational goals. Seemingly, a part of the workload can be reduced scientifically or managed optimally through the TM strategy. By interpreting the present and previous materials, it can be seen that there are essential factors of commonalities between the concepts of EOR and TM and that the successful realization of each of these factors has combined the two mentioned fields. There is a need to pay attention to skills such as creativity and innovation, organizational stress and tension management, manager’s foresight and futurology, strategic decision-making, work-family flexibility, organizational performance improvement, and increased job satisfaction. Through these findings, a theoretical model can be proposed so that in the future other researchers can consider this model and evaluate it in different organizations with qualitative and quantitative methods; proposed theoretical model is shown in Fig. 1.

11

Conclusion

As a result, the manager’s awareness of their leadership style in the organization and familiarity with the principles of TM at the same time can be the solution to organizational relationships and faster performance of tasks or affairs such as operational planning and authority delegation. According to Nouri et al. (2022), since individuals inherently cannot manage their time, without training, despite

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Fig. 1 Proposed conceptual model

having good ideas, they waste time, and their positive thoughts do not reach the stage of implementation and efficiency. Considering the importance and effectiveness of TM in EOR, managers and employees should consciously strive to achieve their own and the organization’s goals and always plan for their TM in order to bring the dynamics of EOR by aligning their goals and interests with the organization’s goals and interests in a managed and real time frame. Typically, it can be said that today, using time or TM in an interpersonal and organizational relationship is a critical and skill issue that can be learned through practice and discipline. On the other hand, the interpersonal and organizational relationship is an activity and does not occur passively. TM is not controlling every second but includes the methods that people through them use the time to improve their personal, professional, and ERs. Therefore, it can be said that the influential and determinative role of TM in the success of organizational relationships with consequences such as increasing the organization’s efficiency, motivating the employees, following up and enhancing the employees’ performance, monitoring the employees’ performance, and regulating the activities is not neglectable.

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Recommendations for Future Research

This study can be a good starting point for further studies in TM and EOR.TM effectiveness in EOR stability and dynamics through more accurate quantitative and qualitative analysis methods requires more research. Such research may clarify processes and their effects on perception, emotion, and performance. Moreover, systematically combining all these aspects may help develop the knowledge of TM

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effectiveness in EOR and improve current TM training programs. Besides, it seems necessary to further investigate the methods through which sustainable TM behaviors can be created. The practical consequences of future research should clarify what effects can be expected from TM, what aspects might be most beneficial for which individuals, and which work characteristics can enhance or hinder positive effects and contribute to the development of effective TM approaches. Another proposition is the focus of future research on specific target groups. Since most studies deal with student samples, further research on TM in ERs between individual and organization can be focused on different organizations to ensure sufficient variation in relevant contextual factors.

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Operational Guidelines for Organization Managers

According to this chapter about the successful realization of the TM process and improvement of the quality of EOR, it is suggested that managers keep their stability through identification, maintenance of the coordinator’s role, involvement of employees in the process management, facilitating, guiding, and being a strategic pattern of creativity for optimal management of time and interpersonal and organizational relationships. According to Piva (2018), the manager coordinator’s role with this perspective that the employees are the process owners is the main factor in organizational value creation and entrepreneurship. If not, the destruction of relationships can bring the organization and the organizational relationships adverse consequences such as the separation and alienation of individual and organizational goals, weakness in extra-organizational relationships, and TM’s weakness. It is also suggested to develop an organized program based on which stress management training for employees, according to different job categories and levels, will be possible by holding special training courses.

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The Degradation of Goals over Time: How Ambiguity and Managerial Cognition Shape Distributions of Project Time and Cost with Evidence from Actual and Simulated Projects David L. McLain and Jinpei Wu

Increasing complexity and rates of change in organizations, their resources, and their environments drive the trend that breaks complex organizational endeavors into more tractable project structures (Ives, 2005; Pich et al., 2002; Williams, 2005). Accompanying this trend, the management of which is a study in decision-making, are advances in project planning, management, and decision-making techniques, including improved planning technology and increased efforts to apply “soft” techniques that draw on knowledge from psychology and behavioral decisionmaking (Andenæs et al., 2021; Pollack, 2007). Unfortunately, the reduction of cost or schedule overruns, an important goal of such advances, has been difficult to achieve (Komal et al., 2020; Standish Group International, 2015). Inadequate planning information and customer changes are just some of the many factors blamed for this overrun persistence (Alexander et al., 2017; Williams, 2005); however, overruns may arise from causes outside those studied in the past (Ika et al., 2020; Williams, 2017). In this chapter, we argue that understanding management-resistant project outcomes is advanced by applying a cognitive, information-framed perspective to project decisions. Previous work has tended to diminish the role of the individual project manager’s decisions, and interactions, in modeling project dynamics and overruns. A cognitive-technical systems perspective is encouraged that suggests overruns are especially likely considering the dynamic interdependence of human decisions and project structure (Ariely, 2000; Daniel & Daniel, 2018; Sicilia et al., 2013). This perspective draws on two broad scholarly domains, those of engineering and psychology, specifically the engineering of complex, dynamic systems and the psychology of decision biases (Eppinger & Browning, 2012; Plous, 1993; Sterman, D. L. McLain (✉) · J. Wu State University of New York at Oswego, Oswego, NY, USA e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Faghih (ed.), Time and Fractals, Contributions to Management Science, https://doi.org/10.1007/978-3-031-38188-1_4

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2000: Tversky & Kahneman, 1974). In the engineering domain, overrun reduction has been sought by identifying structural controls and detailed project models; however, these controls have limited effects, and the detailed models do not fully capture the complexities and dynamics of complex project execution (Love et al., 2016; Williams, 2005). Psychology studies provide insight into human biases that hinder rational project decisions but fall short in explaining the influence of project structure on overruns (Schwenk, 1984). Because managers make decisions that alter project dynamics, combining ideas from both domains may improve our understanding of the distribution of project outcomes. Two research trends encourage and support this cognitive-technical systems perspective. The first trend arises from research into the neural structures and processes that are activated when facing a situation requiring action but perceiving inadequate information to make a confident decision (Andersen & Cui, 2009: Hirsh et al., 2012). The second trend is an increasing interest among management scholars in the impact of information states, specifically risk, uncertainty, and ambiguity, on decision-making, and the relationship between these states of lesser information and the probability of an overrun (Furr & Dyer, 2014; Padalkar & Gopinath, 2016; Schrader et al., 1993; Thiry, 2002). Considered together, these trends illuminate the growing interest in cognition and information as influences on complex systems, including projects (Bjorvatn & Wald, 2018; Eisenhardt & Martin, 2000; Hagen & Park, 2013; Hällgren & Maaninen-Olsson, 2005; Sterman, 2000). The remainder of this chapter proceeds in four steps. First, information states are described. Situational and cognitive factors that induce, amplify, or attenuate reactions to these information states are also discussed. Second, a simulation is used to illustrate how managerial cognition, information states, and their interactions might influence project outcome distributions. Project rework, which is inherently difficult to anticipate but also a common source of uncertainty, is emphasized in the simulation. Third, an argument is made that the interaction between project information states and managerial cognition naturally favors overruns. Fourth and finally, a brief discussion is provided offering suggestions for how an improved understanding of cognition and information can be used to reduce overruns.

1 Information States, Cognitions, and Decisions Classical decision theory is rooted in the assumption that information determines choice (Brim, 1962; Dewey, 1910; Simon, 1960). Decisions are at the center of managing (Simon, 1960); therefore, decisions are at the center of project management. Of the range of information states that describe a project, risk, uncertainty, and ambiguity pose especially difficult challenges to modeling, planning, and decisionmaking (Daft & Lengel, 1986; Ellsberg, 1961; Padalkar & Gopinath, 2016; Pich et al., 2002; Schrader et al., 1993; Thiry, 2002; Weick, 1995). Risk is the probability and magnitude of undesirable project outcomes. It is well defined and commonly incorporated in project models (Eppinger, 2001; Slovic,

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1987). Uncertainty and ambiguity are associated with indistinct, overlapping definitions. Uncertainty, as traditionally defined in the economics literature, is a state of inadequate information where future states of nature are identifiable, but the probabilities of realizing each state are unknown (Raiffa, 1968). Uncertainty is often described as a lack of information and associated with such concepts as knownunknowns or unknown-unknowns (Chua & Sarin, 2002). The latter overlaps with descriptions of ambiguity, which is considered a state of information less well defined than uncertainty because ambiguity also includes a lack of information about the possible future states of nature (Ellsberg, 1961). It is a condition that may be difficult to resolve by gathering more information. In project management, ambiguity has been defined as a condition of indistinguishability that cannot be readily resolved by the acquisition of more information (Thiry, 2002). Also, within project and systems management, ambiguity has been described as the lack of sufficient knowledge of the variables and a model that prescribes actions to achieve predictable outcomes (Pich et al., 2002; Schrader et al., 1993). In common parlance, ambiguity is an inability to define or distinguish understanding of an entity from alternative understandings. This is consistent with a project information state less defined than uncertainty, presenting indefinite comparisons and obscuring possible outcomes. Project ambiguity, more so than risk or uncertainty, is likely to lead to decisions that promote overruns. The explanation for that follows. Unfamiliarity, complexity, incompleteness, and change each contribute to project ambiguity (Blake et al., 1973; Budner, 1962; Gioia & Chittipeddi, 1991; Pich et al., 2002; Yeo, 1995). Each of these factors also increase the difficulty of specifying a clear pathway from decisions to project outcomes (Padalkar & Gopinath, 2016). An important implication is that ambiguity obscures aspects of the project that contribute to overruns. Because ambiguity hinders accurate planning, it is a barrier to project prediction and successful goal accomplishment. Project ambiguity, distinct from risk or uncertainty, thus hinders the achievement of cost, schedule, or performance goals. By obscuring the project’s future, its effects are amplified by cognitive biases and managerial decision behavior. Viewed through the lens of psychology, ambiguity is therefore not only a source of frustration but also an opportunity. When the path from decisions to outcomes is obscured, managers may overlook or dismiss preparations for the potential consequences of ambiguity by offering confident predictions of favorable outcomes as is typical in situations of risk (MacCrimmon & Wehrung, 1988; March & Shapira, 1987). For the purposes of this chapter, we will focus on project ambiguity and define it as an information state of the project such that all possible future states are not identified (unknown-unknowns) nor the probabilities of known states estimated. Interpretations of project states are different but difficult to describe and difficult to compare. The project manager does not have a working project model that leads to predictable and desired project outcomes. The variables that interact in producing project outcomes are incompletely known, as are the relationships among project variables. The project manager may not be able to distinguish between alternative conceptualizations of project elements or identify clear preferences among alternative actions. The structure and operation of many projects present the manager with

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information that makes it difficult to distinguish among alternatives, and this may be amplified or attenuated by unclear goals and preferences among project decisionmakers (Daft & Lengel, 1986). The values and distributions of the probabilities of future project states may be poorly characterized or unknown. Project characteristics may be incorrectly or inadequately understood, making project planning poorly predictive. Under these circumstances, seeking additional information alone often fails to improve plans in a reasonable amount of time. It is unknown whether additional information will resolve the ambiguity because it is difficult to identify where and what kinds of information to seek (Daft & Lengel, 1986; Schrader et al., 1993).

1.1

Evidence Linking Information States to Overruns in a Cognitive-Technical System

An overrun is defined as a positive discrepancy between planned-for resource needs and a project’s actual resource consumption. Precise estimates are necessary to achieve precise goals, making ambiguity, in combination with forces that tend to increase project resource consumption and the tendency of most natural systems to exhibit right-skewed behavior (Smart, 2011), a predictor of overruns. If there is a lack of awareness of possible outcomes, or of the mechanisms leading from the project’s current state to desired outcomes, overruns are more likely (Pich et al., 2002). Among project outcomes, a diagnostic marker of ambiguity-cognition dynamics is found in the outcome distribution. This marker is specifically associated with the study of dynamic system complexity which, along with nonlinearity, is both a source of ambiguity and characteristic of most projects (Sterman, 2000). The distribution marker is the heavy or “fat” tail that commonly appears in depictions of duration or cost outcomes (Lloyd, 2000). This common characteristic of distributions is noteworthy because it is not only used as an indicator of complex system behavior but also provides empirical evidence of a high probability of project overruns (research regarding entrepreneurial projects reviewed in Crawford et al. (2015) and Smart (2011)). Lloyd (2000) identified the nearly widespread occurrence of the fat-tailed outcome distribution in a highly diverse array of projects, including a doctoral studies program with its schedule organized by semesters within a surrounding university structure (Fig. 1a) and a major urban transportation project organized within a new organization (Fig. 1d). Both projects shared not only a fat-tailed time distribution but also duration and cost goals and interrelated component tasks (Mantel et al., 2001; Meredith & Mantel Jr, 2011). In Lloyd’s observation, the particular fat-tailed distribution is a natural outcome of project systems and will even appear when the project is subdivided into time-based segments. Here, I add that this distribution is

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inherent in any system that is managed by a human decision-maker and is subject to finite resources like budget or available time. System interactions force a project away from the planned schedule during execution. This is why many managers of complex projects negotiate a shared understanding among project participants rather than aggressively applying controls, thus allowing project completion to drift beyond the planned schedule (Weick,

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1995). The duration of projects is pushed into the tail of the distribution, which is then blunted by resource limits. Neither risk or uncertainty has the same propensity as ambiguity to produce this type of outcome distribution (Pich et al., 2002). In instances of risk or uncertainty, stochastic rules and management techniques produce more normal distributions of outcomes. However, under conditions of ambiguity, outcomes can greatly exceed these forces and more strongly drive outcomes toward overruns. Figures 1a–d provide graphic evidence of the schedule and cost behaviors of several diverse, real projects. Distinct in Fig. 1a–c are the probability densities in the right tail. This is the distribution shape typical for many projects and is characteristic of complex system behaviors (Carlson & Doyle, 1999; Limpert & Stahel, 1998). Figure 1a shows the durations of students’ doctoral studies in mechanical engineering at a private university in the northeastern United States. The planned time for each project (program of study) is 4 years, but the actual duration distribution is right-skewed. Such programs are tightly structured into semesters with discrete completion points at semester ends. In contrast, the dissertation research portion of the program harbors ambiguity regarding unpredicted additional data collection, unexpected problems, iterative development, or other sources of delay. Schools have decades of experience constructing and supervising such programs, and the necessary courses are well structured and have predictable durations. Regardless, a student’s program often experiences overrun. Figure 1b illustrates the durations of 174 US Air Force projects (Drezner et al., 1993). These military projects are large, complex, long-duration endeavors that routinely experience overruns. Figure 1c shows cost overrun data for the same projects. Two plots appear in Fig. 1c. One plot represents cost growth over the period from the setting of the initial budget to completion of project phase 1 (encompassing planning and design activities). The second plot describes cost growth over the period from the end of phase one to the end of phase two (encompassing development). Despite knowledge gained during the planning and design phase, emergent events and other ambiguities led to final costs that exceeded the initial cost estimates. The distribution pattern for duration overruns is similar to that for cost. Figure 1d focuses on a single large project, the Big Dig transportation infrastructure project in Boston, Massachusetts. Figure 1d depicts the growth in cost estimates that occurred over the two decades of project execution. One observation made from this data is that planning, even in well-structured projects, frequently fails to eliminate overruns. In Fig. 1d, the growth in cost is increasingly positive, indicating that costs did not merely increase but increased at an increasing rate over the duration of this closely watched, large project, despite the managers gaining experience as the project progressed.

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2 How Overruns Emerge from the Interaction Between Project Structure and Managerial Cognition Further understanding of how ambiguity makes it difficult to avoid overruns can be gained by examining three forces in project management and how each interacts to foster ambiguity: the project manager-decision maker, the project itself, and forces external to the project. External forces include the customer, subcontractors, regulators, and the organization in which the project is embedded. Outcome behavior, including overruns, is a dynamic product of these forces whose interests and interactions may be obscured and ambiguous (Lyneis & Ford, 2007). In general, ambiguity obscures the motives and biases of project managers and other actors, increasing the likelihood of overruns.

2.1

Cognition: The Project Manager-Decision-Maker

Hirsh et al. (2012) combined information theory and knowledge of neural information processing to develop a model of reaction to incomplete information. Using the term uncertainty for what this chapter defines as ambiguity, their model is particularly insightful for relating ambiguity to project management because it provides a description of how available information is interpreted and whether that interpretation can support action. Hirsch et al.’s model explains why project information is ambiguous and what must happen for the project manager to make decisions. In the model, ambiguity is associated with entropy, which the person is anxious to reduce so that some alternative actions stand out from others. Entropy is a state in which the information available in the situation is insufficient to distinguish one model of the situation as a better model and predictor of outcomes than alternative models. The project manager makes the decisions that coordinate personnel and resources to move the project toward its goals. Any limitations or biases of the manager regarding decision-making can draw decision-making away from a rational problem-solving process, which then affects project outcomes. These limitations and biases include the many cognitive and psychological characteristics that are ubiquitous among decision-makers and which systematically bias decisions, which in turn influence overruns (Plous, 1993). Of particular interest among the many characteristics of a decision-maker are limitations on the ability to process information, risk distortion and optimism, and escalation of commitment. Processing Limitations Limitations on time and the ability to process information result in suboptimal decision outcomes (Simon, 1955). To accommodate these limitations, project managers use heuristic devices that focus attention on a few pieces of available information and tend to support pre-existing desires (Plous, 1993; Reyna & Brainerd, 1995). Therefore, their resulting decisions only partially incorporate new information and use it to support what is already known. This allows

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ambiguity to persist and fails to remedy the march of the project toward an overrun. When managers engage in this type of thinking, they tend to underemphasize complexity and interactions among project elements, including factors that can overwhelm predictive models and underemphasize rework impact. The result is that overrun potential is underestimated (Flyvbjerg et al., 2002; Flyvbjerg & Budzier, 2011; Lyneis & Ford, 2007; Sterman, 1992). Risk Distortion Although project managers are generally risk-averse (Swalm, 1966), they are also subject to several cognitive biases that tend to underestimate risk. Decision-makers typically think in terms of magnitude rather than probability (Shapira, 1995), which diminishes the importance of probabilities and can cause underestimations of the likelihood of highly probable events (Kahneman & Tversky, 1979). Rework is one such event that promotes overruns. The tendency to think in terms of normally distributed outcomes also underestimates the prevalence of overruns because normally distributed, bell-curve models underrepresent the probability of outcomes in the region where overruns lie (Lloyd, 2000; McLain, 2009). This is not only an assumption among most managers; it is also an assumption underlying most project models (Eppinger, 2001). Another managerial characteristic is pervasive overconfidence in estimating his or her abilities to reduce risks and eliminate unknowns (Grimaldi et al., 2015; Kahneman & Tversky, 1982). This bias is reflective of the general tendency to believe that personal action will reduce the probability of negative outcomes. This results in a reduced emphasis on planning for negative events. The desire to promote a positive image of one’s own managerial abilities and to justify one’s own decisions and commitment of effort also encourages the discounting of risk. This cognitive bias weakens the management of ambiguity because of the high correlation between perceived risk and ambiguity (McLain, 2009). Project participants often rely on social information to understand aspects of a project that are associated with inadequate information (Salancik & Pfeffer, 1978). The result is a tendency to underestimate project unknowns and the potential for overruns similar to how social information influences risk-taking, as reported in a large number of studies of social influence on risk in decision-making (Isenberg, 1986). The project environment is a social context characterized by information exchange and networks of influence and communication. The social interactions among project participants thereby increase the amount of ambiguity a project manager finds acceptable and reduce the amount of effort devoted to countering ambiguity, increasing the potential for overruns. Escalation of commitment. The escalation phenomenon is well studied and refers to the tendency to continue pouring money into a failed decision due to regret over wasting already expended resources, that is, sunk costs (Staw, 1981). Escalation of commitment is particularly threatening to project goal accomplishment and has been linked to large project overruns (Ross & Staw, 1986). The unwillingness to forget the past and to devote effort to recovering unsatisfactory expenditures leads not only to increased cost but also to an increase in project duration. In general, a manager’s cognitions increase pressure to continue a project beyond planned schedule time. Escalation of commitment stems from causes at both the individual and

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organizational levels (Sleesman, 2019). A principal cause at the individual level is self-justification, whereas at the organizational level, the principal driver is institutional inertia (Staw, 1997). Escalation resists new information and promotes ambiguity about actual cost or schedule goals—planned goals are exceeded and replaced with psychological momentum.

2.2

Characteristics of the Project Technical System

Several project characteristics create ambiguity including complexity in the form of interdependencies among project activities, resources, actors, structures (Lyneis & Ford, 2007), rework, and project dynamics. Additional ambiguity can be traced to duration—the length of time over which a project evolves. Complexity and Interdependencies The complexity of interdependencies can overwhelm planning models. Therefore, the models do not explain all paths or outcomes, and this is especially likely when planning for rework. Unfamiliar and complex projects normally require some rework due to, for example, mistakes or customer change requests. It is hard to plan for rework because change requests are unknown at the planning stage and planning for mistakes requires the expectation of failure, in conflict with optimistic management. Therefore, schedules can be seriously affected by the delays these changes and rework introduce into project execution (Eppinger & Browning, 2012). The biased exchange of information can further amplify this ambiguity. Rework Rework is an intermediate force between plan ambiguity and project goals. Studies identify rework as especially influential on project outcomes (Love et al., 2009; Mahamid & Dmaidi, 2019; Pich et al., 2002). The strength and number of interdependencies among tasks moderate and amplify this influence. Furthermore, in complex projects, there is a dense web of interdependencies, and the revision of project goals is common and even expected, especially for unfamiliar projects. However, such events are difficult to plan for simply because it is unknown what particular events will occur and what changes will be required by those events. Although it can be anticipated by adding fixed percentages of extra “reserve” resources during planning, the amount of rework is routinely underestimated when planning a project. This is due to the idea that rework is a failure to properly plan or manage the project, encouraging excessive managerial optimism and underestimation of the likelihood of rework but also flowing from the complexity of task interdependencies. Rarely rework will restart a project from scratch; therefore, the rework must be integrated into a partially completed project and, because of the escalation of commitment, more of the projects is usually retained than is scrapped and restarted. This increases the difficulty of integrating rework into the project. Therefore, despite considerable efforts in planning and increasingly sophisticated methods of managing projects, this type of ambiguity sets up overruns (McLain, 2009).

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An illustration of how one source of ambiguity, rework regardless of source, affects the distribution, and therefore the predictability of project schedules was modeled in a simulation, the results of which appear in Fig. 2. This rework is mitigated by a learning effect, which in the short term slows the project while the project system acclimates to the new way of doing things but in the long term saves time due to method’s improvement. No argument is needed to convince managers that rework increases overrun potential, but this simulation data illustrates how the effect appears in a probability density distribution. In the simulation, delay was calculated as the simple difference between the duration of the two-task execution model and an identical planning model without the simplified rework and learning effects. Many combinations of parameter values are possible; the values used here are just one set of plausible values (see Appendix for details). Project dynamics. Dynamics include those events and changes that happen during project evolution. A common event on many projects is the customer change request. Change requests are exogenous events frequently cited as a leading cause of project delay (e.g., Assaf and Al-Hejji (2006)). Change requests can require rework of a few or many completed tasks. The lack of information during planning about the extent and likelihood of future change requests introduces uncertainty. They also require contract revisions to properly formalize the changes and may require alteration of manuals and training. Although it is possible to shorten project duration, such as when features are dropped or a design is simplified, many change requests have the opposite effect, delaying project completion.

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Project structures are complex dynamic systems that are difficult to model and predict, producing high probabilities of extreme outcomes (Gregory & Piccinini, 2013; Perrow, 1984; Sterman, 1992). The perspective of complex dynamic systems was developed to predict outcome states in systems that have complex and evolving interdependencies among system elements. By applying that perspective, we can model the nonlinear and complex interrelationships among project activities and participants and help reduce ambiguity about project outcomes. However, there is a limit to the predictive ability of complex dynamic systems models. Such models do not identify unpredictable events, and the range of possible outcome can be so large that it is little help in managing the project. In addition, the dynamic interactions between elements of complex projects can lead to “chaotic” behavior and future states difficult to manage through planning (Auyang, 1999). Time is at the heart of project dynamics and is the multiplier associated with most threats to project success. Project duration negatively affects and therefore diminishes the ability to plan a project and positively affects the probability of overruns. Mere duration can increase ambiguity because the longer it takes to complete a project, the more likely that unexpected events can occur that further delay the project or absorb resources. This effect is exacerbated by managerial cognition, because project managers are typically less concerned about the potential for negative outcomes the further those outcomes are into the future.

2.3

Parent Organizations, Customers, and Subcontractors

It can help to describe relationships between ambiguity and overruns by drawing insights from prominent perspectives on organizational structure, specifically the contingency, sensemaking, and agency perspectives. The contingency perspective on structuring the parent organization and managing projects dominates the training of project managers and upper-level management (Donaldson, 2001; Scott, 2002). This perspective leads managers to adopt models of projects that emphasize structure, control, and detailed plans and maps and to quantify the potential for undesired events in terms that limit and linearize their descriptions. The contingency perspective, although it is the standard for organizing and managing project organizations, does not directly accommodate ambiguity and ignores it in planning. Models emphasize what is known and understood. The consequence is insufficient and incomplete controls and plans for what may be consequential, nonlinear project behavior. Because of the popularity of the contingency perspective, ambiguity is particularly difficult to manage and especially likely to contribute to overruns. From the sensemaking perspective, ambiguity triggers the enactment of situational information and the challenging of pre-existing project plans (Weick et al., 2005). The sensemaking perspective promotes organizational learning and resolves ambiguity by encouraging a shared understanding among project participants which then serves as a framework for action. The sensemaking process requires time to

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iteratively test ideas and develop new understandings. This may induce project delays. Despite this, if learning occurs, improvements in the project’s operation may be achieved and overall project efficiency may be increased. The contingency approach can be less adaptable when faced with emergent events that were obscured by ambiguity during project planning. Despite the delays it can cause, the sensemaking approach places a greater emphasis on project dynamics and increases effort devoted to learning, which is a more effective approach to managing emergent events than making frequent exceptions while sticking to a predetermined project plan. Another source of ambiguity is misalignment between the goals of the organization and those of the project manager. This misalignment can diminish the accomplishment of project goals from the perspective of the organization. A useful lens through which alignment between the organization’s and the manager’s goals can be better understood is found in agency theory, which focuses on the use of a formal set of structures to coordinate manager behavior and project goals so that performance uncertainty is reduced (Eisenhardt, 1989). Evidence from studies guided by agency theory shows that the goals of managers and organizations are not perfectly aligned when it comes to investing in a failing project (Garland, 1990). When additional resources are applied to a project that is troubled, these additional resources ultimately increase overrun potential, to the detriment of the organization. In addition, the project manager, being closer to the project, has greater knowledge of the project than is possessed by higher management of the organization overseeing a portfolio of projects (Harrison & Harrell, 1993). The individual project manager, directly responsible and closest to the project, has knowledge including an understanding of which problems are easy or difficult to solve. These managers often prefer to apply resources to problems that can be easily and quickly solved, leading to an accumulation of the more ambiguous and difficult-to-solve problems near the end of the project schedule and an increase in the probability of overrun. According to agency theory, uncertainty, which diminishes over time as additional information arrives, can also be reduced by aligned incentives, but ambiguity, which does not necessarily diminish, makes that alignment difficult. The resulting misalignment contributes to overruns. Relationships with subcontractors also introduce ambiguity into the project. Subcontractors are not within the direct control of the parent organization, except by formal contract. The subcontractor’s protection of knowledge about methods, capabilities, technologies, and its own resource stability may serve as a competitive advantage for the subcontractor; but the limits of control and lack of knowledge of internal characteristics of a subcontractor present ambiguity to the project’s parent organization and can lead to overruns.

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3 Improving the Management of a System of Ambiguity and Cognition Six areas of action will be discussed: (1) improved modeling, (2) creating a learning organization, (3) communicating and building shared understanding among project decision-makers, (4) simplifying, (5) studying other projects, and (6) choosing strategic delays in resource commitments. Many of these approaches diverge from increased formal structuration, or reducing problems to isolated solutions, and introduce increased flexibility into project management as guided by systems thinking (Kapsali, 2011).

3.1

Improved Modeling

Before applying techniques to reduce ambiguity, managers might first establish effective plans for those elements that are not ambiguous and rigorously avoid errors in planning. There is a surfeit of advice to support this recommendation. Project ambiguity must be distinguished from those elements of the project that are uncertain and which can be reduced by gathering additional information. In practice, this occurs when different interpretations are expressed by project participants. For those aspects of the project which are ambiguous, there are ways to improve upon the recommendations derived from traditional project models. Unanticipated, emergent events that lead to rework may be impossible to eliminate, but using advanced modeling techniques, the impact of emergent events can be mapped onto tasks to estimate the extent that specific types of rework can affect project success and overruns. Among models that can help is the design structure matrix (DSM), which provides a graphic and analyzable way to depict complexity and interdependencies in systems, including both feedback and feed-forward interdependencies (described in detail in Eppinger and Browning (2012)). Another tool for modeling the nonlinear and counterintuitive behavior of a project is the dynamic systems model, which provides a way to describe complex relationships between multiple states in complex, dynamic systems (Lyneis & Ford, 2007; Sterman, 2000). Dynamic systems models expose the effects of ambiguity associated with the inherent delays in information exchange among interconnected project tasks.

3.2

Create a Learning Organization

Dynamic management techniques that respond quickly to emergent events can be helpful. One of the most effective dynamic management techniques is to foster a learning organization (Senge & Suzuki, 1994). Simple cause-effect and self-focused mental models, unlike models that match the complexity of project situations and are

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team-based, are ill-suited to solving the problems that arise from the ambiguity of a contemporary project. The creation of a learning organization is just such a management approach. It is designed for the complexities of modern organizations and uses team thinking to solve ambiguous problems. This integrated approach improves problem-solving and the operation of a complex system. There are several core principles relevant to the learning approach. Project members must seek mastery in discerning the contrast between current reality and their visions for what they believe can be achieved. Personnel must recognize their own mental models and challenge those models in an ongoing process of enactment and sensemaking (Weick, 1995; Weick et al., 2005). They must also seek a shared vision of the project with other project personnel and adopt a team approach to learning that operates through collaborative managing and problem-solving. Project members must also apply systems thinking to better perceive the dynamics of feedback, information delay, and interconnectedness among project elements as they produce project outcomes. By distributing knowledge among all project participants, and solving problems with an enhanced understanding of the unique and complex characteristics of the project, the learning organization approach better responds to the emergent and complex challenges that arise out of project ambiguity.

3.3

Improve Communication and Negotiation Among Project Decision Makers

Another approach to reducing the negative effects of ambiguity, and project delays in particular, is to improve communication across the project (Lloyd, 2000). Improved communication should include ongoing negotiation among decisionmakers to redefine the project model, which, once redefined, reduces ambiguity about action (Daft & Lengel, 1986; Weick, 1995). Reshaping communication to emphasize distinctions among alternative views of a problem reduces equivocality in choosing among alternative actions. Shifting communication toward the identification of distinctive project characteristics and placing less emphasis on more, often uninformative, data can help manage project ambiguity. A critical communication channel for reducing overruns is between project managers and customers. Frequent communication with the customer speeds awareness of potential change requests and can avoid some changes by informing the customer of the implications of those changes for project goals. Frequent communication also provides opportunities for negotiating a shared understanding with the customer. Another critical channel is between project management and the direct personnel performing project work. Direct personnel are the first to identify technical problems and to identify method’s improvements. While this is a core component of many quality management programs, less often recommended is the need to open information pathways between the customer and direct personnel. By increasing the information available in this channel, direct personnel can better meet the goals of

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the customer, and not just those of project management, thereby removing a layer of ambiguity regarding project personnel’s understanding of customer’s goals. Figure 3 provides some indirect evidence in support of the effect of improved communication on project cost. The project manager for a large urban hospital in the western United States introduced a weekly meeting where current problems were discussed among all hospital and contractor project managers. The meetings attacked several types of ambiguity. Emergent events were examined from a shared perspective and tackled quickly. No longer could problems remain relatively unknown to those project members best able to solve them. Problems were discussed in the meeting, and everyone in a managerial position, including contractors and the hospital’s upper management, was made aware within the week. Individuals were assigned responsibility for solving specific problems. Complex interrelationships were coordinated among managers at the meeting. Needed changes were discussed. The incorporation of weekly meetings into project management reversed the hospital’s prior practice of discouraging meetings, which reduced problem-focused communication. The hospital’s project coordinator credits the low incidence of cost overruns to this improved system of communication.

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Simplify: Reduce Interdependencies and Complexity

Complexity and interdependencies are important, related sources of ambiguity because delays arising from interactions and the overwhelming number and variation of possible events produced cannot be fully grasped during planning. Therefore, we can reduce ambiguity by reducing complexity and interdependencies. For example, research by Eppinger and Browning (2012) found that reducing the number and temporal separation of interdependencies reduces the risk of severe delays.

3.5

Study Other Projects

Using data gathered from other similar projects can help to estimate the potential for unplanned outcomes including overruns. Benchmarking against these projects can identify where and when problems might occur and how to or how not to respond. For example, identify project organizations that manage change requests well and examine the policies they apply to deal with those requests. When those requests can be limited by policies or other organizational structures, they can be reduced as threats to project budgets. Note that techniques for handling large amounts of ambiguous data are rapidly proliferating and improving, providing new avenues for reducing ambiguity (George et al., 2014; for a review see Lavalle et al. (2013)).

3.6

Delay Some Decisions

One approach that introduces flexibility is to delay important decisions. The delay of decisions regarding project goals can reduce wasted effort and rework (Brennan & Trigeorgis, 2000). This approach to decision-making takes several forms, including real options analysis, incremental trial-and-error decision-making, and other pathdependent management processes (Adner & Levinthal, 2004). Of course, the effect that delay has on overrun potential can be positive or negative depending on other factors. On the one hand, delaying difficult decisions while solving simpler problems increases the difficulty of problem-solving near the end of the project, which induces overruns. On the other hand, delaying certain decisions can wisely avoid the need for rework later in a project, when rework can seriously threaten on-time project completion (de Neufville, 2008; Woodward et al., 2011). This is a tenet of dynamic strategic planning that has sometimes been called the postponement strategy. This approach encourages the resolution of ambiguity inherent in early project decisions prior to making those decisions. A postponement strategy requires a conscious and intelligent application of postponement; but deployed in collaboration with those affected by the decisions, it can lead to fewer problems and faster development times (Yang et al., 2004).

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4 Conclusion At first blush, seeking to understand and manage project overruns by focusing on the character of project information may not seem the most direct path to reducing those overruns. What we have tried to do in this chapter is to argue, using definition and illustration, how project information quality, and ambiguity in particular, provide a useful way to view overruns and project management more generally, from the cognitive-technical systems theoretical framework, and how this view can lead to reductions in overruns.

Appendix The simulation model employed to illustrate the effect of rework on project duration was run using Analytica modeling software. Delay was calculated as the difference between planned and actual times for each simulation of the project. The project simulation was repeated 1000 times. The composition and number of tasks in the planning model are matched in the “actual” model except for the addition of the possibility of rework and a modification for learning. Nominally, each task takes 1 day to complete. Actual duration for any single task differs from the nominal time by sampling from a uniform distribution in a range of 95–105% percent of planned duration. Time was also incorporated for inter-task coordination and sampled from a uniform distribution with a range from about 0.14–0.16 days. The probability of a first rework event is 10%. There is a diminishing probability for each subsequent rework event, 6, 4, 2, 1, and 0.5%, respectively, leveling off at the minimum value of .01% and remaining at that value until reaching the limit of ten reworks. The amount of each task that is reworked is sampled from a normal distribution with a mean of 0.5 and standard deviation of 0.25. It is possible for rework to reduce the project’s overall duration, but that possibility is small. Sterman (2000) refers to a study in which 66% of tasks in a project were reworked. Because Sterman’s research describes projects with a greater number of tasks than the simulation and because the simulation makes multiple reworks possible, the mean value of rework in the simulation was more conservative at 0.5. Repeats of tasks due to rework do not take as long as initial task completion in recognition of learning effects. A single rework takes 92% of initial time and a lower limit of 79% of initial time is reached at the fifth rework. Learning is initially rapid and then levels off for greater amounts of rework. The values are 92, 86, 82, 80, and 79%, respectively. These figures follow from research that suggests that learning results in repeated work taking about 70% of the time it took during initial completion (Mantel et al., 2001).

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The right skew introduced by rework is apparent from a visual examination of the simulation data. A statistical examination suggests the data significantly deviates from a bell-curve normal distribution. Kolmogorov-Smirnov (KS = .101, p = .013) and Shapiro-Wilk tests (W = .916, p < .001) reject normality.

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Time to Respond: Identification, Proximity, and Safety at Work David L. McLain

1 Introduction Safety has broad relevance to both practitioners and researchers whether in the airplane cockpit, on the battlefield, in the factory, on the road, on the Internet, in a healthcare facility, or in a pandemic that has emphasized the importance of individual choice in achieving collective and individual safety (Shoss, 2021). A critical link in the chain from threat awareness to action is safety engagement, that is, the individual’s prioritization of attention and effort to maintain or achieve safe outcomes in an environment of other work tasks. Although several safety models emphasize cognition, the goal of this chapter is a cognitive safety model that not only recognizes safety understanding, which is common to many models, but also emphasizes threat presence, improving the relationship between safety information and its cognitive processing (Johnson, 2003; Rabia et al., 2006; Rogers, 1975; Shoss, 2021). This presence, underrepresented in other models, increases attention to the temporal and physical closeness of danger. The proposed cognitive, information-based model of safety engagement arises from studies and literature in safety and the neurosciences that describe how threat information is established and processed. Two categorical, information processing influences on an individual’s cognitive momentum are central to the model: identification and proximity. Identification encompasses the awareness and understanding of a threat and the corresponding safe responses developed through experience and learning. Proximity is the presence, intensity, closeness, and immediacy of the threat that arises from information in the immediate situation. The confluence of these two influences, shaped by control over the threat and response options, is safety engagement. D. L. McLain (✉) State University of New York at Oswego, Oswego, NY, USA e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Faghih (ed.), Time and Fractals, Contributions to Management Science, https://doi.org/10.1007/978-3-031-38188-1_5

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Fig. 1 Identification and proximity compete with cognitive momentum to influence safety engagement

The chapter proceeds as follows. First, a model of safety engagement is presented followed by a discussion of some underlying assumptions. Second, the elements of the model are described with emphasis on the identification and proximity subsystems of information and information processing. Third, examples are provided that explain how identification and proximity might be applied in practice (Fig. 1).

2 Safety Models Extensive reviews of safety models appear elsewhere and those reviews will not be discussed in detail; however, some common, relevant issues are noted (Burke et al., 2011; DeJoy, 2005; Goncalves Filho & Waterson, 2018; Hughes et al., 2015; Khan et al., 2015; Marais et al., 2006; Swuste et al., 2014). The discussion here will cover supporting studies that describe cognitive and individual representations of safety and threat information, neuroscientific distinctions in information processing, and the translation of information into attention and effort prioritization. I will cite some studies supporting the content and structure of the model but note there are many relevant studies and not all can be cited in one chapter. Most existing safety models emphasize knowledge and underrepresent the effects of presence and urgency, assuming individuals process all safety information rationally and systematically subject only to the cognitive limits of information processing capacity (March & Simon, 2005). These models are therefore “cold cognitive,” emphasizing knowledge about safety but underrepresenting the intensity and emotional power of being in a hazardous situation, close to threat (Janis & Mann, 1977; Rabia et al., 2006). Model assumptions. Like all models and theories, this model rests on some assumptions. The model is information-driven and describes cognition at the level of the individual. Of specific interest are individuals in occupational contexts where safety may compete for priority with work tasks. The central influence is information. Pieces of information, perceived, framed, and interpreted, arising from both the

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situation and accrued knowledge, either sustain work priorities or induce a realignment of priorities relative to safety. Not only information revealing a threat but information about situation dynamics, such as a deterioration in safeguards or a change in a threat or the rate of a threat’s development, are model influences. Learning about safety is an influence; however, the model emphasizes the current situation. The model does not assume the individual feels he or she has complete control over the situation. Group safety actions are outside the domain of this model.

3 Foundations The proposed model recognizes dual process views (e.g., dual process theory, Groves & Thompson, 1970; Kahneman, 2011)) and recent neurocognitive studies of information processing in response to threat (LeDoux, 1998; Mobbs et al., 2010; Pichon et al., 2012; Sun et al., 2020) to explain changes in cognitive momentum with respect to prioritizing safety (e.g., Ajzen (1991), Janis and Mann (1977), Zipf (1949)). Momentum The model begins with cognition prioritizing task activities not dominated by safety concerns. Behavioral or psychological momentum means the drive to continue the current task or way of thinking, in the absence of sufficient motivation or threat that shifts that drive to a different task or way of thinking (Markman & Guenther, 2007; Nevin et al., 1983). We tend to continue what we are doing if there are no signals requiring change and we are designed to expend minimum effort to accomplish any task (Zipf, 1949). Proximity and identification must, together, supplant task momentum with safety engagement. They must jointly exceed the threshold necessary to redirect momentum toward safety and exceed the inertia of continuing a task that the individual has minimized effort to perform. The more this task momentum is strong or resistant, the more difficult it is to redirect and the more intense is the information needed to achieve redirection. Information and Safety Engagement We can only act based on information, regardless of the accuracy or completeness of that information. Information is therefore the primary, if assumed, input to all cognitive theories of individual behavior and socio-technical system dynamics. Information itself has several facets including source, content, quality or clarity, and timing, which not only describe a threat but also suggest responses and the degree of personal responsibility for action. In the proposed model, information cues initiate cognitive processes which determine whether and how much task momentum shifts toward safety. Speaking broadly, some safety information is accumulated in Kahneman’s (2011) “type 2” fashion which consists of conscious, unstressed, deliberate, and analytical thinking. This supports learning and maps information onto the individual’s repository of established safety information and is processed by the brain’s executive function in a systematic manner. This type of information processing occurs before experiencing a specific hazardous situation in which the information is applied.

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In contrast, some information cues, experienced in the specific hazardous situation, induce the amygdala to a heightened emotional state and take precedence over calm analysis, inducing increased intensity and a sense of urgency (LaBar et al., 1998; LeDoux, 1998, 2003; Sun et al., 2020). These two information processing systems are not entirely separate as influences on safety engagement, however, because the intensity of engagement in the situation is determined by a combination of the understanding that is built over time and the threat intensity that is triggered by the demands of the situation. Understanding helps determine the intensity of response, and the urgency of the threat helps determine what aspects of understanding come into play as well as what form of engagement, such as direct action or escape, is motivated. Both systems rely on some established and stored memory regarding threats and safe responses, while also inducing a sense of the urgency of the threat. Identification In the model in Fig. 1, these two ways or systems of experiencing and responding to threats are mirrored in two components: identification and proximity. Identification manages the knowledge or information built from training, study, and experience regarding safety threats, vulnerability to threats, and behavioral responses (Griffin & Neal, 2000; Guo et al., 2016; Mohammadfam et al., 2017). Many safety principles and much information about threats can be learned long before exposure to a threat, and these accumulate as safety knowledge. It includes the accumulated interpretation of information gained from interaction with hazards and from the vicarious observation of the safety experiences of relevant others. Norms, or social expectations, also include safety information and arise from the observation of coworkers and from beliefs regarding what others would do in this situation. This cultural and climate information distinguishes a cavalier from a safety-conscious work environment. This information resides in long-term memory, and a retrieval process applies this information to the current threat. It is essential to identify the kind and seriousness of a threat and appropriate responses. Shaped partly by individual differences, the extent of this is well established in long-term memory and aids effective threat responses (Cunningham et al., 2005). Proximity Proximity is more specific to the current situation and describes a threat’s unique intensity; situation-specific dynamics; physical, temporal, and social closeness; and imminence of harm. This second system determines what aspects of the first system are relevant in determining the closeness of the threat and the need for attention, effort, and quick response. The combination of these two information systems is a major determinant of situational safety engagement. Neurocognitive research reinforces this organization into two information systems. One system is associated with identifying information and thoughtful cognitive processing that relies on learning and establishing a knowledge base in memory. The second system is more immediate, is associated with situational and threatspecific cues, and follows the processing path associated with stress and fear—it is the path of emotion (LeDoux, 1998; Sun et al., 2020). Increasing intensity of activity in this second system can increase errors in performing tasks but is also able to motivate greater safety engagement (Mobbs et al., 2010; Pichon et al., 2012).

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Exposure to danger induces fear and, like other emotions, increases activity in the amygdala, among other structures (LeDoux, 1998; Mobbs et al., 2010; Sun et al., 2020). If the threat is less proximal, the orbitofrontal cortex will exhibit activity that suggests a less dangerous situation, and general cortical attention can be devoted to other tasks (Mobbs et al., 2010). Although heightened fear increases threat priorityit also lowers the priority of other tasks (Pichon et al., 2012). The Outcome: Safety Engagement The outcome of interest in this model is safety engagement—the prioritization of safety in a hazardous situation, specifically commanding attention and effort so that safety takes center stage among all other cognitive demands. This prioritization requires overcoming the threshold for redirecting effort, that is, overcoming the momentum concentrated on other tasks. The model follows information through a cognitive process through two systems corresponding to understanding and closeness. The two core information processing systems in the model arise from the two categories of information and the neurocognitive systems that process the information. Specific kinds of safety information tend to induce activity more in one than the other system. Therefore, each influence acts on each system somewhere along a continuum from weak to strong. Next, I define both systems and describe the relative impact of various safety influences on each.

4 The Model Elements in More Detail Identification Identification is defined here as information and its processing, developed through experience and learning, that establishes the individual’s understanding of threats and responses. It is more than just recognizing a threat. Identification also includes understanding threat variations, dynamics, risks to others, short and long-term impacts, and effective as well as ineffective responses. It includes the individual’s established attitude toward safety in general and toward safety around specific threats. Identification is the degree the specific hazard is understood. Understanding encompasses the hazard’s characteristics, consequences, effective responses, and contextual interactions (Guo et al., 2016; Vinodkumar & Bhasi, 2010). In addition to experience and deliberate study, organizational, professional, and social expectations also shape identification, making the identification system rest on information gathered, interpreted, and established before experiencing a specific hazardous situation (reviews: Burke et al. (2011), Guldenmund (2000), Robson et al. (2012)). In the absence of threat urgency, identification is based on cold cognitive information processing primarily in the prefrontal cortex. Identification encapsulates familiarity and complexity (Intini et al., 2019; Song & Schwarz, 2009). The limits of knowledge and experience define the boundaries of familiarity and, therefore, determine the limits of threat recognition. The degree of recognition affects not only quick action but also the level of anxiety due to fear of imminent or serious harm. Similarly, identification limits the threat complexity that

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can be quickly grasped. Exceeding these limits makes a threat uncertain or ambiguous, increasing the cognitive demand and stress of response. Individual differences other than personal knowledge and experience also affect identification and response. The many differences are too numerous to fully discuss in one chapter but include competitiveness; sensitivity to public image; risk sensitivity, also known as risk-taking propensity; impulsivity; and intelligence which is a factor in managing the complexity of some threats and acquiring knowledge about how to effectively take safe actions. Identification, jointly with proximity, tests the threshold at which engagement shifts from other tasks to safety. This threshold may be low with the individual responding quickly after threat awareness, or it may be high such as when the individual works around a slowly worsening threat or a threat that is considered tolerable and stable. Incoming threat information is interpreted with respect to that threshold. Engagement tends to be a sudden shift from other tasks to safety. The outcome is not a smooth, graduated response even though identification, or the associated proximity of threat, changes in a smooth, gradated manner. Stated another way, the information processed leads either to continuance along one’s current path or redirection of priority and cognitive momentum toward safety. Identification includes a determination that safety is controllable and can be affected by personal action (Schieman & Plickert, 2008). Perceived threat control is determined partly by established information and partly by situational information, which relates control to both identification and proximity. The degree of control over the danger is an important influence on both proximity and the form that safety engagement will take. More about this is presented in the next section. Barriers to identification are inversely related to knowledge and understanding. That is, identification is weak when we lack sufficient knowledge or information to know what the threat is and what actions lead to safety (Vinodkumar & Bhasi, 2010). Unreliable, incomplete, or obscured information also weakens or slows identification. Distractions and misinformation, such as camouflage or threat mimics, also work against identification. These factors can make safety engagement more effortful, stressful, difficult, or delayed. Proximity Proximity, the second system, describes information and processing about the presence, closeness, immediacy, and intensity of the threat, both physical and temporal. This system is situation-specific and induces what Janis and Mann (1977) referred to as hot cognitive information processing. Proximity is associated with anxiety, fear, and urgency and is predominantly associated with emotion-laden information processing in the amygdala and associated limbic structures. Proximity processing can demand cognitive resources and distract from and hinder other task cognitions (Mobbs et al., 2010) but can also quickly prioritize cognition around threat management. This is an important reason why proximity is a key factor in, for example, transportation accidents where threat response places heavy demands on cognition needed to interpret the threat and identify rapid responses while maintaining complex vehicle operation.

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Presence, closeness, and immediacy include the sense of exposure to others around or like us, personal vulnerability, the need to make preparations or stop a process before it is unstoppable, and the part of personal responsibility for action that is driven by our responsibility or abilities relative to exposed others. The dynamic nature of the threat such as rapid development or unpredictable change also increases proximity. Proximity is in the moment, is quickly amplified, and can become extreme if a signal such as a computer virus warning appears on screen or a dog runs into the street in front of the car we are driving. This amplifies the sense that time to control the situation is short and increases the sense of urgency. Proximity affects mental intensity and the motivation to take timely action. This urgency can encourage the allocation of attention and enhance motivation up to the point that urgency becomes runaway fear and panic that confuses decision-making and greatly hinders vigilant and systematic thought and response. Proximity is affected by the degree threat identification is well established, such as thorough training that triggers well-rehearsed actions that reduce cognitive impairment due to fear. Ambiguous threat signals that lack familiarity are obscured, have excessive complexity, and may more easily lead to panic and ineffective response. Proximity is especially affected by the identification of the specific threat (Namian et al., 2016). An ambiguous threat and partial identification are associated with a higher level of proximity than if the threat is well identified. A poorly understood or obscured threat may translate into intense proximity. Proximity, coupled with the degree of control over the threat, predicts the form of engagement, that is, fight, flight, or freezing (Bracha et al., 2004; Cannon, 1929; Schmidt et al., 2008). The response to proximity information is also influenced by the individual’s threat sensitivity or awareness (Cunningham et al., 2005). Proximity is even induced when a threat is merely brought into conscious thought, as when an individual is reminded about a health-threatening lifestyle behavior. The consequences of exposure to a hazard can seem near or far, whether physically or in time. Several studies in mice, affirmed in surveys of humans, detail how physical closeness affects the response to threat (Fischer et al., 2011; Heath et al., 1998; Woods et al., 2008). Contingent on escape path availability, very close threats induce either escape or a fighting response. More distant threats induce heightened alertness and risk assessment. The degree to which the individual considers the hazard a close threat and response a personal responsibility is threat proximity. It induces the urgency of the need for action. Doubt also increases stress and a sense of urgency to resolve the doubt. This adds to the stress of proximity. Proximity is sensitive to time, that is, the intensity of proximity is affected by how much time is needed to respond. This includes the time needed to identify both the threat and a safe response. Proximity is also affected by how quickly the threat will deliver harm, an aspect of the temporal discounting effect (Kim & Zauberman, 2009). Decreased identification or increased proximity both have the effect of increasing stress—which is the reaction to the threat, therefore, increasing perceived risk (Busemeyer & Townsend, 1993; Edland & Svenson, 1993). The appearance of

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multiple threats in a short time or rapid increases in the threat can intensely increase proximity and overload information processing, leading to exit or panic. There is also a social aspect to proximity. The individual may take responsibility for a threat to others such as members of the team or other groups to which the individual feels connected (Fischer et al., 2011; Sanne, 2008). In contrast, a reduction in proximity may occur when risk is socially distributed. This distribution of responsibility is well researched as the risky shift phenomenon or the reduction of perceived risk by individuals as members of a group (Janis & Mann, 1977; Polman & Wu, 2020; Schimmenti et al., 2020; Stoner, 1961). In general, the intensity of proximity is increased by factors that personalize or make the situational threat a direct risk to the individual. Personalization brings ownership and personal connection to that assessment. Proximity makes the threat a responsibility of the individual and is the degree to which that individual connects the existence and understanding of the threat and response actions to negative outcomes to the self. It is not only a threat; in general, it is a threat to me or someone for whom I am responsible, such as a spouse, child, subordinate, or coworker (e.g., Minkler (1999), Wikler (2002)). This includes factors influencing personal vulnerability such as health status or other unique characteristics that make the individual uniquely vulnerable to a specific threat. This knowledge partly influences identification because it is a knowledge gained about general health that is constructed before exposure to a specific situation, but it is also an influence on proximity in that awareness of the specific threat in combination with understanding personal vulnerability to that threat influences the threat’s proximity and motivates the urgency to act. Proximity is also affected by other individual differences, such as locus of control or risk orientation (Rotter, 1966; Wallston et al., 1987) and, as mentioned, personal, as distinct from others’, responsibility for safety (e.g. Minkler (1999), Wikler (2002)). Situational control reflects the situation or structures which determine whether the individual can or is permitted to take action to reduce the threat. This includes both situational, structural barriers to action and policies that allocate authority to act. Perceived situational or threat control may be amplified or attenuated by personality.

5 Additional Influences and the Identification-Proximity Relationship Having reviewed evidence and theory that supports identification and proximity as drivers of safety engagement, a few comments are warranted regarding other influences on safety engagement and how identification and proximity interrelate. Control and Its Effects on Identification and Proximity Control is identified by cognitive theory as a necessary condition for change and as influential on the translation of intent into action (Ajzen, 1991). Control is a combination of factors that influence the degree that action is believed to result in effective mitigation of

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threat and avoid other undesirable outcomes. It can be explained in the form of a question, “Do I control an action that might reduce the threat?” Not independent from the two core constructs in the model, control infuses an important factor in the process of translating information into engagement. Control, as used here, describes the perceived constraints on acting safely and it affects proximity by constraining response options and the ability to influence the threat. Control includes the ability to alter the situation or protect oneself without repercussion or harm and is affected by the belief that the hazard can be changed. Some hazards cannot be avoided or changed. Information identifying control comes not just from the hazard but also from other situational, social, and organizational or policy factors. This means, among other things, that control includes the availability of time to assess risks, access escape routes, or command defensive actions. The ability to control the threat or enact effective responses is related to proximity because this ability affects the time needed for effective actions (reviewed by Blanchard et al. (2011)). Control is influenced by the availability of resources and the opportunity to apply those resources to achieve safety. Recognizing and understanding an imminent threat are insufficient to make action happen. The exposed individual must have the capabilities, that is, the resources needed for effective response including time and the opportunity to act. The individual must believe he or she controls the situation, safety resources, or situation outcomes. These bits of information, which align with identification, determine the extent of proximity’s sensitivity to control. Other aspects of control include independence and responsibility. Independence and responsibility are a compilation of factors that answers questions like “Am I authorized to act; am I responsible for acting, are others more able or responsible for acting; will my actions reduce or eliminate the threat?” If actions are dictated by others or by constraining policies, perceived control is reduced. Independence also asks the question, “If I act, will others support my decision even if the outcomes are not as intended?” These, too, are issues of control. Control also reflects the judgment that personal action, and not just the actions of others, including management and coworkers, is necessary and desirable to achieve safe work outcomes. This sense of responsibility is partly known before the appearance of a threat (identification) and is partly determined by the specific threatening situation (proximity). Finally, incomplete knowledge, that is, unfamiliarity with the threat and effective actions, reduces perceived control over the situation and is fueled by the perceived incapacity to identify effective action. Information Influences on Identification Understanding information influences on identification is helped by Ajzen’s (1991) theory of planned behavior (TPB), a model of behavioral intention. Much safety engagement is planned, that is, based on the intent to be safe by being prepared and knowledgeable about hazards and safe responses. That represents much of identification. First in the formation of the repository of safety information is personal knowledge and experience (Griffin & Neal, 2000; Guo et al., 2016; Mohammadfam et al., 2017). Identification derives from information that makes both the threat and safety responses understood.

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Identification also describes the relationship of the individual to the threat. Influences on the identification knowledge base therefore can be categorized loosely as information about threats, responses, and social or cultural expectations. Knowledge describing threats and safe responses may be acquired by study or experience either directly or vicariously. The more accessible this knowledge, the faster the individual can confidently identify threats and respond. Unfortunately, knowledge alone does not always lead to an effective response. Effective responding requires control over action and a match between the cognitive demands and time pressures of the situation. Safety training limited to describing threats and proper responses is therefore valuable but insufficient. Consider knowledge retrieval time, which varies among individuals. This time may limit effective responses. In addition, stress induced by situational pressures, an aspect of proximity, can work against rapid knowledge retrieval and response. So too can distractions or other competing demands on cognitive resources (Craik, 2014). Social Information and Identification At the point of exposure to a hazardous situation, cues from others can have a strong influence on the individual’s actions, especially when other sources of information seem insufficient (Salancik & Pfeffer, 1978). Social information influences affect both identification and proximity, but their influences on identification are especially interesting. Safety culture and leadership set general attitudes toward personal and others’ safety and establish the relationship between safety and other work tasks, which shapes safety identification (Cooper, 2000; Hofmann & Morgeson, 1999; Zohar, 1980; Zohar & Luria, 2005). A social safety culture that devalues risk or amplifies risk-taking also distorts identification. Furthermore, knowledge gained through vicarious learning can occur by observation of the time that has passed and the number of interactions that comparable others (similar others in a similar situation) have experienced without harm, shaping identification about rare threats and threats with severe consequences (Askew & Field, 2008). Coercion to perform versus act safely, or a situation of high competitive pressure, can diminish the individual’s attention to safety when safety could distract from other tasks (McLain & Jarrell, 2007). In general, social influence can encourage or discourage effort devoted to safety and raise or lower the individual’s threshold at which safety takes priority (McLain, 2016). The Information Component of Proximity Many of the elements of proximity information processing are related to threat characteristics, the personal connection to exposed individuals, or the time available to act. Together, these categories describe the perceived closeness of the threat. Unfortunately, the quality and clarity of information in these categories are often ambiguous. Ambiguity can affect perceived proximity because with ambiguity, the threat is unclear or the seriousness or urgent need for a response is unknown. This “not knowing” can lead many individuals to experience a heightened level of proximity. Ambiguity has the effect of impairing the cognitive processing of threat information and slowing response. It can take many forms including situational complexity, unfamiliarity, and incomplete, obscured, illogical, or changing information (McLain, 1993). Threat and task complexity also obscure the threat and make

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safe responses more difficult to identify. Multiple hazards or barriers to action add complexity and increase proximity because additional time will be needed to assess the situation and respond safely. In contrast, the number of hazard interactions that have been previously experienced without harm attenuates proximity. Unfamiliar hazards may elicit a less rapid and programmed response. Particularly demanding is information describing threat dynamics. This information adds complexity to the assessment of a threat, the need to assess what the future threat will be, and how rapidly the threat is developing or dispersing. Another aspect of proximity information, in addition to an outcome uncertain in magnitude or form, is the immediacy of situation outcomes, that is, near or far in the future. The example of smoking behavior may be helpful here. Smoking is a very personal choice, but the immediate anxiety to satisfy the urge is balanced against stress over future illness potential. Stated another way, proximity is shaped by the immediacy or imminence of harm or a state that is dangerous and not amenable to threat reduction, elimination, or avoidance. Increasing the time till harm attenuates proximity. The time that has passed since interacting with a specific threat, on the other hand, can amplify ambiguity and therefore proximity if relevant information has been forgotten and familiarity lost, in that time. Conversely, time can attenuate proximity as the seriousness of the threat is no longer fresh in memory. The complexity and somewhat conflicting predictions regarding the effects of time on proximity are areas for future research. Among the situational factors that can moderate proximity are task demands that, collectively, constitute the demands the task places on the cognitive and physical resources available to the exposed individual. Task demands usually conflict with efforts required to achieve maximum safety (McLain & Jarrell, 2007). The number and compatibility of threats and tasks and the degree tasks are tightly coupled affect cognitive resources and system safety (Leveson, 2016; Perrow, 2011). Personal health status influences both identification and proximity. A diabetic person is more at risk from some threats than a nondiabetic individual. The same might be said for a person with heart disease and obesity or who is at an age that increases vulnerability to an infectious agent. Feeling a connection with people who also have that health condition may also affect identification. An individual with fair skin is more vulnerable to bright sunlight; however, health status also influences identification such as the knowledge that a drug allergy makes the individual vulnerable to that drug. Health status factors are, therefore, complex influencing factors. Social comparisons can also influence the sense that harm is close and imminent. The sense that someone who was harmed is “close” in the type of work performed, hazards experienced, or vulnerability increases the proximity of future similar hazards. It is a common observation that we do not take a risk as seriously if harm occurs to someone with whom we have no close connection or who is far away in geography or time. The sense of personal threat changes, however, when we identify with the affected person (Askew & Field, 2008). That person may be a friend or relative, but, in general, it is someone with whom the individual feels a personal connection. Connection amplifies proximity. The relationship between time and

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proximity can also have a social aspect. Vicarious learning, or the observation of others’ time since threat interaction and the number of interactions they experienced without harm, may also influence proximity. The Identification-Proximity Relationship The relationship between identification and proximity has elements of the joint interactions of observation and fear, calm and stress, facts and feelings, impersonal and personal, objective and subjective, awareness and presence, and, more generally, understanding and closeness. The interactive relationship creates a sense of urgency and intensity regarding response which leads to the strength of safety engagement. Identification largely relies principally on information established before threat exposure. For this reason, it is increased proximity that is the more direct instigator of safety prioritization in a threat situation. fMRI (functional magnetic resonance imaging) evidence indicates that proximity can heighten alertness but also, as it increases, induce errors in frontal lobe cognition (Schiller et al., 2008). Conversely, identification influences the awareness of a threat and a sense of its seriousness, reducing proximity because the threat and proper response are understood or triggering heightened concern because the seriousness of the threat is quickly recognized. Identification and proximity are both interdependent and counterbalancing, that is, greater identification helps reduce the translation of proximity into panic, but identification also enables a recognition of the speed with which action to reduce the threat must occur and can therefore attenuate or amplify threat proximity.

6 Model Summary The identification and proximity model of safety engagement identifies information as the essential foundation on which safety decisions are made. That information is the input to an awareness that action regarding a hazard is needed. The model describes cognitive processing of that information and the integration of situational information cues with the individual’s unique experience, knowledge, personality, and ways of interpreting safety information. Relatively little attention in most recent safety models is given to information as an influence on decisions and behavior around hazards, despite the venerable role of information in risk estimation when describing threats and risk’s essential categorization in the certainty-risk-uncertainty-ambiguity theory of information and choice (Alvarez et al., 2018; Knight, 1921). In this model, information triggers awareness of a hazardous situation and connects safety knowledge, hazard characteristics, others, and the individual’s anticipations and concerns to safety engagement. The elements depicted in the model are not independent. The border between identification and proximity is indistinct, but the separate categorization of information and processing has practical benefits in predicting engagement and analyzing accidents while keeping the model simple.

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One final note regarding the model: at least two factors affect the difference between a model of safety cognition as conceived and how that model might predict safety in practice. Those factors are (1) information completeness and quality and (2) human biases in interpreting information (Hirsh et al., 2012; Slovic, 1987; Tversky & Kahneman, 1979). These factors influence the integration of safety information into a situational understanding which produces a level of urgency to choose actions that avoid or mitigate the threat. Unlike the traditional magnitude and likelihood model of perceived risk (Knight, 1921; Kogan & Wallach, 1964), the identification-proximity model does not require thinking in terms of probabilities but rather is compatible with theory and findings that individuals think of risks in non-probabilistic terms (March & Shapira, 1987; Parady et al., 2020; Slovic, 1987). Outcome magnitude, unlike probability, influences identification by categorizing the threat as consequential and influences proximity, for example, if the magnitude is threatening to an unacceptable degree. I propose that the framing of threat information explains some threat responses. For example, if a choice is framed as potential gains, information about the proximity of loss is absent. The same applies to loss framing, where information emphasizes the anxiety-enhancing proximity information and prioritizing engagement of safe outcomes. A more extensive discussion of the framing and content of threat and safety information is beyond the scope of this chapter but points to needs for future research.

7 Conclusion One avenue to improving safety is improving our understanding of the cognitive systems that mediate between the information we receive about hazards and our engagement with the protective actions that secure our safety. To contribute to that understanding, this chapter proposed that identification and proximity, incorporating not only safety knowledge and training but also the temporal and spatial information describing a threat, are key influences on safety engagement in a work context. For examples of how the model might help our understanding of safety in practice, see the Appendix.

Appendix Applying the Model COVID-19 and Self-Protection Avoiding contraction of COVID-19 at work or school provides a good illustration of the model. At the onset of the pandemic, individuals experienced low levels of identification due to a lack of relevant knowledge and conflicting information about effective prevention. Experts and laypeople

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alike faced an unfamiliar virus for which the mechanisms of transmissibility were uncertain. Some of the earliest and highest levels of proximity were among healthcare, especially emergency room, employees. These employees engaged in traditional sanitary and personal protective actions, but uncertainty about the threat and the most effective safety actions limited safety engagement. Improved identification was needed to increase engagement and achieve more effective safety actions. Proximity remained a persistent and serious concern as workers viewed the threat as close and imminent. A focus on improving understanding of the threat and protective actions was where effort could best improve effective safety practices. The lack of familiarity with the threat and the magnitude of potential harm intensified proximity. Gradually, information describing self and other protective actions, coupled with social pressures and requirements, increased individuals’ safety engagement. Identification gradually increased, focusing engagement. Actions including social distancing and mask wearing, heightened sanitation, and working or studying from home reduced proximity but increased identification. These actions contributed to individuals’ increased safety engagement with respect to COVID-19. Once vaccines became available, a large percentage of the at-risk population pursued vaccination to further reduce the threat. Although widespread introduction of vaccines may have reduced proximity, social and institutional requirements have sustained levels of safety engagement above what individuals exhibited prior to the pandemic. This engagement appeared as continued protective behaviors such as mask wearing, sanitary practices, and social distancing. Transportation Incident Investigation and Analysis During the data gathering and analysis phases of an incident investigation, data is gathered to enable discrimination between alternative assessments of the causes of a destructive incident. Potential causal factors, including technical, environmental, and human, are noted, and a conclusion is drawn about the likely causal factors (for examples, see National Transportation Safety Board accident reports, 2021). Data describing the states of various systems are supplemented with employee interviews and policy reviews, among other activities. A reading of several reports reveals that many identified influencing factors can be categorized as identification or proximity factors, simplifying and clarifying the factors leading up to each incident. An example of this factor reclassification can be applied in the National Transportation Safety Board accident report, RAB-21-04 “Union Pacific Railroad Employee Fatality.” In brief summary, a train was moving across a roadway and collided with a truck, resulting in the death of the railroad employee riding on the rear of the train. Identification factors are noted as are the extent and recency of licensing and training of the two actors in the incident, a “remote control” train operator and a truck driver. The truck driver had multiple driving violations in the previous 12 months; however, both the remote operator and truck driver had satisfactory licensing and training for their responsibilities. Proximity factors are identified, too, as the multitude of impinging information cues facing the conductor and the threat of the truck, which did not respond to two

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warnings from the remote operator (threat dynamics), are clearly noted. Missing from the report are information about the work pressures facing both individuals. Was the truck driver or the remote operator behind schedule? Both were engaged in the momentum of their work tasks, which could not be redirected to greater attention to safety, resulting in the threat being realized in a fatal incident. It could not be determined why the remote operator did not provide “ground protection,” as company policy required in this situation but from the perspective of the safety engagement model; this is a lack of sufficient effort being directed to safety. Overall, using only the information in the accident report and applying the identification and proximity model, the situation can be viewed as one in which identification for the truck driver revealed an individual difference in the form of poor safety decisions and proximity for the remote operator included multiple cognitive demands. Task momentum for both individuals exceeded safety engagement needs.

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Schmidt, N. B., Richey, J. A., Zvolensky, M. J., & Maner, J. K. (2008). Exploring human freeze responses to a threat stressor. Journal of Behavior Therapy and Experimental Psychiatry, 39(3), 292–304. Shoss, M. (2021). Occupational health psychology research and the COVID-19 pandemic. Journal of Occupational Health Psychology, 26(4), 259–260. Slovic, P. (1987). Perception of risk. Science, 236(4799), 280–285. Song, H., & Schwarz, N. (2009). If it’s difficult to pronounce, it must be risky: Fluency, familiarity, and risk perception. Psychological Science, 20(2), 135–138. Stoner, J. A. F. (1961). A comparison of individual and group decisions involving risk. Doctoral dissertation, Massachusetts Institute of Technology. Sun, Y., Gooch, H., & Sah, P. (2020). Fear conditioning and the basolateral amygdala. F1000Research, 9, 53. Swuste, P., Van Gulijk, C., Zwaard, W., & Oostendorp, Y. (2014). Occupational safety theories, models and metaphors in the three decades since World War II, in the United States, Britain and the Netherlands: A literature review. Safety Science, 62, 16–27. Tversky, A., & Kahneman, D. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263–291. Vinodkumar, M. N., & Bhasi, M. (2010). Safety management practices and safety behaviour: Assessing the mediating role of safety knowledge and motivation. Accident Analysis & Prevention, 42(6), 2082–2093. Wallston, K. A., Wallston, B. S., Smith, S., & Dobbins, C. J. (1987). Perceived control and health. Current Psychology, 6(1), 5–25. Wikler, D. (2002). Personal and social responsibility for health. Ethics & International Affairs, 16(2), 47–55. Woods, J., Eyck, T. A. T., Kaplowitz, S. A., & Shlapentokh, V. (2008). Terrorism risk perceptions and proximity to primary terrorist targets: how close is too close? Human Ecology Review, 15(1), 63–70. Zipf, G. K. (1949). Human behavior and the principle of least effort. Addison-Wesley Press. Zohar, D. (1980). Safety climate in industrial organizations: theoretical and applied implications. Journal of Applied Psychology, 65(1), 96–102. Zohar, D., & Luria, G. (2005). A multilevel model of safety climate: cross-level relationships between organization and group-level climates. Journal of Applied Psychology, 90(4), 616–628.

Part II

Fractals

Fractals and Nonlinear Dynamic Modeling in Energy Economics: A Comprehensive Overview Mehdi Emami-Meybodi

and Ali Hussein Samadi

1 Introduction In the 1980s, by analyzing economic time series, nonlinear behaviors and structures were identified (Panas & Ninni, 2001). These structures provided the ground for development and evolutions in the economic analysis of various markets, and nonlinear analysis techniques paved the way for studying time series in economics. Chaos theory and fractal structures are the most important nonlinear approaches that have been considered in economic studies, especially in energy markets. With the outbreak of the energy crisis in the 1970s and structural changes in energy markets, the focus of the studies was on analyzing the nonlinear dynamics of the energy prices time series. Various crises and changes in the energy sector’s laws, regulations, and policies in energy-exporting and energy-importing regions and countries primarily affected the rise or fall of energy prices. Thus, their impact on the world’s economy was imposed. For example, Serletis and Andreadis (2004), by referring to structural changes in the North American energy industry (such as the amendment to the US Natural Gas Policy Act of 1978, the Gas Deregulation Act of 1989, the deregulation of the energy market in Canada in the mid-1980s, and, in general, efforts to deregulate and increase the efficiency of the North American energy industry) emphasize the importance of using dynamic modeling to explain price fluctuations in the North American gas and crude oil market. Numerous studies have emphasized the existence of complex and nonlinear structures in energy markets, especially the global crude oil market (Adrangi et al., M. Emami-Meybodi (✉) Department of Economics, Meybod University, Meybod, Iran e-mail: [email protected] A. H. Samadi Department of Economics, Shiraz University, Shiraz, Iran e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Faghih (ed.), Time and Fractals, Contributions to Management Science, https://doi.org/10.1007/978-3-031-38188-1_6

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2001; Alvarez-Ramirez et al., 2002, 2008; Alvarez-Ramirez & Escarela-Perez, 2010; David et al., 2019; Ghosh et al., 2016; He et al., 2007). Despite such structures in the energy prices time series, Mandelbrot (1963) showed that the seemingly random signals of a price time series, if appropriately examined by means of advanced statistical techniques, possess inherent structure and can be quantitatively characterized via conventional statistical metrics for distributions and special indices (e.g., drift exponent) for long-term variations. In other words, Mandelbrot’s fractal theory is compelling and accurate for price time series analysis because it allows the study of its statistical distribution classes (Gerogiorgis, 2009). According to the researchers’ interest in analyzing the nonlinear dynamics of energy markets using fractal techniques and structures, this chapter attempts to provide a comprehensive overview of previous studies in the energy markets over the past two decades to provide clear insights from existing analyses in this field. By identifying research gaps in energy market issues and challenges and methodologies, a clear path can be drawn for future studies. The present chapter is organized into four sections. Section 2 examines developments in fractal technique methodologies in energy studies and explains the research gap in this section. In Sect. 3, previous studies in energy with a fractal approach are examined in detail thematically. Thematic content analysis of existing studies and research gaps are other subsections of this section. Section 4 is devoted to summarizing and concluding.

2 Fractal in Energy Economics: Study of Methodological Developments Mandelbrot and Van Ness’s (1968) identification and development of fractal geometry provided new insights into analyzing nonlinear dynamics of energy price time series. Since the 2000s, the fractal approach in energy economics has received particular attention. Thematically, there has been significant development in energy and emission market analysis. However, from a methodological point of view, several developments have enhanced the analysis power of fractal instruments in energy studies. This section aims to analyze the previous studies in the field of energy economics with a fractal approach from a methodological point of view. For this purpose, first the fractal methodology and the development in the tools are analyzed. Then, research gaps in the use of tools in fractal structures will be presented in studies that have not received much attention so far and have acceptable potential in analyzing the nonlinear dynamics of the energy market.

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Fractal Methodology and Developments

Rescaled range (R/S) statistics, Hurst exponent, and fractal dimension form the basis of fractal methodology in studying economic time series. Researchers in the field of economics, and especially in financial markets, mainly introduced and developed these methodological tools in fractal structures in the 1990s. Since then, various developments have taken place to improve fractal tools. Since the basis of these developments was the R/S statistic and Hurst exponent, first in the fractal methodology section, this technique and its modifications have been stated. Then, in the section on methodological developments, the development of these tools in the economics of financial markets and energy is explained. Finally, the research gap in the methodology of fractal structures in energy economics studies is examined.

2.1.1

Fractal Methodology: Basic Techniques

In the field of computers, Landman and Russo (1971) showed the relationship between computer components (internal elements, C) and their relationship to the 2 terminal environment (T ) as an allometric relationship T / C 3 : Also, if T denotes “surface” and C denotes “volume,” the relation T1/2 / C1/3 will be equivalent to the above relation. Therefore, the quantities T1/2 and C1/3 will represent some features of the computer linear size. They also showed that computer efficiency is actually a function of a specific parameter d. Mandelbrot (1982) showed that this parameter d is the same as the “fractal dimension” and the relation T / C(d - 1)/d will be established. This relationship indicates an optimal condition for balancing the internal and external communication of the system (Frontier, 1987). The development of fractal dimensions in economics was first considered in financial studies, and in the 1990s, significant developments were made in these studies. In the 2000s, the fractal approach was introduced in energy economic studies, and much of these developments were used in fractal tools. In 1991, Peters published a book on the analysis of chaos and fractal theories in financial markets, in which he interpreted in detail the look of nonlinear dynamic modeling from both chaotic and fractal aspects. He examines in detail the three key issues of fractal dimensions, fractal time series, and Hurst exponent. These three issues form the core of the energy studies methodology. Fractal Dimensions A good example for calculating fractal dimensions is the coastline. Due to the unevenness of the coastline (and other natural phenomena), the use of Euclidean geometry cannot accurately show the dimensions of the phenomenon. Mandelbrot used a method to calculate the fractal dimensions of this phenomenon. In this method, fractal dimensions are calculated by measuring the properties of these roughnesses. To do this, the number of rings with a specified diameter that can completely cover the shoreline is counted. As the diameter of the rings increases, it

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becomes clear that the number of rings has an exponential relationship with the radius of the ring. This relationship is in the form of Eq. (1): N  ð 2  r ÞD = 1

ð1Þ

where N is the number of rings, r is the radius, and D is the fractal dimension. By sorting this relation and displaying its logarithmic form, we will have Eq. (2): D=

Log N Log ð1=2  r Þ

ð2Þ

For example, the fractal dimensions of the Norwegian coastline are estimated at 1.52 and the British coastline at 1.3. This means that the Norwegian coastline is more rugged than the British coastline because it is closer to the fractal dimension of number 2 (Peters, 1991). Similarly, studies, especially in the 1990s, used fractal dimensions in the stock market and comparisons between different stocks. Because the standard deviation for data with or without serial dependency (like most economical time series variables) will be poor efficiency, the use of fractal dimensions can compare the volatility of two stock returns over time. The larger the fractal dimension of a time series, the more rugged it is or in other words, the more it fluctuates. Fractal Time Series The efficient market hypothesis (EMH), introduced in the studies of Bachelier (1900) and Cootner (1964), was proposed by Samuelson (1965) and mathematically proved that future price fluctuations are random. Samuelson (1965) presented a relatively broad theorem by offering a somewhat general random price change model. Based on this theorem, it was shown that the price differences of the next period are related to the price differences of the previous period (if not completely independent). This feature was introduced as a Martingale property. Subsequently, Fama (1970) introduced the EMH for financial markets. This study, which can be considered the entry of EMH into the field of economics, assumes the market as “efficient” in which prices always fully reflect the available information (Uritskaya & Serletis, 2008). In the EMH, future price changes are determined only by new information. In other words, future information is not dependent on past information. An EMH is that investors react immediately to new information so that the future has nothing to do with the present or the past. The question is do people actually make that decision? They often wait for the information to be verified and do not take action until the trend occurs. The amount of verified information needed to form a trend varies, but improperly combined information can lead to biased random walk formation. Hurst studied this in the 1940s and then by Mandelbrot in the 1960s. Mandelbrot called it the fractional Brownian motions, now known as the fractal time series (Peters, 1991).

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Hurst Exponent Hurst (1951) was a hydrologist who worked for years on the Nile to control the water reserves behind the dam. He was looking for an ideal level of reserves that would never be emptied or overflowed. In model construction, it is common to assume that the uncontrollable part of the system (in Hurst, rainwater inflow) follows a random walk. When Hurst decided to test his hypothesis, he introduced us to a new statistic: the Hurst (H) exponent. H has many applications in time series analysis. This statistic has few basic assumptions about the system under study and can classify time series. It can also distinguish between a random series and a nonrandom series (even if the random series is non-Gaussian) or in other words a series that does not have a normal distribution. Hurst also found that most natural systems do not follow a Gaussian random walk process. Hurst measured how reservoir levels could fluctuate around the average level. It is to be expected that the range of this fluctuation can vary depending on the length of time used for the measurement. If the series is random, the amplitude increases with the square root of time. This is the same T1/2 mentioned earlier. To normalize the measurement over time, Hurst decided to create a dimensionless ratio by dividing the range by the standard deviation of the observations. Hence this analysis was called rescaled range or R/S. Hurst found that most natural phenomena follow a biased random walk process (a trend with noise). The stability of the trend and the noise level can be measured through the relationship between R/S and time or in other words how high the value of H is above 0.5 (Peters, 1991). R/S Statistics Following Qian and Rasheed (2004), the hurst exponent can be calculated by R/S analysis. For a time series, X = X1, X2, . . ., XN, R/S analysis method is as follows: 1. Calculate mean value m:

m=

1 n

n

Xi

ð3Þ

i=1

2. Calculate mean adjusted series (Y ): Y t = X t - m t = 1, 2, . . . , n

ð4Þ

3. Calculate cumulative deviate series (Z ): t

Zt =

Y t t = 1, 2, . . . , n i=1

4. Calculate range series (R):

ð5Þ

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R = max Z t - min Z t t = 1, 2, . . . , n

ð6Þ

5. Calculate standard deviation series S:

St =

1 t

t

ðX t - uÞ2 t = 1, 2, . . . , n

ð7Þ

i=1

Here u is the mean value from X1 to Xt. 6. Calculate R/S: ðR=SÞt = Rt=St t = 1, 2, . . . , n

ð8Þ

Note ðR=SÞt is averaged over the regions [X1, Xt], [Xt + 1, X2t] until [X(m - 1)t + 1, Xmt] where m = floor (n/t).1 In practice, to use all data for calculation, a value of t is chosen that is divisible by n. Hurst found that (R/S) scales by power law as time increases, which indicates ðR=SÞt = c  t H

ð9Þ

Here c is a constant, and H is called the Hurst exponent. To estimate the Hurst exponent, plot (R/S) versus t in the log-log axes. The slope of the regression line approximates the Hurst exponent. For t < 10, ðR=SÞt is not accurate; thus we shall use a region of at least ten values to calculate rescaled range. If the time series is a random walk, H must be 0.5. But if H is different from 0.5, then the observations will not be independent. Each observation contains a “memory” of all that has already happened. This is not short-term memory (also called Markovian), but long-term memory lasts forever. Also, closer events (in terms of time) have a more significant effect than distant events. Using Hurst exponent, the impact of the present on the future can be expressed as Eq. (10): C = 2ð2H - 1Þ - 1

ð10Þ

where C is the measure of the relationship between present and future. Based on the value of H, three situations can occur as the following: 1. H = 0.5: In this case, the value of C will be 0. This means that the series is random and uncorrelated. The present does not affect on the future, and the probability density function will be normal. It is worth noting that it has always been assumed The floor function is the function that takes as input a real number x and gives as output the greatest integer less than or equal to x, denoted floor(x).

1

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that natural phenomena have a normal distribution, whereas Hurst showed that most of them have an H value greater than 0.5, and therefore this traditional hypothesis is rejected. 2. 0 ≤ H < 0.5: In this case, we deal with an unstable (or ergodic) system, which usually also refers to the inverse mode. In other words, if the system is already in a high state, it is expected to be in a low state in the next period and vice versa. The level of system instability also depends on how close the H-exponent is to zero. The closer it is to zero, the closer C will be to -0.5, which indicates a negative and inverse relationship that will be very volatile. 3. 0.5 < H ≤ 1: In this case, we will have the persistent or trend-reinforcing mode, so that if the series was at a high (low) level in the previous period, it is expected to continue its positive (negative) trend in the next period. In this case, the trend is obvious, so that by increasing the value of H close to one, the stability and increasing behavior trend of the system increases. Persistent series are a biased random walk or fractional Brownian motion (FBM). Persistent time series, that is, 0.5 < H ≤ 1, have fractal characteristics because they can be described as FBM. In FBM, there is a connection between events over a time scale. Because of this association, H indicates the probability of events occurring. For example, H = 0.6 means a 60% chance that if the last move is positive, the next move will also be positive. Because every point has not equally likely to occur (like a random walk), the fractal dimensions of the probability distribution are not 2 but a number between one and two. Mandelbrot (1972) showed that the inverse of H is the same as the fractal dimension. If H = 0.5, then it will be two because a random walk can fill a page. But the dimension of H = 0.7 is equal to 1.43. Using the logarithm of Eq. 9, we can represent Eq. (11): Log

R = H  Log ðN Þ þ Log ðcÞ S

ð11Þ

The Log R/S curve slope relative to Log N gives us an estimate of H. We expect the time series to converge to H = 0.5 at very long N values because the effect of memory is reduced due to reaching a point and the impossibility of measuring it. Mandelbrot (1972) also showed that the autocorrelation function (ACF) is not suitable for the long-term memory process (it must be Gaussian) (Peters, 1991). In 1994, Peters published a book on fractal analysis of financial markets, which provided more detailed fractal structures and methodological tools for market analysis in economics and investment analysis. In the 1990s, another development was proposed in the methodological tools of the fractal approach proposed by Lo (1991). Lo (1991) examines long-term memory with short-term dependence on daily and monthly stock return indices over several periods. He argued that Hurst exponent had already been modified by Mandelbrot and others in several important ways (e.g., Mandelbrot and Taqqu (1979), Mandelbrot and Wallis (1968, 1969a, b, c, d, e)). However, such corrections are not designed to distinguish between short-term and long-term dependencies. In the

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stock return time series, it has been shown that in Lo and MacKinlay’s (1988, 1990) studies , such data show a significant dependence on the short term. Therefore, any empirical study of long-term memory in stock returns must first consider the existence of a higher frequency correlation. By modifying the R/S, this study appropriately developed an experimental statistic that is applicable to short-term dependence. Lo (1991) pointed out that to develop a method for diagnosing long-term memory, the distinction between long-term and short-term statistical dependence must be precise. One of the most widely used concepts of short-term dependency is the concept of “strong mixing” due to Rosenblatt (1956), a measure of the reduction of statistical dependence between events separated by longer intervals. From an exploratory point of view, if the time interval between two dates, the maximum dependence between events on both dates, decreases slightly, it is a strong mixing time series. By controlling the reduction rate of dependence between past and future events, the usual rules of large numbers and central limit theorems can be extended to dependent sequences of random variables. R/S Modified (Qn or V’s Statistics) Lo (1991) stated that to distinguish between long-term and short-term dependencies, the R/S statistic must be modified so that its statistical behavior should be constant relative to a general class of short-term memory processes, but for long-term memory, processes must deviate. The Qn statistic expressed this by the form of Eq. (12): Qn =

1 σ n ðqÞ

k

k

X j - X n - Min

Max

1≤k≤n

1≤k≤n

j=1

Xj - Xn

ð12Þ

j=1

where σ 2n ðqÞ =

1 n

n

Xj - Xn

2

þ

j=1 q

= σ 2x

þ2

ωj ðqÞγ j , j=1

2 n

q

n

ωj ð q Þ j=1

Xi - Xn Xi - j - Xn i = jþ1

j ωj ðqÞ = 1 , qþ1

ð13Þ q 1.5 β > 2→persistence in the form of long - term trends 3. α < 1.5 β < 2→anti - persistence, a hallmark of negative feedbacks 3. Zhou (2008) proposes a method called multifractal detrended cross-correlation analysis (MF-DCCA) to investigate the multifractal behaviors in the power law cross-correlations between two time series, which can be applied to diverse complex systems such as economics, finance, and so on. This method can be used to investigate the multifractal relationship between two nonstationary time series. Wang et al. (2013) following Zhou (2008) and Podobnik and Stanley (2008) employed MF-DCCA to describe and understand the behavior of cross-correlations between energy and emission markets. Following Wang et al. (2013), supposing that there are two time series (e.g., returns) {xi} and {yi} with the equal length N, where i = 1, 2, . . ., N, the DCCA method can be introduced as follows: 1. Calculate the cumulative deviation of each time series and then obtain two new sequences: k

k

ðxi - xÞ, Y ðkÞ =

X ðk Þ = i=1

ðyi - yÞ, k = 1, 2, . . . , N

ð21Þ

i=1

2. Divide two sequences {X(k)} and {Y(k)} into Ns = int (N/s) nonoverlapping intervals V.

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~ v ðiÞ and Y~ v ðiÞ by a least3. For each interval V, define the “local trends” X squares fit of the sequences. Then, the detrended covariance can be defined by

f 2 ðν, sÞ =

1 s

s

X ½ðν - 1Þs þ i - X ν ðiÞ i=1

ð22Þ

× Y ½ðν - 1Þs þ i - Y ν ðiÞ for each interval V, V = 1, 2, . . ., Ns and f 2 ðν, sÞ =

1 s

s

X ½N - ðν - N s Þs þ i - X ν ðiÞ i=1

ð23Þ

× Y ½N - ðν - N s Þs þ i - Y ν ðiÞ for V = Ns + 1, Ns + 2,. . ., 2Ns 4. The detrended covariance fluctuation function F 2DCCA ðsÞ can be calculated by averaging over all intervals, that is,

F 2DCCA ðsÞ =

1 2N s

2N s

f 2 ðν, sÞ:

ð24Þ

ν=1

If the two-time series {xi} and {yi}, are power law cross-correlated, then the DCCA method reduces to the DFA method. In practical terms, FDCCA(s) reduces to the detrended variance FDFA(s) described in the DFA method, that is, 1 F DFA ðsÞ = 2N s

1=2

2N s

f ðν, sÞ 2

:

ð25Þ

ν=1

5. By analyzing the log-log plots of FDCCA(s) versus s, the scaling behavior of the fluctuation function can be obtained. If the two time series {xi} and {yi} are power law cross-correlated, then F DCCA ðsÞ / sλ ,

ð26Þ

where is a cross-correlation scaling exponent. Three cases of can be summarized as follows: (i) If > 0.5, the cross-correlations between the two time series are persistent (positive), namely, an increase (a decrease) in one time series is likely to be followed by an increase (a decrease) in the other time series.

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(ii) If < 0.5, the cross-correlations between the two time series are antipersistent (negative), which is an opposite situation to the case (i). (iii) When = 0.5, the two time series are not cross-correlated, that is, there are no correlations between the two time series. 4. In Alvarez-Ramirez et al.’s (2009) study, the DFA technique is introduced as lagged (F(τ, θ)~τH(θ)). In addition to this function, multi-scaling is also considered. In other words, the fluctuation function F(τ, θ) may not be described as a power law. In fact, the dynamics of complex systems are determined by fluctuation components that interact at various time scales. Systems of this type are known as multiscale. In such a case, the power law framework is defined by calculating the scale-dependent Hurst exponent (H (τ, θ)) as a logarithmic derivative of F(τ, θ) on the time scale τ: H ðτ, θÞ =

5.

6.

7.

8.

d logðF ðτ, θÞÞ d logðτÞ

ð27Þ

The local Hurst exponent H (τ, θ) reflects the characteristics of the signal scale x(t) in the neighborhood of the time scale τ because the noise behavior F(τ, θ) of the above derivative cannot be calculated directly and the αβ filter (following Kingsley and Quegan (1997)) has been used. Gu and Zhou (2010): A moving average was used to detrend multi-time series analysis in this study. In other words, multifractal detrended moving average analysis (MF-DMA) was introduced. They developed MF-DMA algorithms to analyze one-dimensional multifractal measures and higher-dimensional multifractals, which is a generalization of the DMA method. Feng et al. (2011): The application of the ARFIMA model, previously introduced by Hosking (1981), was expressed in the energy market and compared different methods of market efficiency in the fractal framework. They used this model to study the influence of current carbon price on future carbon price movements. Wang (2014a, b): The MF-DFA was proposed by Kantelhardt et al. (2002) used in energy markets. MF-DFA can deal with nonstationary series and is based on the identification of the scaling of the qth-order moments depending on the signal length and is more general than the standard DFA. Like the multifractal analysis, the method of MF-DFA can also describe multifractal nature of energy prices signals. David et al. (2019): A new index for calculating the fractal dimension and measuring efficiency (EI) was introduced in this study. The Hall-Wood estimator that proposed by Hall and Wood (1991) is a box-counting estimator that takes into consideration small scales. This was used to calculate fractal dimension. David et al. also investigated the fractal structure of time series data for two time periods, before and after an event. In fact, in this study, the effect of an event during the time series under investigation was investigated.

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9. Ma et al. (2021): In this study, to improve the time series predictive power, the fractal model was combined with neural networks and an optimization algorithm. In summary, the outlook for developments in fractal methodology can be summarized as follows: 1950–1970: 1970–1990: 1990–2000: 2000–2010:

2010–2020: 2020–present:

2.2

Introduction to fractal geometry Calculation of fractal dimensions and its application in different fields Introduction of fractal time series and development of rescaled range (R/S) methodology Expanding the application of fractal time series in financial economics and energy economics with a focus on case study, along with the introduction of detrending models for fractal time series analysis and moving from monofractal to multifractal from 2005 onward Focus of studies on energy market efficiency and introduction of fractal-based models to compare two nonstationary time series Moving toward combining predictive memory-based neural networks (such as LSTM (long short-term memory) neural networks) and optimization algorithms with fractal analysis to improve prediction accuracy

Fractal Methodology in Energy Economics: Research Gap

In this section, the existing methodologies in energy studies along with the studies conducted in them are given in Table 1. As can be seen, the focus of energy studies has been on two main approaches to fractal structure: 1. Hurst exponent calculation and rescaled adjusted range (R/S) statistics 2. Detrended fluctuation analysis, DFA, or multifractal DFA However, other approaches to this structure have been developed in recent years that can be considered in the field of energy economics. These approaches have been used in low-frequency energy studies (sometimes one study). These approaches include the following: A. V’s Statistics (Following Lo (1991)) In 1991, Lo introduced a modified statistic for estimating Hurst exponent, called the V’s statistics, which can also be used to estimate the length of long-term memory. However, in a study in the field of financial economics (Teverovsky et al., 1999), it was shown that with increasing delay q, Vq statistic shows more

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Table 1 Methodologies used in energy economic studies in fractal framework Row 1

Methodology Fractal dimension and Hurst exponent (rescaled adjusted range, R/S statistics)

Year 2002

2011

Author(s) Alvarez-Ramirez et al. Serletis and Andrideas He et al. Dong et al. Bianchi et al. Feng et al. Kristoufek and Vosvrda Liu et al. Cheverda Maksyshko Norouzzadeh et al. Alvarez-Ramirez et al. Zhang and Wang Wang et al. Ghosh et al. Zhao et al. David et al. Liu et al. He et al. Dong et al. Liu et al. Wang et al. Lu Utriskaya and Serletis Zhang and Wang Alvarez-Ramirez et al. Feng et al.

2019

Ftiti et al.

2009 2021

Gerogiorgis Ma et al.

2

2004

3 4 5 6 7

2007 2009 2010 2011 2014

8 9

2019 2020

10

Detrended fluctuation analysis (DFA) and MF-DFA

2007

11

2008

12 13 14 15 16 17 18 19 20 21 22 23

2010 2014a, b 2016 2016 2019 2020 2007 2009 2019 2013 2020 2008

24 25 26 27

28 29

V’s statistics (based on Lo (1991)) To determine the length of the long-term memory period Detrended cross-correlation analysis (DCCA) and MF-DCCA Detrended fluctuation analysis (DFA) and Fourier power spectrum Lo’s modified R/S Lagged detrended fluctuation analysis (lagged DFA) Fractional autoregressive fractional integrated moving average (F-ARIMA) Detrended moving average cross-correlation analysis (DMCA) MF-DMA Scaling law Fractal-LSTM-FOA

Source: Research findings

2010 2010

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bias. This issue can also be examined in energy studies. The optimal length q can also be estimated using econometric methods. B. Detrended Cross-Correlation Analysis (DCCA) and MF-DCCA One of the important issues in the field of energy economics for researchers is the correlation between the two time series that different techniques have been used to study it in studies. However, in fractal structure, the MF-DCCA technique makes it possible to examine the correlation between two time series in the context of fractal structures. C. Lagged Detrended Fluctuation Analysis (Lagged DFA) The existence of delay effects on the autocorrelation of price time series is one of the issues that has been considered in energy studies. However, the lagged DFA technique provides a structure for investigating this issue. D. Fractional ARIMA A group of processes with intrinsic autocorrelations are the integrated fractal autocorrelation moving average (ARFIMA) processes. Their ability to model the short-term and long-term fractal behavior of time series makes them highly attractive for energy price time series analysis. E. Detrended Moving Average Cross-Correlation Analysis (DMCA MF-DMA) Some fractal techniques for detrending are based on the moving average. Such techniques are complementary to the MF-DCCA technique, which can be widely used in energy time series analysis.

3 Fractal and Nonlinear Modeling of Energy Economics: A Thematic Analysis of Studies The introduction of fractal geometry by Mandelbrot and Van Ness (1968) and the development of related tools in the analysis of price fluctuations and its predictability in financial markets paved the way for the introduction of the fractal technique into the analysis of energy prices time series in the 2000s. In this decade, fractal characteristics were analyzed in energy market prices time series (Alvarez-Ramirez et al., 2002; Bianchi et al., 2010; Dong et al., 2009; He et al., 2007; Serletis & Andreadis, 2004). Subsequently, studies developed this approach in energy economic analysis. In this section, it has been tried to review previous studies with the approach of paying attention to issues and challenges in energy markets. The final goal of this section is to show the content analysis of the studies and, finally, to present the research gap in the analysis of energy markets with a fractal modeling approach.

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Literature Review

In this section, previous studies with the approach of using fractal technique have been reviewed separately for different decades in order to consider the developments created in each decade.

3.1.1

Before the 2000s

Hurst (1951) introduced the concepts of fractal geometry and fractal dimensions. Mandelbrot (1972, 1975, 1982) and Mandelbrot and Van Ness (1968) subsequently supplemented the R/S statistic. In the early 1980s, other researchers focused on the application of fractal geometry in various fields, including economics and especially financial issues. The development of theoretical concepts and the development of methodologies in fractal geometry to make it more practical in the analysis of economic time series can be considered the main focus of studies in the last years of the twentieth century. In Sect. 2.1, methodological developments and evolutions in this decade are analyzed. In the years before the 2000s, the focus of studies was on the development of methodologies, and the main focus was on the discussion of financial markets. However, the few studies that have analyzed issues in the energy markets over the years have paved the way for the development of nonlinear analysis, including fractal modeling. In the following, only the study of Jenkins (1995) is mentioned. – Jenkins (1995): Short-term pricing analysis of crude oil He by stated that, in the past decades, the nature of the world oil system has evolved from a stable controlled system to one with high fluctuations in crude oil prices provides a small model of part of the oil logistic system. It then analyzes the model output against the current price of Brent crude oil using a series of developed models in the field of nonlinear dynamics. This study uses the work of Peters (1991) and Wolf et al. (1985) for Lyapunov’s exponent and the work of Grassberger and Procaccia (1983) for correlation dimensions. Initially, periodic behaviors (such as seasonal trends) are identified and eliminated using the autocorrelation function. Next, the series orbital period is specified. This period is a set of observations required to cover data from all segments of the function level. Peters (1991) uses a version of Hurst exponent to develop estimates, but this depends on relatively small changes in the slope of the curve. In this study, the conventional chi-square test (used to estimate the similarity between two sets of data) is modified to provide a measure of the similarity of a series of time series subsets to complete time series. For all analyses, the subheading size required to produce the chi-square test less than 10 was used as the orbital period. Lyapunov’s largest exponent is then examined.

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In general, this study has mainly used chaos theories to analyze the dynamics of crude oil prices. However, the usefulness of using nonlinear models in the analysis of energy economics, including fractal models, suggests.

3.1.2

The 2000s (2000–2009)

The focus of studies in the 2000s is on analyzing the existence of fractal structures and the effect of long-term memory on time series data on energy prices. The crude oil and sometimes natural gas markets are the most important energy markets that have been studied in this decade. In the following, these studies will be examined in more detail. – Panas and Ninni (2001): Nonlinear analysis of oil price behavior in the energy market Analysis of product price behavior in economics is one of the important issues that has focused on its nonlinear dynamics in recent years. Panas and Ninni (2001) are investigating the nonlinear behavior and turbulence in oil prices for Rotterdam and Mediterranean market oil products. In this study, BDS test statistics, Brock theory, Eckman-Ruelle conditions, correlation dimension, entropy, and Lyapunov exponent have been used. The results show that there is considerable evidence of chaos in a large number of petroleum products in the study area. This study is based on previous studies in the field of economics (including Frank and Stengos (1989); Scheinkman & LeBaron, 1989a, b); Blank (1991); Hsieh (1991); DeCoster et al. (1992); Yang and Brorsen (1993); Fang et al. (1994); Kohzadi and Boyd (1995)) have provided strong evidence for the existence of nonlinear structures2 in the behavior of economic time series. Panas and Ninni (2001) using the AR-GARCH model showed that the data (daily prices of petroleum products in the Rotterdam and Mediterranean markets from January 4, 1994, to August 7, 1998, that is, 1161 observations) are deviated and the hypothesis of their normal distribution is rejected. – Alvarez-Ramirez et al. (2002): Multifractal analysis of crude oil prices Examining the existence of multifractal structure (due to the correlation between Hurst exponent in a price series with increasing time scale) is a new approach in

2

Nonlinear analysis of time series is important for three reasons:

– The effort devoted to study time series reflects the fact that nonlinearities convey information about the structure of the series under study. – These nonlinearities provide insight into the nature of the process governing the structure of these time series. – In the absence of information about the structure of these time series, it is difficult to distinguish the stochastic from the chaotic process (Panas & Ninni, 2001).

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analyzing the nonlinear dynamics of energy markets. Alvarez-Ramirez et al. (2002) considered the dynamics of fractal structures in the time series of crude oil prices. In this study, the trend of daily world crude oil prices (including Brent, WTI, and Dubai (Persian Gulf) in the period 1981–2000) is analyzed with a multifractal approach. A scaled Hurst exponent has been used for this purpose. The results indicate that the crude oil market is a persistent process with long memory effects. Also, Hurst exponent correlation analysis at different time scales indicates the existence of multifractal structures in the crude oil market. Also, the crude oil market is consistent with the assumption of random walk, only on time scales from day to week. – Serletis and Andreadis (2004): Fractal structure analysis of North American energy markets This study examines the fractal dimensions of North American energy markets using daily observations of WTI crude oil prices and Henry Hub natural gas prices in Louisiana during the 1990s. One of the aims of this study is to distinguish between deterministic and stochastic prices time series. Serletis and Andreadis (2004) provide evidence that the crude oil and natural gas price series can be examined in the context of a random fractal time series. Overall, the results of this study show that the WTI time series have a stochastic multifractal time series structure with turbulent behaviors. In the case of the Henry Hub natural price, only one stochastic fractal model has been identified. This study analyzes the nonlinear behaviors in the time series of WTI daily crude oil prices (January 2, 1990, to February 28, 2001, including 2809 observations) and Henry Hub natural gas prices (January 24, 1991, to February 28, 2001, including 2521 observations); various steps were taken as follows: First, following Spiegel (1988), the randomness of time series was investigated using the above and below test. After confirming the randomness of the time series, Hurst exponent was calculated following Mandelbrot (1982) and Papaioannou and Karytinos (1995), as a result of which, the existence of a fractal structure with long memory was identified in both series. Furthermore, by confirming the existence of fractal structures, the study of fractal noise model has shown that both price series were noisy in nature. Also, the scaling behavior is expressed using power spectrum. Then, using the structure function test, the distinction between deterministic and stochastic time series is explained. The results of this section show that the fractional Brownian motion behavior is rejected for both series, but the fractal noise behavior is confirmed. Multifractal analysis answers the question, is a time series in different time scales a fractal or not? If yes, is this time series fractal homogeneous or multifractal? This study provides evidence of the absence of multifractals in the natural gas price time series and its presence in the WTI time series. Another important point of this study is analysis of the turbulent behavior hypothesis, which was proposed by Ghashghaie et al. (1996) in financial markets. Although this hypothesis has been criticized by Mantegna and Stanley (1999), this

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study showed that the WTI time series behaves in a chaotic manner according to this hypothesis. But this behavior was not confirmed in the price of natural gas. – He et al. (2007): Fractal characteristics and long run memory in oil market In this study, the fractal characteristics of Brent crude oil, WTI, gasoline prices time series in Rotterdam and Singapore, R/S method, and Hurst exponent are investigated. V’s statistical method3 is also used to obtain the length of non-intermittent cycles of long memory. In fact, this chapter seeks to identify the system information memory that disappears after N days. The results show that the Brent price time series follows a random walk, and therefore, it is difficult to predict price behavior. But other price time series have had uptrends with strong long memory. Another finding of this work is that the longer investment period, the less risk and uncertainty the investment faces. He et al. (2007) focused on several questions. First, do investors face the same risks and uncertainties in different investment periods? Second, how do we define short-term and long-term investments numerically? And third, how do we distinguish between noise traders (Black, 1986) and fundamental traders? They try to provide answers to the above questions by using R/S analysis and its characteristic values, with Hurst exponent. He et al. (2007) showed that according to AlvarezRamirez et al. (2002), random fluctuations are the result of short-term noisy activities of traders whose speculation increases market uncertainties and risks, cause price behavior look like Brownian motions, and are therefore difficult to predict. They showed that at different investment time scales, the uncertainties and risks those investors have to deal with vary. As a result, quantifying noise traders from underlying traders and defining long-term, medium-term, and short-term investments is a very important and valuable task. Calculating Hurst exponent at different time scales can help in analyzing different levels of risk and uncertainty in different investment periods. – Norouzzadeh et al. (2007): Multifractal characteristics in Spain electricity market In this study, the MF-DFA technique has been used to numerically investigate the correlation, stability, multifractal properties, and hourly price scaling behavior for the Spanish electricity market. For this purpose, a scaled exponent and a generalized Hurst exponent have been used to analyze multifractal behavior. The results indicate that the time series of the examined price is a nonstationary and anti-persistent series. The increase in spot prices is an anti-correlated process over a time scale. The Hurst exponent correlation in time scales also indicates the existence of multifractal structures in the Spanish electricity market. Also, the existence of anti-correlated

3

The main purpose of this statistic is to identify nonperiodic cycles with its relative mapping. If the statistic curve V is horizontal, the time series is random (following a random walk); otherwise, there is long memory in the data. If there are critical points, the N value of LogN at that point is the same as the nonperiodic period.

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situation has caused the loss of profit opportunities in the electricity market, which is perhaps the most important reason for the impossibility of storing electricity. Norouzzadeh et al. (2007) introduce an important feature regarding the modeling of dynamic price behavior in the energy market, especially the electricity market. According to the researchers in this study, modeling efforts should focus on models that are able to cover multidimensional features in the market. In terms of policy, the use of multifractal models to calculate the value of derivative contracts in the electricity market, such as options, has also been proposed. – Alvarez-Ramirez et al. (2008): Analysis of short-term predictability of crude oil markets with fractal approach Analysis of nonlinear dynamic behavior of crude oil prices (Brent, WTI, and Dubai (Persian Gulf)) during the period 2007–2008 using Hurst exponent estimation to examine the existence of autocorrelation between price time series in this study has been done. For this purpose, the DFA technique (which focuses on the internal structure of market fluctuations in different time horizons) is used. Analysis of Hurst exponent time scale changes has shown that over long horizons, the crude oil market is consistent with the efficient market hypothesis. However, significant autocorrelations cannot be ignored for time horizons smaller than 1 month. This means that the market exhibits a time-varying short-term inefficient behavior that becomes efficient in the long run. – Uritskaya and Serletis (2008): Quantification of multidimensional inefficiencies in the electricity market One of the basic characteristics of efficient markets is the lack of correlation between price increases at any time scale, which leads to random price behavior. This work proposes a new approach to measuring the deviation from the efficient market situation based on scale-dependent fractal exponent analysis, which identifies correlations at different time scales. For this purpose, the two electricity markets of Alberta and Mid-Colombia and the natural gas market of AECO Alberta have been studied in order to compare the two types of energy that can be stored and non-stored. The results show that price fluctuations are inefficient in all studied markets. Electricity prices also have complex multiscale correlational behavior that has not been demonstrated by monofractal methods in previous studies. The focus of Uritskaya and Serletis (2008) is on the EMH. The theoretical foundations of the EMH that are introduced in Sect. 2.1.1 consider the market as “efficient” in which prices always fully reflect the available information. – Dong et al. (2009): Multifractal analysis in the time series of global crude oil prices In this research, the fractal properties of the crude oil market are analyzed using the R/S method of daily prices of WTI and Brent. The results show that the Hurst exponent value for both markets is greater than 0.5, indicating a persistent trend and long memory in the data. Also, using V’s statistics, the length of memory (the length of the turning points of the LogT-Vn diagram) was calculated, which shows the

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results of 12 days of memory for both series. This indicates very low memory effect in prices. Dong et al. (2009) have also been able to examine the dynamics of nonlinear behavior of crude oil prices in the world with fractal structures. The important point in this study is to compare the time series of prices in the crude oil market for the ability to absorb risk. However, a large part of the memory effect in both the WTI and Brent time series is related to short periods. In other words, in the long run, it becomes difficult to predict the prices. – Gerogiorgis (2009): Fractal scale analysis of crude oil price evolutions Gerogiorgis (2009) examines the fractal structure of the WTI and Brent crude oil price series in price changes with varying degrees of time separation. Due to the variable time periods (from one-day period to one-year period), fractal structures are clearly present in both price series. The fractal structure of crude oil price changes shows the interaction of both short-term and long-term effects on the intrinsic structure of crude oil prices before and after 2008.

3.1.3

The 2010s (2010–2019)

Studies in the 2010s have focused on measuring the efficiency of energy markets based on the EMH and examine the cross-correlation between the time series of energy prices. In this direction, methodological developments have taken place for the development of energy price analysis, which are described in Sect. 2.2. In general, the researchers tried to analyze the fluctuations and noises in the energy prices trend by the introduction of new techniques along with fractal structures and better accuracy and detail. This can also help energy policymakers. The following is a detailed description of the studies conducted in this decade. – Alvarez-Ramirez and Escarela-Perez (2010): Modeling and efficiency of the oil market with a multi-scaling autocorrelation approach Market efficiency studies have focused on identifying autocorrelations in price time series. In the case of the crude oil market, there is evidence of weak efficiency over a wide range of time scales. This issue is still controversial. In Alvarez-Ramirez and Escarela-Perez’s (2010) study using the lagged DFA technique, the effects of delays in price autocorrelation in terms of a multi-scale Hurst exponent in the period 1986–2009 have been investigated. The results show significant deviations from efficiency related to delayed correlations, so imposing a random walk on crude oil prices increases forecasting costs. Evidence is steadily in favor of returning prices to the mean, emphasizing the importance of properly combining delay effects and multiscale behavior in dynamic crude oil price modeling. Unlike other studies that have suggested efficient behavior for large time scales, this chapter shows significant deviations from efficiency in the market. Positive or negative autocorrelations may be masked by the effects of delay.

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– Bianchi et al. (2010): Analysis of fractal characteristics in some European electricity markets This study examines the prices of electricity trade in some European markets (such as Italy, Germany, and the Nordic countries) with a multifractal approach. For this purpose, Hurst exponent estimation has been done in a different way of previous studies. The results of Hurst exponent estimation as a random model (which allows it to change over time) showed that the multifractional Brownian motion is a suitable model for expressing the dynamics of electricity prices. – Zhang and Wang (2010): DFA fractal analysis of Chinese energy markets In this research, the relationship between the returns of 16 stocks related to the Chinese energy market and five important stock market indices in the forms of absolute returns, second- and third-degree returns with fractal DFA approach, and square wave returns are examined and compared. The results show that the Chinese energy market confirms fractal properties and stability based on the modified R/S statistics introduced by Lo (1991) in the long memory. – Feng et al. (2011): Fractal analysis of carbon price fluctuations Feng et al. (2011) examined the carbon price fluctuations using the EU ETS trade data in a nonlinear framework. The study followed the following steps: 1. Using a random walk model including serial correlation tests and variance ratio to check whether the history of carbon price information is reflected in current prices or not. The results of this section show that the carbon price did not have a random walk, and the information was not fully reflected in the current price. 2. Using R/S statistics, modified R/S statistics, and ARFIMA model to check the memory of carbon price history. The results of this section indicate the existence of short memory of carbon prices. 3. Using chaos theory to analyze the effect of internal carbon market mechanisms on carbon prices. The results of this section show that the dimensions of the carbon price correlation are increasing. The maximal Lyapunov exponent is also positive and large. In this study, three points are worth considering. First, the price time series analysis with fractal approach in the emissions market and its efficiency analysis have been considered. In this study, it is shown that there is a significant deviation from efficiency in carbon prices that allows price forecasting. Second, the fractal technique is combined with the ARIMA regression model. In this study, the ARFIMA model is introduced with the fractal dimensions d. Third is about the theory of turbulence, in which the function Cr (m) and the Lyapunov function are presented with a time lag of τ. In other words, chaos theory with delay effects has been used. Overall, this study offers a new perspective on understanding the carbon market from a dynamic and nonlinear perspective. – Xiong et al. (2012): Fractal energy measurement and analysis of singularity energy spectrum theory

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In this study, the singularity exponent (SE), which is a characteristic parameter of fractal and multifractal signals, is introduced. Most studies have sought to capture spatial signals or fractal distinctions. This study sought to evaluate fractal energy measurement (FEM) and singularity energy spectrum theory (SEM) using SE as an independent dimension. For this purpose, the present research first studies the energy measurement and energy spectrum of a fractal signal in the singularity domain and introduces related concepts. – Kristoufek and Vosvrda (2014): Commodity market efficiency analysis Kristoufek and Vosvrda (2014) investigate the market efficiency of 25 commodity types in the groups of metals, energy, soft goods, cereals, and other agricultural products using fractal indicators. The results show that the heating oil, WTI crude oil, cotton, wheat, and coffee had the highest efficiency, respectively. From the group point of view, the group of energy commodities has the highest and other agricultural products the lowest efficiency. A positive relationship between fractal dimension and Hurst exponent has also been identified in the data. – Wang et al. (2014a, b): Cross-correlation between energy markets and emissions with fractal and multifractal analysis In this study, a new approach proposed to investigate the correlation between energy markets and emissions, that is, the relationship between oil and gas, oil and CO2, and gas and CO2 price return rates in the framework of fractal and multifractal structures in the period 2005–2013. This study introduces the DCCA approach. The results show that the market correlation follows the power law but the stability is weak. The results of DCCA multifractal approach showed that correlated markets are nonlinear and fractal in nature. The results of the rolling window method also showed that the recent global financial crisis has had a significant impact on market dynamics in the short and long term. Previous studies have focused on analyzing the presence of fractal structures, memory effects, and efficiency deviations in time series of energy prices. However, in this study, the fractal approach to energy markets has moved toward crosscorrelation between time series of energy prices. This approach seeks to examine the relationship and direction of prices in energy markets. By generalizing the DCCA model to investigate the multifractal behavior of cross-correlations between two time series, the MF-DCCA model is introduced. In this approach, the correlation between the two time series can be examined in terms of multifractal and monofractal. – Wang et al. (2014a, b): Multifractal analysis of electricity market In this study, empirical mode decomposition (EMD) introduced to decomposition of basic heterogeneous microstructures in the Australian electricity market. In the next step, MF-DFA analysis is used to analyze the fractal characteristics of EMD. The results indicate the existence of significant fractal features in the market under study.

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– Ghosh et al. (2016): Multifractal behavior of electricity bid price in Indian energy market Based on the fact that there is a complex nonlinear correlation between the cost of a product in the industry and power price fluctuations, this study examines electricity price fluctuations in the Indian energy market with a multifractal approach. The results show that the fluctuations are multifractal in terms of time, but the degree of fractal has been varying in different regions of the market. – Zhao et al. (2016): Characteristics of multifractal fluctuations in China’s coal prices Zhao et al. (2016) considered the coal energy market due to its 60% share in total energy consumption in China and the importance of its profound impact on energy development, especially in the thermal electricity trade. Multifractal theory MF-DFA has been used to analyze coal price fluctuations. The results show that the price of coal has multifractal features. In this study, a quarterly fluctuation index (QFA) was used to enhance the predictability of the fractal model when prices fluctuated sharply. The reason for using such an index is that by changing the parsing intervals (in this study from 11 weeks to 16 weeks), price fluctuations have become clear and difficult to interpret. Therefore, QFI has been analyzed to examine the effects of this feature on the price of thermal energy coal to help governments and companies to effectively predict and understand prices. As a new indicator, QFI offers a new complement to energy price research methods. It also enables the government to have a better understanding of the characteristics of coal prices. Zhao et al. (2016) suggested that, together with in-depth research on QFI, a similar index could be introduced into other energy price studies to gain a better understanding of volatility characteristics. – David et al. (2019): Measuring the efficiency of the ethanol and gasoline market in Brazil using DFA David et al. (2019) examined the fractality of the ethanol and gasoline market in Brazil as one of the largest producers of ethanol in the world. In this study, a new efficient index (EI) is also proposed. The data are for two periods (one from 2011 to 2015 before the impeachment of the Brazilian president and the other from 2016 to 2018, which includes the period after the impeachment and the adoption of new government policies in the Brazilian energy sector). The results show that the market is moving toward better efficiency for the gasoline market after the change in government policy. – Ftiti et al. (2019): Relationship between energy efficiency and trade volume with multifractal approach This study examines the volume-return relationship between the two major energy markets (oil and gas) during the global financial crisis and the fractal approach in the United States based on data from New York Mercantile Exchange (NYME) future contracts. The results show that there is a multifractal relationship

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between return and volume in both markets under all-time scales, which indicates that the correlation between return and volume is nonlinear, thus rejecting the efficiency hypothesis. Also, the magnitude of fluctuations during the downtrend and uptrend affects the return-volume relationship differently. Ftiti et al. (2019) considered that multifractals need more than one Hurst exponent to describe the time series. Therefore, a model based on detrended moving average cross-correlation analysis (DMCA), which is a supplement to the DCCA method, and a quantitative criterion MF-X-DMA multifractal detrended moving average analysis have been used. – Liu et al. (2019): Long-term memory dynamics of crude oil prices Fluctuations in oil prices and exchange rates are the most important factors affecting the oil trade of non-US countries. Accordingly, this research seeks to investigate the effect of these two issues with a fractal approach. First, the gap between nominal and real oil prices is examined in the time series of the Russian Crude Oil Exchange, the Dubai Crude Oil Exchange, the Oman Crude Oil Exchange, the WTI Crude Oil Exchange, and the Brent Crude Oil Exchange. The results of all the price series examined in the period 2013–2018 indicate the existence of long-term memory features. In this chapter, V’s statistics is also used.

3.1.4

The 2020s (2020–Until Now)

Studies in recent years have attempted to combine fractal dimension analysis in energy and emission markets with approaches that analyze oscillating and noise behaviors more accurately. This issue was also considered in the studies of the 2010s. This shows the potential of fractal technique, especially multifractal in combination with other models to develop the analysis of nonlinear dynamics of time series of energy prices. In the following, the studies that have been analyzed in the energy markets with fractal approach in the last decade are reviewed. – Cheverda and Maksyshko (2020): Predicting the dynamics of world oil prices in the framework of fractal In this study, considering the importance of the role of oil prices in the global economy, fractal analysis examines the dynamics of Brent oil prices for the period 2013–2019. The results indicate the existence of long-term memory. Also, due to the inertial property, the use of R/S sequential analysis method has allowed the construction of fuzzy sets of time series memory depth, and a detailed retrospective analysis of the dynamics of changes in memory depth properties has been performed during the observation period. – Liu et al. (2020): Measuring the efficiency of the carbon market in China

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In this study, EMH versus fractal market hypothesis (FMH) is examined to analyze the results of market efficiency more closely. Seven Chinese carbon markets4 are evaluated in this research. Liu et al. (2020) used the variance ratio (as EMH) and DFA (as FMH) tests to measure the market efficiency. Overall, the results of data analysis for the period 2013–2019 show that the efficiency of China’s carbon markets is low. Also, compared to EMH, FMH has been able to better measure the efficiency of carbon markets. – Lu (2020): Fractal characteristics of the crude oil market Lu (2020) used the MF-DCCA technique to investigate the relationship between spot and future crude oil prices for noise analysis in the time series WTI oil future market and OPEC (Organization of the Petroleum Exporting Countries) spot oil market. The results show that the future crude oil market is positively related to spot crude oil markets and there are multifractal structures between them. The analysis of these structures has also shown that the long-term correlation of time series is the main reason for the above results. – Tabares-Ospina et al. (2020): A new technique for measuring the fractal dimensions of electrical energy In this study, a quantitative estimator of spatial complexity is proposed to investigate the fractal dimensions of the degree of fluctuations of the daily electric charge curve. The fractal dimension method allows us to discover a new numerical method for calculating the integral of a function using the trapezoidal law by dividing the curve into fractal segments. – Li et al. (2021): Estimating wind energy consumption capacity based on multifractal theory Li et al. (2021) investigated the characteristics of wind energy fluctuations with multifractal approach and its relationship with consumption capacity. The oscillation process is also clustered with similar characteristics. The results confirm the method in a sample of a regional power company in China. In this study, the effect of adjustable parameters in the model on consumption capacity is quantitatively analyzed. – Ma et al. (2021): Predicting stock dynamics of renewable energy companies based on fractal-FOA-LSTM In this study, to improve the forecast accuracy and stability of the stock trend model, the combined fractal-FOA-LSTM method is proposed. First, the properties are selected using the FOA (fly optimization algorithm) along with the fractal dimension, and then, the selected indicators are used as system input. And by proposing a two-input LSTM (long short-term memory) network prediction model

4

Beijing, Guangdong, Hubei, Shanghai, Shenzhen, Tianjin, and Chongqing are seven carbon markets in China.

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and optimizing its parameters, the best parameters for different data can be selected automatically. This experiment on four sets of UCI (University of California Irvine) database and Shanghai Composite Index and using experimental analysis of Shanghai Composite Index and S & P500 proved the effectiveness of the method under study.

3.2

Fractal in Energy Economic Studies: Thematically Research Gap

After analyzing the studies on the dynamics of energy prices by examining the existence of fractal structures, in this section, the aim is to present the issues that have been neglected in previous studies and are among the important issues and challenges in the field of energy markets. In other words, this section seeks to provide a research gap in the field of energy economics within the framework of fractal structures. For this purpose, first the classification of the analyzed topics in the previous studies (which are described in Sect. 3.1) is given. Then, by examining the issues in the field of energy that have been considered in studies with other approaches, the research gap of this section is presented. Table 2 presents the list of the main and subtopics of the studies along with the year of study, authors, case study, and their time period. In general, ten main issues have been considered in these studies: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Time series analysis of crude oil prices (petroleum products) Time series analysis of natural gas prices Time series analysis of electricity prices Time series analysis of coal prices Efficiency of crude oil market (petroleum products) Energy market efficiency (in general) Electricity market efficiency Analysis of energy stock markets Cross-correlation between two energy prices time series Carbon market analysis (emission market)

In conclusion, the three main topics of “analysis of fractal characteristics of the time series of energy market prices”, “efficiency of energy markets (and emission)” and “cross-correlation between the two time series of energy markets” are the most important topics considered in previous studies. To identify the research gap in the field of fractal analysis of energy economic issues, studies published in the energy journals since 2015 have been reviewed. In Table 3, the frequency of journals publishing studies related to energy economics with fractal approach is given. As can be seen, the Energy Economics, Energy, and Physica A had the highest frequency of publication of these studies.

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Table 2 Studies in the field of energy economics with fractal approach in terms of subjects Row 1

Main subject Crude oil price time series analysis (petroleum products)

Year 1995

Author(s) Jenkins

2001

Panas and Ninni

2002

AlvarezRamirez et al.

4

Long-term memory in the crude oil price

2007

He et al.

5

Short-term predictability of the crude oil market

2008

AlvarezRamirez et al.

6

Crude oil price series analysis

2009

Dong et al.

7

Crude oil time series fractal scale The longterm memory of crude oil prices affected by exchange rates Crude oil price dynamics Oil and gas spot price forecast

2009

Gerogiorgis

2019

Liu et al.

China imports from Russia, Oman, Dubai, WTI, and Brent

2013–2018

2020

Cheverda and Maksyshko

Brent oil price

2013–2019

2003

Agbon and Araque

WTI spot oil price and New York city

1982–2003

2

3

8

9

10

Time series analysis of

Case study Brent, WTI, and Henon Crude Oil Price Series Rotterdam and Mediterranean petroleum markets Brent (North Sea-Europe), West Texas Intermediate Cushing (USA), and Dubai (Persian Gulf) Brent and WTI crude oil and Rotterdam and Singapore Leaded gasoline prices Brent (North Sea—Europe), West Texas Cushing (USA), and Dubai (Persian Gulf) WTI (West Texas Intermediate) and Brent daily crude oil prices WTI and Brent

Time periods 1986–1990 1991–1994

Sub-subject Crude oil pricing in the short term The chaos behavior in the crude oil market Hurst analysis of crude oil prices

1994–1998

1981–2000

1987–2006

1987–2007

1986–2008

1986–2008

(continued)

Fractals and Nonlinear Dynamic Modeling in Energy Economics. . .

151

Table 2 (continued) Row

Main subject

Sub-subject

Year

Author(s)

oil and gas prices 11

12

Time series analysis of electricity prices

13

14

15

16

Time series analysis of coal prices

17

Crude oil market efficiency (petroleum products)

18

19

20

Energy market efficiency Electricity market efficiency

North American Energy Market

2004

Serletis and Andreadis

Multifractal features of the electricity market Fractal features of the European electricity market Multifractal analysis of electricity markets Multifractal behavior of electricity bids Multiple fractal fluctuations in coal prices

2007

Norouzzadeh et al.

2010

Bianchi et al.

Modeling and efficiency of the crude oil market Ethanol and gasoline market efficiency Commodities market efficiency Investigating inefficiency in the electricity market

Case study gate natural gas price WTI crude oil price and Henry Hub natural gas price Spain electricity spot market

Time periods

1990–2001

1998–2006

German EEX, the Italian IPEX, and the Nordic countries Nord Pool Four electricity markets in Australia

2006–2009

2004–2014

2016

Ghosh et al.

Indian Energy Market

2012–2014

2016

Zhao et al.

2006–2013

2010

AlvarezRamirez

A steam coal free-onboard (FOB) price in Qinhuangdao Port, China’s largest port of coal storage and transportation WTI crude oil price

2019

David et al.

2011–2015 2016–2018

2014

Kristoufek and Vosvrda

Ethanol and gasoline prices series in Brazil US commodity

2008

Utriskaya and Serletis

Alberta and Mid-Columbia (Mid-C) Electricity Market, and AECO

2001–2006

1986–2009

2000–2013

(continued)

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Table 2 (continued) Row

21

Main subject

Analysis of energy stock markets

22

23

24

Cross-correlation between two energy time series

Sub-subject

Year

Author(s)

Fractal analysis of Chinese energy markets

2010

Zhang and Wang

Predicting the stock market dynamics of renewable energy companies Fractal analysis of the cross-correlation between energy and emission markets

2021

Ma et al.

2014a, b

Wang et al.

Cross-correlation between energy efficiency (oil and gas) and

2019

Ftiti et al.

Case study Alberta natural gas market Chinese stock market and five stock indices (Shanghai Composite Index, Shenzhen Component Index, Dow Jones Industrial Average index, Nasdaq Composite Index, the Standard and Poor’s 500 Index) China

Energy Prices: Intercontinental Exchange Europe (ICE) Brent Crude Oil Futures, New York Mercantile Exchange (NYMEX), and Henry Hub Natural Gas Futures. CO2 prices: ICE European Climate Exchange (ECX) EU Allowance (EUA) Futures Crude oil and natural gas future contracts collected from the New York

Time periods

2000–2009

–

2005–2013

2007–2010

(continued)

Fractals and Nonlinear Dynamic Modeling in Energy Economics. . .

153

Table 2 (continued) Row

Main subject

25

26

27

Carbon market analysis (emission market)

Sub-subject its trade volume Cross-correlation between future and spot crude oil prices Carbon price volatility Carbon price efficiency

Year

Author(s)

Case study

2020

Lu

Mercantile Exchange WTI oil futures market and OPEC spot oil market

2011

Feng et al.

2020

Liu et al.

The European Union Emission Trading Scheme Beijing, Guangdong, Hubei, Shanghai, Shenzhen, Tianjin, and Chongqing (seven carbon markets in China)

Time periods

2016–2019

2005–2008

2013–2019

Source: Research findings Table 3 Frequency of journals publishing fractal energy studies: 2021–2015 Journal title Energy Economics Energy Physica A Applied Energy Applied Economics Fractals Global Energy Issues Chemical Product and Process Modeling Financial Markets and Derivatives Bifurcation and Chaos Mathematical Problems in Engineering Electrical Power and Energy Systems Financial Strategies of Innovative Economic Development Journal of Cleaner Production

Frequency 7 2 2 1 1 1 1 1 1 1 1 1 1 1

Source: Research findings

A review of these journals identified topics that could be analyzed in the form of fractal structures but have not yet been addressed:

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A. In fractal structures, cross-correlation can be analyzed between two time series in energy markets (multifractal detrended cross-correlation analysis (MF-DCCA) approach). In energy economic studies, the following issues have been analyzed with other techniques that can be examined in the form of fractal models. These issues are in order of priority (most frequent in studies) as follows: 1. The relationship between the stock market and the energy market (crude oil prices, price shocks, etc.): This is an issue that has a high frequency and is still one of the most important issues in the energy economics. 2. Cross-correlation between energy prices and time series of macroeconomic variables such as exchange rate 3. The correlation between inflation in the energy sector and housing prices B. In a number of fractal studies, the market efficiency has been measured. The crude oil, natural gas, and electricity markets are the main markets that have been considered. However, the prices time series of other energy markets such as LNG (liquefied natural gas), coal, heating oil, and renewable energy can also be considered. C. Unconventional energy resources, which have played an important role in the energy security of countries in recent years, have not been studied in a fractal context. In particular, it is important to consider the following: 1. Fluctuations in shale gas prices (due to significant uncertainties in the development of its reserves) 2. Long-term relationship (study of the memory effect) oil and gas prices and the effect of shale gas developments D. Some issues related to renewable energy have also been neglected. In existing fractal studies, the main focus has been on fossil fuels, including oil and gas, and almost no attention has been paid to the issue of renewable energy. The following issues in the field of renewable energy can be considered in the fractal context: 1. The correlation between renewable energy and CO2 emissions 2. The correlation between renewable energy and economic variables time series 3. Examining the renewable energy prices systematic risk and oil prices 4. Analysis of uncertainty in solar power generation contracts 5. The correlation between oil prices (or fossil fuel prices) and renewable energy 6. Profit dynamics of renewable energy companies E. The issue of emission and environmental economics is one of the important topics in recent years that has rarely been considered in fractal studies. The following issues may be considered in this research field: 1. The correlation between energy and carbon prices 2. Measuring the efficiency of the carbon market with the fractal approach and comparing it with the Malmquist index

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3. Analysis of the efficiency of environmental taxes (carbon tax) 4. Efficiency of CO2 reduction policies 5. Analysis of carbon emission behavior, before and after the Paris agreement F. The subject of the Covid-19 pandemic is also one of the new topics that its effect on energy economics can be examined with a fractal approach: 1. Covid-19 and its effect on time series trends in energy prices (electricity, crude oil, gas, etc.) 2. The effects of Covid-19 on the emission market

4 Conclusion This chapter, with the approach of review analysis, tried to analyze the energy economic studies that have examined the correlation behaviors of energy prices with fractal methodology, in terms of thematic and methodological developments. One of the important points confirmed by the results of previous studies is the high ability of fractal modeling to analyze nonlinear dynamics in the time series of energy prices. This issue has led researchers to pay attention to this methodology and its development. Methodologically, the fractal dimension, the Hurst exponent, and the R/S statistic form the basis of the fractal structure in economic time series analyses. Subsequently, various developments were made in these tools. These developments paved the way for the study of energy economic studies from monofractal to multifractal. DFA, MF-DFA, MF-DCCA, and ARFIMA are tools that have been developed in energy economic studies over the last two decades. However, methodological gaps in energy studies are still visible. Due to the high ability of MF-DCCA model in analyzing the correlation between two time series of energy prices, the ability to analyze the delay effects on the fractal properties of energy prices in Lagged DFA technique, the ability to distinguish between short and longterm fluctuations in time series with V’s statistic technique, and finally the combination of the ARIMA econometric model with the fractal dimension are techniques that have been somewhat neglected in energy studies. One of the points to be considered in the development of fractal methodology tools in energy studies is that most of the fractal tools introduced in financial market studies have been developed after a time delay in energy economic studies. This can be due to the nature of high-level fluctuations, nonstationaries, and frequency of the prices time series in these markets, which analyze them require, development of statistical physics tools, signal analysis, and, in general, nonlinear modeling. Therefore, in filling the research gap of nonlinear time series analysis of prices in energy markets, it will be interesting to follow the developments of fractal methodology tools in future studies of financial markets. From the thematic aspect, three main subjects have been the focus of fractal energy market studies: “the fractal characteristics analysis of the energy prices time

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series,” “measuring the energy markets efficiency (and emission),” and “the crosscorrelation between the two time series of prices in the energy markets” are among these issues, given that there is still a significant thematic research gap that could pave the way for future fractal research in energy markets. These issues, which can largely fill the thematic research gap in energy studies with a fractal approach, can be summarized as follows: 1. Correlation of prices time series in energy markets and prices time series in financial markets 2. Correlation of prices time series in energy markets with prices time series in other sectors of the economy (such as exchange rates, housing prices, etc.) 3. Paying attention to the energy market efficiency, such as LNG, unconventional energy sources, and renewable energies 4. Developing attention to issues related to the emission market and especially the correlation between carbon prices and other energy prices

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COVID-19 and Fractal Characteristics in Energy Markets: Evidence from US Energy Price Time Series Mehdi Emami-Meybodi

, Sakine Owjimehr

, and Ali Hussein Samadi

Abbreviations DFA DID EMH FMH HH MF-DFA NYH C Gasoline NYH H Oil PJM WTI

detrended Fluctuation Analysis difference-in-differences efficient market hypothesis fractal market hypothesis Henry Hub natural gas multifractal detrended fluctuation analysis Conventional Gasoline Heating Oil PJM West (Electricity) West Texas Intermediate

Highlights • We examine the efficiency of the most significant US energy markets (crude oil, gasoline, heating oil, natural gas, and electricity) in the pre- and postpandemic era • Using the multifractal detrended fluctuation analysis (MF-DFA) approach • Multifractal spectrum in all US energy markets has increased significantly postpandemic

M. Emami-Meybodi Department of Economics, Meybod University, Meybod, Iran e-mail: [email protected] S. Owjimehr (✉) · A. H. Samadi Department of Economics, Shiraz University, Shiraz, Iran e-mail: [email protected]; [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Faghih (ed.), Time and Fractals, Contributions to Management Science, https://doi.org/10.1007/978-3-031-38188-1_7

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• The outbreak of COVID-19 has reduced the efficiency of all energy markets (except PJM)

1 Introduction Energy prices serve a leading role in the performance of the global economy. This role has increased the incentive to study the dynamics of these prices (AlvarezRamirez et al., 2008) systematically. One of the significant reasons for this role is the influence of different incidents on severe price fluctuations in different energy markets. The energy crisis of the 1970s pushed up crude oil prices. Other significant events, such as the 1991 Gulf War, the Iraq War of 2003, and the financial crisis of 2007–2008, have significantly impressed sharp fluctuations in energy prices in recent decades (Alvarez-Ramirez & Escarela-Perez, 2010). The chain of these events and their synthesis have led to the dynamic analysis of energy prices as a focus of ongoing studies. Given the prominence of energy prices and their roles in the global economy and considering the performance of the economies of energy exporting and importing countries, studies from the 1970s onward have thrived to analyze price fluctuations in energy markets in varied ways. These efforts have led to the development and evolution of fluctuation analyses and chaos methods in price time series. Until the early 2000s, the principal focus of these studies was to examine the stationary and non-stationary processes in energy price returns. In a vast area of studies, field researchers have considered the analysis and comparison of energy price volatility with a focus on crude oil prices with other commodity markets (Plourde & Watkins, 1998), energy price fluctuations in future trading, and the estimation of price risk indicators (Cabedo & Moya, 2003; Giot & Laurent, 2003; Sadorsky, 2006; Weiner, 2002). Besides Alvarez-Ramirez et al. (2008) addressed variance decomposition of price fluctuation. The introduction of fractal geometry by Mandelbrot and Wallis (1968) and the development of related tools in the analysis of price fluctuations and their predictability in financial markets have provided the basis for the introduction of fractal techniques into the analysis of energy prices time series in the 2000s. Throughout the present decade, fractal characteristics have been analyzed in the prices time series in energy markets (Alvarez-Ramirez et al., 2002; Bianchi et al., 2010; Dong et al., 2009; He et al., 2007; Serletis & Andreadis, 2004). This approach focuses on the short-term and long-term correlation of the price time series (Lo, 1991). Following the developments in price time series analysis, efficient market hypothesis (EMH), developed by Fama (1970) in financial markets, stepped into energy market studies in the 2000s. Serletis and Rosenberg’s (2007) and Serletis and Bianchi’s (2007) significant deviations from the EMH for the energy market revealed both on a specific time scale and on an average scale. However, by introducing the detrended fluctuation analysis (DFA) model for financial markets, Uritskaya (2005a, b) showed that the presence or absence of long-term correlations can be systematically lower or

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higher than the mean for the same time series depending on the time scale studied. According to Uritskaya and Serletis (2008), this is a significant problem in developing appropriate mathematical tools to quantify and model the market inefficiencies. They proposed a novel approach to analyzing price dynamics in markets with arbitrary correlation patterns based on scale-dependent fractal exponent. This exponent is evaluated by implementing the DFA algorithm for price fluctuations at different time scales. Following this study, the focus of research on energy prices from the late 2000s and onward in 2010s shifted to a market efficiency with a fractal approach (Alvarez-Ramirez & Escarela-Perez, 2010; David et al., 2019; Feng et al., 2011; Kristoufek & Vosvrda, 2014; Liu et al., 2020). At the end of 2019, an outbreak of “unexplained pneumonia” occurred in Wuhan. On January 30, 2020, the WHO listed the then-freshly discovered coronavirus as a public health emergency of international concern. Finally, on February 11, this organization termed it “COVID-19.” The official announcement of the pandemic of the disease on March 11, 2020, led to significant fluctuations in energy prices including crude oil (Jia et al., 2021). According to the WEO (2021) report, the economic recovery in late 2021 put so much pressure on energy prices that crude oil prices rose from $20 a barrel in mid-2020 to approximately $70 in mid-2021. Natural gas spot prices around the world witnessed a steady rise and hit their highest levels in Europe in the second half of 2021 (more than ten times the lowest record in June 2020). High prices for natural gas and coal pushed electricity prices up in many markets, especially in areas with relatively low renewable energy production. The COVID-19 pandemic, which led to a virtually unprecedented drop in new investment in oil and gas in 2020, intensified the rise in energy prices. The COVID-19 pandemic crisis and its impact on energy markets might be considered the most significant event after the 1970 crisis and the recession of 2007–2008. Given the significant impact of this phenomenon on sharp fluctuations in energy prices and the latest developments in relevant studies in recent years, the present study aims to examine the fractal characteristics and measure the efficiency of the US energy markets (as one of the most significant energy markets in the world) including the crude oil and some significant petroleum products, natural gas, and electricity markets with the MF-DFA approach and the impact of the 2020 pandemic crisis on this market. Previous studies have confirmed the existence of multifractal (rather than monofractal) structures in energy markets and in the efficiency studies of these markets. This approach has received less attention though. Hence, one of the contributions of the present chapter is the measurement of efficiency in the markets studied with the MF-DFA technique. Considering a diverse range of energy markets, unlike previous studies that focused on one market (mainly crude oil), the study on the impact of the COVID-19 pandemic as a great recent event affecting the world’s energy market is among other contributions to the present study. The following sections of the chapter are as follows: In Sect. 2, a review of methodological developments and empirical studies is provided. An analysis of the US energy markets and the role of the pandemic crisis in its fluctuations are reviewed

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in Sect. 3. Section 4 describes the methodology. Finally, Sects. 5, 6, and 7 provide key results, discussions, and suggestions.

2 Literature Review The EMH, introduced in the studies of Bachelier (1900) and Cootner (1964), was theorized by Samuelson (1965) and mathematically proved that future price fluctuations would be random. Subsequently, Fama (1970) introduced the EMH into financial markets. He considers the market as “efficient” in which prices always reflect the available information completely. Initially, this hypothesis was considered to examine stock price efficiency in financial markets (Qian & Rasheed, 2004; Peters, 1991; Corazza & Malliaris, 2002; Grech & Mazur, 2004). In the following, Peters (1991) considered the EMH as an immediate reaction of investors to new information and the lack of future connection to the present and the past. However, most people wait for the information to be verified and do not take action until the process is in place, but improperly combined information can lead to the formation of a biased random walk. This was studied by Hurst in the 1940s and then by Mandelbrot in the 1960s. Mandelbrot dubbed it “fractional Brownian motions” presently known as the “fractal time series” (Peters, 1991). Thus, in the 1990s, the introduction of fractal structures to examine the efficiency of markets in the field of economics was provided. Energy markets, due to oscillating and nonlinear structures (Agbon & Araque, 2003; Panas & Ninni, 2001) and the analysis of their behaviors in the context of fractal structures, have been considered from the 2000s (e.g., Dong et al. (2009), Gerogiorgis (2009), He et al. (2007), Serletis and Andreadis (2004), Uritskaya and Serletis (2008)). In the meantime, examining the efficiency of energy markets with a fractal approach is a recent research concern. Alvarez-Ramirez et al. (2008) examined the EMH regarding world’s crude oil prices. In this study, Hurst exponent estimation in the framework of DFA in 1987–2007 has been utilized to examine the market efficiency. A closer glance at market efficiency could be achieved by combining the fractal approach with a standard signal analysis tool. This issue is analyzed in Uritskaya and Serletis (2008) using two techniques, namely, DFA and Fourier power spectrum, to evaluate the efficiency of two types of energy markets with storage capacity (AECO Alberta natural gas) and without storage capacity (Alberta and Mid-Colombia electricity). The results demonstrated that price fluctuations are inefficient in all markets studied. One of the highlights of fractal energy studies in the 2000s is the move from mono-fractal to multifractal models. This approach in Alvarez-Ramirez et al. (2002) was introduced to analyze the crude oil prices. The development of energy market efficiency studies is a topic that has received more focus in the 2010s. Given that in energy markets, price autocorrelation has a delaying effect, Alvarez-Ramirez and Escarela-Perez (2010) analyzed the crude oil market efficiency (such as WTI) in the 1986–2009 using lagged DFA technique. This research portrayed significant

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deviations from efficiency in the market, as opposed to other papers that have suggested efficient behavior for large time scales. Delay effects might mask positive or negative autocorrelations. Kristoufek and Vosvrda (2014) analyzed the market efficiency of different commodities utilizing a fractal approach, for example, Hurst exponent, fractal dimension, and Hall-wood test estimator. In previous studies, the effect of a specific event on the efficiency of energy markets has not been considered much. This issue in David et al. (2019) was regarded. The impeachment of the president of Brazil in 2016 and the adoption of new policies in the energy sector of this country influences this study to examine its impact on the efficiency of the ethanol and gasoline markets using the DFA technique. The results show that the market is moving toward better efficiency for gasoline market after the change in government policy. Another significant event that could affect the efficiency of worldwide energy markets is the outbreak of COVID-19. Major studies conducted in 2021 have examined the economic impact of COVID-19 on the energy sector with difference-in-difference (DID) models, econometric, and general equilibrium models such as CGE. The effect of the pandemic on the reduction of electricity consumption in China’s Hunan Province in the early stages of the pandemic is addressed in the study of Ai et al. (2022). Also, Huang and Liu (2021) studied the risk reduction of falling shares of Chinese energy companies in the post-COVID-19 period with the DID technique. Pradhan and Ghosh (2021) analyzed the impact of pandemics on the energy sector and macroeconomic variables using CGE approach. Jia et al. (2021) conducted a similar study in India and China. The results in both studies reveal the effects of the pandemic on reducing carbon emissions. Other studies have attempted to use econometric approaches to examine fluctuations in energy consumption and prices in the preand post-pandemic periods of COVID-19. VAR is the most significant technique used in this regard (Hammoudeh et al., 2021; Si et al., 2021; Smith et al., 2021). Table 1 summarizes some studies conducted in the field of energy market efficiency based on the fractal approach. The present study aims to analyze the efficiency of the US energy markets (crude oil, gasoline, heating oil, natural gas, and electricity) in the period before and after the outbreak of COVID-19 using the MF-DFA. In general, based on experimental studies and the latest developments in methodology, a few points regarding the contributions of the present study should be considered: 1. Studies examining fractal structures in the energy market have emphasized the existence of multifractal behaviors in these markets (Alvarez-Ramirez et al., 2008; David et al., 2019; Ftiti et al., 2019; Ghosh et al., 2016; Liu et al., 2020; Norouzzadeh et al., 2007; Wang et al., 2014; Zhang & Wang, 2010; Zhao et al., 2016). However, most studies conducted via DFA technique have examined efficiency.

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Table 1 Summary of some studies in the field of energy sector efficiency with the fractal approach Row 1

Main topic Energy market efficiency

Subtopic Fractal structure in the US energy market

Time series WTI Henry Hub natural gas

Authors Serletis and Andreadis (2004)

2

Efficiency in Canadian electricity and natural gas markets

Uritskaya and Serletis (2008)

3

Predictability of the international crude oil market US crude oil market efficiency

Alberta and Mid-Columbia Electricity Market AECO Alberta natural gas market Brent, WTI, and Dubai (Persian Gulf) WTI

4

5

Market efficiency of various goods (energy and non-energy)

US commodity

6

The efficiency of the Brazilian ethanol and gasoline market

Ethanol and gasoline prices in Brazil

AlvarezRamirez et al. (2008) AlvarezRamirez and EscarelaPerez (2010) Kristoufek and Vosvrda (2014)

David et al. (2019)

Methodologies Hurst exponent structure-function test turbulent behaviors DFA and combination with Fourier power spectrum

DFA

Lagged DFA multi-scaling

Hurst exponent fractal dimension Hall-Wood estimator DFA efficient index (EI) Hall-Wood estimator

2. Studies on the efficiency of the US energy market have focused mainly on the crude oil market; nonetheless, other markets including natural gas, electricity, and gasoline are less studied. 3. The study of the COVID-19 pandemic and its impact on the energy sector, considered in the 2021 studies, has mainly dealt with the impact of this health phenomenon on energy consumption and other macroeconomic variables with econometric and general equilibrium approaches. However, now, about 2 years after the onset of this pandemic, adequate data are available for the post-pandemic period (the time series of prices in daily frequency), and it is possible to examine the efficiency of energy markets pre- and post-pandemic with fractal approaches, an issue that has not been addressed in studies so far.

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3 US Energy Markets and COVID-19 Pandemic To analyze the US energy markets, five categories of markets are studied, crude oil, gasoline, heating oil, natural gas, and electricity, based on time series data published by the US Energy Information Administration (EIA) at www.eia.gov.1 The data studied in this chapter comprise the traded price of energy in five aforementioned markets in daily frequency. A summary of the energy price time series is given in Table 2. Because the purpose of this study is to investigate the effect of the COVID-19 pandemic on the price efficiency of the US energy markets, the analysis of these markets has been performed in two periods, before and after the onset of the pandemic. Table 3 describes the period studied for the two sections. For the possibility of correct comparison between the two periods, the length of the days studied for each period is approximately 480 days. On March 11, 2020, the WHO officially announced that the COVID-19 virus had been detected in Wuhan, China. Therefore, this date is considered a basis for the starting point in this study. To analyze the selected energy markets in the USA and calculate its efficiency, price return as r t = Log p pt has been used. Figure 1 shows the trend of changes in t-1

energy price returns in selected US markets before and after the outbreak of the Table 2 Selected US energy markets Energy type Crude oil Gasoline Heating oil Natural gas Electricity

Energy market West Texas Intermediate Conventional Gasoline Heating oil Henry Hub natural gas PJM West

Data series Cushing, OK WTI Spot Price FOB

Abbreviation WTI

New York Harbor Conventional Gasoline Regular Spot Price FOB New York Harbor No. 2 Heating Oil Spot Price FOB Henry Hub natural gas spot price

NYH C. Gasoline NYH H. Oil

PJM WH Real-Time Peak

PJM

HH

Table 3 US energy market analysis time periods

Start day End day

1

Period 1 (before COVID-19 pandemic) April 23, 2018 March 10, 2020

Period 2 (after COVID-19 pandemic) March 11, 2020 January 24, 2022

Crude oil data available in http://www.eia.gov/dnav/pet/pet_pri_spt_s1_d.htm Natural gas data available in https://www.eia.gov/dnav/ng/ng_pri_fut_s1_d.htm Electricity data available in https://www.eia.gov/electricity/wholesale/

Apr 23, 2018 May 23, 2018 Jun 23, 2018 Jul 23, 2018 Aug 23, 2018 Sep 23, 2018 Oct 23, 2018 Nov 23, 2018 Dec 23, 2018 Jan 23, 2019 Feb 23, 2019 Mar 23, 2019 Apr 23, 2019 May 23, 2019 Jun 23, 2019 Jul 23, 2019 Aug 23, 2019 Sep 23, 2019 Oct 23, 2019 Nov 23, 2019 Dec 23, 2019 Jan 23, 2020 Feb 23, 2020 Mar 23, 2020 Apr 23, 2020 May 23, 2020 Jun 23, 2020 Jul 23, 2020 Aug 23, 2020 Sep 23, 2020 Oct 23, 2020 Nov 23, 2020 Dec 23, 2020 Jan 23, 2021 Feb 23, 2021 Mar 23, 2021 Apr 23, 2021 May 23, 2021 Jun 23, 2021 Jul 23, 2021 Aug 23, 2021 Sep 23, 2021 Oct 23, 2021 Nov 23, 2021 Dec 23, 2021 Jan 23, 2022

Apr 23, 2018 May 23, 2018 Jun 23, 2018 Jul 23, 2018 Aug 23, 2018 Sep 23, 2018 Oct 23, 2018 Nov 23, 2018 Dec 23, 2018 Jan 23, 2019 Feb 23, 2019 Mar 23, 2019 Apr 23, 2019 May 23, 2019 Jun 23, 2019 Jul 23, 2019 Aug 23, 2019 Sep 23, 2019 Oct 23, 2019 Nov 23, 2019 Dec 23, 2019 Jan 23, 2020 Feb 23, 2020 Mar 23, 2020 Apr 23, 2020 May 23, 2020 Jun 23, 2020 Jul 23, 2020 Aug 23, 2020 Sep 23, 2020 Oct 23, 2020 Nov 23, 2020 Dec 23, 2020 Jan 23, 2021 Feb 23, 2021 Mar 23, 2021 Apr 23, 2021 May 23, 2021 Jun 23, 2021 Jul 23, 2021 Aug 23, 2021 Sep 23, 2021 Oct 23, 2021 Nov 23, 2021 Dec 23, 2021

Apr 23, 2018 May 23, 2018 Jun 23, 2018 Jul 23, 2018 Aug 23, 2018 Sep 23, 2018 Oct 23, 2018 Nov 23, 2018 Dec 23, 2018 Jan 23, 2019 Feb 23, 2019 Mar 23, 2019 Apr 23, 2019 May 23, 2019 Jun 23, 2019 Jul 23, 2019 Aug 23, 2019 Sep 23, 2019 Oct 23, 2019 Nov 23, 2019 Dec 23, 2019 Jan 23, 2020 Feb 23, 2020 Mar 23, 2020 Apr 23, 2020 May 23, 2020 Jun 23, 2020 Jul 23, 2020 Aug 23, 2020 Sep 23, 2020 Oct 23, 2020 Nov 23, 2020 Dec 23, 2020 Jan 23, 2021 Feb 23, 2021 Mar 23, 2021 Apr 23, 2021 May 23, 2021 Jun 23, 2021 Jul 23, 2021 Aug 23, 2021 Sep 23, 2021 Oct 23, 2021 Nov 23, 2021 Dec 23, 2021 Apr 23, 2018 May 23, 2018 Jun 23, 2018 Jul 23, 2018 Aug 23, 2018 Sep 23, 2018 Oct 23, 2018 Nov 23, 2018 Dec 23, 2018 Jan 23, 2019 Feb 23, 2019 Mar 23, 2019 Apr 23, 2019 May 23, 2019 Jun 23, 2019 Jul 23, 2019 Aug 23, 2019 Sep 23, 2019 Oct 23, 2019 Nov 23, 2019 Dec 23, 2019 Jan 23, 2020 Feb 23, 2020 Mar 23, 2020 Apr 23, 2020 May 23, 2020 Jun 23, 2020 Jul 23, 2020 Aug 23, 2020 Sep 23, 2020 Oct 23, 2020 Nov 23, 2020 Dec 23, 2020 Jan 23, 2021 Feb 23, 2021 Mar 23, 2021 Apr 23, 2021 May 23, 2021 Jun 23, 2021 Jul 23, 2021 Aug 23, 2021 Sep 23, 2021 Oct 23, 2021 Nov 23, 2021 Dec 23, 2021 Apr 23, 2018 May 23, 2018 Jun 23, 2018 Jul 23, 2018 Aug 23, 2018 Sep 23, 2018 Oct 23, 2018 Nov 23, 2018 Dec 23, 2018 Jan 23, 2019 Feb 23, 2019 Mar 23, 2019 Apr 23, 2019 May 23, 2019 Jun 23, 2019 Jul 23, 2019 Aug 23, 2019 Sep 23, 2019 Oct 23, 2019 Nov 23, 2019 Dec 23, 2019 Jan 23, 2020 Feb 23, 2020 Mar 23, 2020 Apr 23, 2020 May 23, 2020 Jun 23, 2020 Jul 23, 2020 Aug 23, 2020 Sep 23, 2020 Oct 23, 2020 Nov 23, 2020 Dec 23, 2020 Jan 23, 2021 Feb 23, 2021 Mar 23, 2021 Apr 23, 2021 May 23, 2021 Jun 23, 2021 Jul 23, 2021 Aug 23, 2021 Sep 23, 2021 Oct 23, 2021 Nov 23, 2021 Dec 23, 2021

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0.2 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 Crude Oil, WTI Return Spot Price Series

0.11 Conventional Gasoline, New York Harbor Return Spot Price Series

0.06

-0.04 0.01

-0.09

-0.14

0.06 0.04 0.02 0 -0.02 -0.04 -0.06 -0.08 -0.1

Heating Oil, New York Harbor Return Spot Price Series

0.1 0.08 0.06 0.04 0.02 0 -0.02 -0.04 -0.06 -0.08 -0.1

Natural Gas, Henry Hub Return Spot Price Series

0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4

Electricity, PJM West Return Spot Price Series

Fig. 1 Energy prices return trend in selected US energy markets: before and after the COVID-19 pandemic period. (Source: EIA data and research findings)

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COVID-19. Some significant points from the diagrams drawn in Fig. 1 can be considered: 1. From the end of the first period (before the outbreak of COVID-19), that is, around February 1, 2020, when the WHO designated the virus as a global alert and as COVID-19, to the beginning of the second period (after the outbreak of COVID-19), that is, toward the end of May 2020, which is the first 4 months of a worldwide pandemic outbreak, sharp fluctuations are observed in almost all energy markets. In other words, this reveals the strong impact of the pandemic on America’s most significant energy markets. Although the market trend has returned to normal after the first 4 months of the pandemic outbreak, its impact on the post-pandemic period needs to be analyzed in some way. 2. The trend of price return fluctuations after the initial 4-month period of the COVID-19 outbreak is not the same in all energy markets compared to the period before the pandemic outbreak. In other words, the impact of the pandemic on energy price returns has not been the same in all markets. Some markets, including the heating oil market, have experienced more sharp fluctuations after the period of the pandemic outbreak than fluctuations in the previous period of COVID-19 compared to other markets for crude oil products. Descriptive statistics of the return-time series on selected US energy prices are presented in Table 4. The results demonstrate that the kurtosis coefficient in all markets is greater than 3 indicating more kurtosis (more distribution around the average return) than the normal distribution. The Jarque-Bera statistic exhibits the entire time series of energy price returns in the US market, before and after COVID19, rejecting the hypothesis of normal distribution. In addition, reviewing the ADF test statistics for the time series of energy prices confirms non-stationary for all energy price time series (except natural gas prices in the second period). Therefore, a nonlinear analytical framework for studying the efficiency of energy markets is more appropriate than other approaches. Finally, Fig. 2 presents the standard deviation of the time series of energy price returns before and after the COVID-19 pandemic period (σ) as an increase over the time scale (τ) in the form of a moving window. The results show that all energy prices return time series are nonstationary. In other words, the standard deviation of increments in the time series of returns is not saturated relative to the time scale. In a non-stationary situation, spurious correlations may be detected over time. Therefore, direct calculation of correlation behavior, Hurst exponent, spectral density exponent, etc. could lead to unreliable results. Accordingly, it is necessary to use this type of time series with methods that are not sensitive to non-stationaries such as MF-DFA (Norouzzadeh et al., 2007).

Source: EIA data and research findings

Mean Median Maximum Minimum Standard deviation Skewness Kurtosis Jarque-Bera Probability Prob (ADF test for energy price)

Return price WTI Period 1 Period 2 -0.0006 0.0015 0.0003 0.0015 0.0616 0.1849 -0.1222 -0.1194 0.0114 0.0220 -2.5106 1.5924 33.0406 26.7883 18127.8 11232.4 0.0000 0.0000 0.8459 0.6703 Conventional gasoline Period 1 Period 2 -0.0005 0.0008 0.0001 0.0021 0.0469 0.0965 -0.0881 -0.1302 0.0100 0.0174 -1.3903 -1.4976 17.0746 21.8472 4013.6 7132.0 0.0000 0.0000 0.7806 0.8709

Heating oil Period 1 Period 2 -0.0005 0.0007 0.0002 0.0015 0.0455 0.0486 -0.0770 -0.0802 0.0081 0.0132 -1.5687 -0.9447 21.5619 9.5309 6910.6 905.2 0.0000 0.0000 0.9591 0.9656

Table 4 Descriptive statistics of energy price returns time series in selected US energy markets Henry hub Period 1 -0.0003 0.0000 0.1246 -0.1260 0.0173 -0.2324 16.1783 3412.4 0.0000 0.4496

Period 2 0.0007 0.0000 0.3238 -0.4452 0.0421 -1.0659 44.7042 34221.8 0.0000 0.0000

PJM Period 1 -0.0005 -0.0036 0.4853 -0.3145 0.0803 0.2772 8.0476 507.1 0.0000 0.2429

Period 2 0.0014 0.0004 0.2794 -0.3362 0.0793 -0.0376 4.8355 64.4 0.0000 0.4721

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WTI-Period2

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0.010

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0.002 0.000 0

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0.03 0.02

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0 400

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τ

Fig. 2 Moving window of standard deviations of energy prices return versus time scales in selected US energy markets. (Source: EIA data and research findings)

4 Methodology DFA is introduced by Peng et al. (1994). In the DFA technique, the time series with length N is divided into (N/s) equal parts, and the average function of the detrended fluctuation is expressed as relation 1:

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F 2 ðsÞ  sH

ð1Þ

where H is the Hurst exponent. Kantelhardt et al. (2002) generalized the DFA method to MF-DFA, which makes it possible to identify the multifractal behavior of the data. They performed the MF-DFA technique in five steps as follows: In the first stage, we would specify the profile: For this purpose, time series x(i) with length N and average x is considered and the profile is calculated as relation (2): i

jxðkÞ - xj i = 1, 2, . . . , N

yðiÞ =

ð2Þ

k=1

In the second stage, we divide the profile y(i) into int Ns  N s part with length s that would not overlap. Since in most cases the length of the time series is not an exact multiple of the time scales, a small portion of the end of the profile remains. Therefore, in order not to ignore this part of the time series, the division process is performed once again from the end of the time series. So finally, 2 Ns of parts are obtained. In the third stage, we calculate the local trend of each of the 2 Ns parts using the fitting of the least squares of the time series and determining the variance as in relation (3): F 2 ðυ, sÞ 

1 s

s i=1

fy½ðυ - 1Þs þ i - yυ ðiÞg2

ð3Þ

This variance is calculated for each part υ of the time series such that υ = 1,. . ., Ns. The variance for υ = Ns + 1, . . ., 2Ns is also calculated as Eq. (4): F 2 ðυ, sÞ 

1 s

s i=1

fy½N - ðυ - N s Þs þ i - yυ ðiÞg2

ð4Þ

where yυ is a polynomial fitted to the υ part. In the fourth stage, averaging the whole parts to calculate the qth-order fluctuation function, F q ðsÞ 

1 2N s

1=q

2N s

F ðυ, sÞ 2

q=2

ð5Þ

υ=1

In the fifth stage, we determine the scaling behavior of the fluctuation function by analyzing the logarithmic-logarithmic curve Fq(s) in terms of s for different values of q. For this purpose, the fluctuation function is written as relation (6):

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F q ðsÞ  sH q

173

ð6Þ

Hq is the generalized Hurst exponent. If the logarithm-logarithmic curve Fq(s) is plotted in terms of s for different values of q, the slope of the regression line is the generalized Hurst exponent. If Hq is dependent on s, the series in question has multifractal properties; otherwise, it will be single-fractal. Hq, is just one of several types of scaling components used to parameterize a time series with a multifractal structure. The usual method in MF-DFA literature is to use Hq, the scaling exponent, τ(q), beas calculated in relation (7): τðqÞ = qH q - 1

ð7Þ

Then τ(q) becomes the singularity exponent of the order q, that is, h(q), and the singularity spectrum of the order q, that is, D(q) (Kantelhardt et al., 2002): hð qÞ =

DðqÞ = q

dτðqÞ dq

dτðqÞ - τ ð qÞ dq

ð8Þ

ð9Þ

The MF-DFA technique has been widely implemented to identify long-term autocorrelation in financial markets such as stock markets, foreign exchange markets, and gold markets (Zhuang et al., 2015). The correlation function is expressed based on Hurst exponent as relation (10): C = 2ð2h - 1Þ - 1

ð10Þ

If the Hurst exponent is equal to 0.5, the correlation is equal to zero. If the Hurst exponent is equal to 1, the correlation coefficient will also be 1, which indicates a completely positive correlation. If the Hurst exponent is between 0 and 0.5, there is anticorrelation behavior. This means that if the time series in the previous period are high, they will most likely be low in the next period. When the Hurst exponent is between 0.5 and 1, the time series is correlated and has long-term memory at all time scales. For instance, daily price changes are related to future daily price changes. Moreover, weekly price changes are related to future weekly price changes (Norouzzadeh & Jafari, 2005). Weak efficiency dynamics of financial markets can also be identified using the generalized Hurst exponent. For a weak efficient market, all types of volatility must have a random walk behavior. In other words, the Hurst exponent of a different order q must be equal to 0.5. Accordingly, several different criteria have been used to calculate inefficiency in different studies. A simple criterion that has been widely used is Eq. (11) (Zhuang et al., 2015):

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ED = jhðq = 2Þ - 0:5j

ð11Þ

A higher value of ED indicates a larger deviation of the second-order Hurst exponent from 0.5. Hurst exponent is a measure of the long-term correlation and fractality of the time series. If a series is random and unrelated, the Hurst exponent value will be 0.5, and the ED value will be zero. Consequently, the higher the ED value, the more inefficient the market. Since the second-order Hurst exponent cannot account for all-time series fluctuations, another criterion would be used to calculate inefficiencies based on different values of the Hurst exponent at different orders: DME =

1 qmax - qmin þ 1

qmqx

EDðqÞ

ð12Þ

q = qmin

For an efficient market, the DME value, like ED, will be zero. Another similar criterion (Eq. 13) is introduced which considers only the characteristics of large and small fluctuations: DMEE =

1 ½EDðqmin Þ þ EDðqmax Þ 2

ð13Þ

Finally, another criterion that is widely used is the relation (14): ME =

1 ðjh ðqÞ - 0:5j þ jhmax ðqÞ - 0:5jÞ 2 min

ð14Þ

5 Empirical Results The empirical results consist of three parts. First, the curves obtained from the analysis of MF- DFA related to each data for both periods are calculated. Then, the generalized Hurst exponent results are reported, and various inefficiency criteria are calculated at the end. Figure 3 demonstrates the fractal features of various energy markets in the USA before and after COVID-19. Based on Fig. 3, it can be witnessed that all markets, although having different spectra, have multifractal properties in both periods. The widest spectrum is the Henry Hub natural gas price in the pre-and post-COVID-19 periods. Thus, the fractal feature of this market is more than other markets studied in both periods. Comparing the width of the multifractal spectrum for different markets pre- and post-COVID-19 shows that the fractality characteristic in the US energy markets has increased due to COVID-19. The Hurst diagram’s nonlinear (parabolic) relationship with increasing q confirms this.

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a. Crude Oil

b. Conventional Gasoline Fig. 3 The generalized Hurst exponent diagram in terms of order q and multifractal spectrum. (a) Crude oil, (b) conventional gasoline, (c) heating oil, (d) natural gas spot, and (e) electricity. (Source: Research findings)

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c. Heating Oil

d. Natural Gas Spot Fig. 3 (continued)

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e. Electricity Fig. 3 (continued)

Table 5 Generalized Hurst exponent in different degrees’ q and width of the multifractal spectrum before COVID-19 q -4 -3 -2 -1 0 1 2 3 4 qmax-qmin

Crude oil 0.65 0.631 0.63 0.588 0.565 0.542 0.521 0.501 0.484 0.299

Conventional gasoline 0.663 0.647 0.631 0.615 0.602 0.588 0.573 0.557 0.541 0.243

Heating oil 0.619 0.598 0.576 0.549 0.524 0.499 0.475 0.453 0.433 0.339

Natural gas spot 0.743 0.7 0.649 0.595 0.544 0.49 0.435 0.382 0.337 0.709

Electricity 0.233 0.215 0.194 0.171 0.145 0.117 0.088 0.06 0.034 0.363

Source: Research findings

The figures of the Hurst exponent in different orders of q exhibit that in all markets, the slope of the Hurst exponent in terms of q is negative and uniform before COVID-19; however, Hurst slope is not uniform and has less slope at negative qs (small fluctuations) than positive qs (large fluctuations) after COVID-19 due to the fluctuations created in the markets. Tables 5 and 6 also report the values of the generalized Hurst exponent in different orders and the width of the multifractal spectrum for different markets, before and after COVID-19, respectively. Figure 4 also reveals the changes in Hurst exponent values by energy markets before and after the pandemic outbreak, as can be witnessed that the generalized

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Table 6 Generalized Hurst exponent in different degrees’ q and width of the multifractal spectrum after COVID-19 q -4 -3 -2 -1 0 1 2 3 4 qmax-qmin

Crude oil 0.845 0.839 0.813 0.788 0.759 0.683 0.564 0.467 0.403 0.761

Conventional gasoline 0.689 0.673 0.653 0.63 0.598 0.544 0.467 0.394 0.341 0.592

Heating oil 0.639 0.623 0.604 0.581 0.551 0.507 0.443 0.376 0.322 0.565

Natural gas spot 0.68 0.656 0.624 0.685 0.526 0.409 0.221 0.07 0.018 1.059

Electricity 0.307 0.283 0.256 0.231 0.205 0.177 0.143 0.104 0.065 0.481

Source: Research findings

0.8

1 0.8

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0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

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HH Natural Gas (Before COVID-19)

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4

0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 -4

-3

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-1

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PJM Electricity (Before COVID-19) PJM Electricity (After COVID-19)

Fig. 4 The generalized Hurst values in terms of q values in the pre- and post-COVID-19 periods. (Source: Research findings)

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Table 7 Ranking the inefficiency based on different criteria before COVID-19 Energy market inefficiency DME DMEE ME Inefficiency ranking based on DME Inefficiency ranking based on DMEE Inefficiency ranking based on ME

Crude oil 0.101 0.15 0.15 5

Conventional gasoline 0.106 0.121 0.121 3

Heating oil 0.103 0.169 0.169 4

Natural gas spot 0.221 0.354 0.354 2

Electricity 0.368 0.382 0.382 1

4

5

3

2

1

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5

3

2

1

Source: Research findings

Table 8 Ranking the inefficiency based on different criteria after COVID-19 Energy market inefficiency DME DMEE ME Inefficiency ranking based on DME Inefficiency ranking based on DMEE Inefficiency ranking based on ME

Crude oil 0.29 0.38 0.38 3

Conventional gasoline 0.196 0.2955 0.2955 4

Heating oil 0.176 0.282 0.282 5

Natural gas spot 0.367 0.529 0.525 1

Electricity 0.316 0.338 0.338 2

2

4

5

1

3

2

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5

1

3

Source: Research findings

Hurst exponent for all markets decreased with increasing q. This means that the long-term memory characteristic in small fluctuations is more significant than that of the large fluctuations. Another conclusion that can be drawn from Fig. 4 is that Hurst values for negative and positive qs are influenced by COVID-19. In most markets, the Hurst exponent has increased for negative qs, that is, small fluctuations after COVID-19. That is, the predictability of small fluctuations has increased. However, in the case of large qs, or significant fluctuations, the opposite is true. That is, after COVID-19, the predictability of large fluctuations has decreased. Tables 7 and 8 compare the efficiency of energy markets pre- and postCOVID-19. Table 7 shows that before COVID-19, electricity/natural gas was the most inefficient market by all three criteria, DME, DMEE, and ME, respectively. Hence, according to all three criteria, crude oil, conventional gasoline, and heating oil had the lowest inefficiencies.

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0.60 0.53 0.50 0.38 0.38

0.40

0.34

0.35 0.30

0.30 0.28

0.17

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0.15 0.10

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0.00 Before COVID-19 WTI

Conv. Gasoline

After COVID-19 Heating Oil

HH Natural Gas

PJM Electricity

Fig. 5 The trend of changes in the efficiency values of the American energy markets in the pre- and post-COVID-19 periods. (Source: Research findings)

Table 8 presents the ranking of energy market inefficiency post-COVID-19. By comparing this table with Table 7 and Fig. 5, it can be seen that COVID-19 has increased the inefficiency of all markets except electricity. Electricity, which was the most inefficient market in pre-COVID-19 era, has improved slightly in terms of efficiency post-COVID 19, and as other markets have become much more inefficient, the electricity ranking has improved from 1 to 3.

6 Discussion In the US crude oil and petroleum product market, including gasoline and heating oil, the results of the MF-DFA analysis of energy price efficiency demonstrate that long-term memory is more volatile in short-term periods than in long-term ones. In reviewing the validity of this finding, Alvarez-Ramirez et al. (2002), AlvarezRamirez and Escarela-Perez (2010), He et al. (2007), and Liu et al. (2020) have emphasized the distinction between fractal structures in the short and long terms in the crude oil market; however, the studies of Alvarez-Ramirez et al. (2008) and Dong et al. (2009) explicitly state that in the WTI crude oil market, the effect of memory and price predictability in the short run is greater than that of the long run. In other words, based on the findings of the present study, in the longer run, the crude oil market has moved toward efficiency. As in Fig. 6, which shows the trend of WTI price changes in the two periods under review, in the previous period of pandemic outbreak, an almost efficient situation can be considered for the WTI market. However, with the outbreak of the pandemic as a significant and influential event in the energy markets, the trend of price dynamics and its efficiency has been significantly influenced, so that a sharp deviation from efficiency is observed in this period. At negative qs (fluctuations with

COVID-19 and Fractal Characteristics in Energy Markets. . .

New York Harbor Conventional Gasoline

2.5 2 1.5 1 0.5 0 Apr 23, 2018 Aug 23, 2018 Dec 23, 2018 Apr 23, 2019 Aug 23, 2019 Dec 23, 2019 Apr 23, 2020 Aug 23, 2020 Dec 23, 2020 Apr 23, 2021 Aug 23, 2021 Dec 23, 2021

Dec 23, 2021

Aug 23, 2021

Dec 23, 2020 Apr 23, 2021

Apr 23, 2020

Aug 23, 2020

Dec 23, 2019

Aug 23, 2019

Dec 23, 2018 Apr 23, 2019

Apr 23, 2018

Aug 23, 2018

3 2.5 2 1.5 1 0.5 0

New York Harbor No. 2 Heating Oil 3

Apr 23, 2018 Aug 23, 2018 Dec 23, 2018 Apr 23, 2019 Aug 23, 2019 Dec 23, 2019 Apr 23, 2020 Aug 23, 2020 Dec 23, 2020 Apr 23, 2021 Aug 23, 2021 Dec 23, 2021

WTI 100 90 80 70 60 50 40 30 20 10 0

181

Fig. 6 Energy prices trends in the US crude oil energy markets and petroleum products in the preand post-COVID-19 periods. (Source: EIA data)

short period), the value of the generalized Hurst exponent is significantly increased compared to the same values in previous period. In other words, the effect of memory on fluctuations with short periods has increased compared to previous period. In this case, the correlated situation is between WTI price returns, and this inefficiency can lead to price forecasting and profit in oil future trades. However, for positive qs, the generalized Hurst exponent values are decreasing compared to the previous period and moving toward inefficiency and anticorrelated status. Together, these two paths, as shown in Fig. 6, have established an overall upward trend for WTI prices in the post-pandemic period. Overall, the COVID-19 pandemic has led to the performance of the WTI market, which was the second lowest inefficient in the previous period, to be ranked fourth in the next period among the five energy markets. In other words, the WTI market has become more inefficient. In the case of the gasoline market, as in the WTI market, in the previous pandemic period, there was a deviation from greater efficiency in the short run, but overall, the relatively efficient situation is visible. With the outbreak of the COVID-19 pandemic, the efficiency of the gasoline market has also been influenced, so the severity of the deviation from the efficiency situation is significant in the difference between the fluctuations of short-term and long-term periods. In the short run, there is a relatively high correlated situation between price returns. Besides, similar to the WTI market, in fluctuations with longer periods, the generalized Hurst exponent value decreased compared to the previous period and moved toward the anticorrelated inefficient situation, which can lead to price increases as expected (Fig. 6). In general, inefficiency in this market has increased in the post-pandemic period. The trend of efficiency changes in the heating oil market has almost followed the path of WTI and gasoline markets. However, the severity of inefficiency in this market has been less than other oil markets after the outbreak of the pandemic. Generally, the increase in multifractal features in the US oil energy market after the outbreak of the pandemic indicates the formation of several factors in reducing efficiency and increasing forecasting power in this market. According to a US report, Short-Term Energy Outlook (STEO) (2021), world crude oil prices fell sharply

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Henry Hub Natural Gas

PJM WH Real Time Peak

Jan 23, 2022

Jan 23, 2022

Jul 23, 2021

Oct 23, 2021

Jan 23, 2021

Apr 23, 2021

Jul 23, 2020

Oct 23, 2020

Jan 23, 2020

Apr 23, 2020

Jul 23, 2019

Oct 23, 2019

Jan 23, 2019

Apr 23, 2019

Jul 23, 2018

Oct 23, 2018

Apr 23, 2018

Apr 23, 2018 Jul 23, 2018 Oct 23, 2018 Jan 23, 2019 Apr 23, 2019 Jul 23, 2019 Oct 23, 2019 Jan 23, 2020 Apr 23, 2020 Jul 23, 2020 Oct 23, 2020 Jan 23, 2021 Apr 23, 2021 Jul 23, 2021 Oct 23, 2021

160.00 140.00 120.00 100.00 80.00 60.00 40.00 20.00 0.00

7 6 5 4 3 2 1 0

Fig. 7 Energy prices trends in the US natural gas and electricity markets in the pre- and postCOVID-19 periods. (Source: EIA data)

about 4 months after the outbreak of COVID-19, which fell from $50 a barrel to $12 due to continuous withdrawals and declining stock volumes; it has been steadily increasing. The prevalence of new corona strains and the possibility of disruptions in crude oil supply are factors that have put pressure on crude oil prices due to OPEC+ decisions and increased drilling rates by US oil and natural gas producers. Thus, in general, the response to the growth of energy demand in the world after the outbreak of the pandemic, and consequently the reduction of world oil stocks and the risk of mismatch between supply and demand growth, has increased an inefficiency in this market leading to inefficiency, and the power of forecasting will increase in the short term in the US crude oil and oil product market. In the case of Henry Hub natural gas market, the generalized Hurst exponent value in the pre-pandemic period has always been more than 0.5 and relatively high in short-term fluctuations. In other words, there was a correlated inefficiency situation between price returns. According to STEO (2021), the global demand for liquefied natural gas in the USA remains high, limiting downward pressure on natural gas prices in the years following the COVID-19 outbreak. Significant differences between US Henry Hub prices and spot prices in Asia and Europe, and declining inventories in Europe well below their 5-year average, have contributed significantly to US LNG demand. These issues are among the multiple factors leading to a reduction in market efficiency as present in Fig. 7. In other words, the intensification of the memory effect on Henry Hub’s price returns after the outbreak of the pandemic has followed such a pattern. In the US electricity market (PJM West market for instance), the results show that in the pre-pandemic period, the magnitude of the generalized Hurst exponent is always less than 0.5 in all qs; there exists a significant deviation from efficiency. A high level of anticorrelated status is observed during this period. The formation of a continuous upward price trend in the previous period of the pandemic outbreak is an evidence of this claim according to Fig. 7. In the post-COVID-19 period, the generalized Hurst exponent value is still less than 0.5, and the same anticorrelated inefficiencies are still present in this market. Although these values have increased somewhat compared to the previous period and as a result, the PJM market

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efficiency situation has improved in Fig. 5, it cannot be considered as a valid reason for the market to move toward efficiency. One reason for this is that the possibility of predicting the price and influencing future contracts and arbitrage is relatively low due to the nature of the impossibility of storage or the high cost of storage equipment, which is practically not very economical. The identification of inefficiency in this market obtained in the present study has already been confirmed in Uritskaya and Serletis (2008).

7 Conclusion and Policy Implications Economic studies suggest that periods of energy market inefficiencies can be mainly related to predictable economic conditions such as seasonal demand or the effects of a natural disaster (such as a cold winter period). In this study, it was demonstrated that the outbreak of the COVID-19 pandemic has been able to influence the fractal structure pattern and the efficiency of US energy markets, especially in the short run. Short-term inefficiency can influence the decisions of investors in these markets, so that using analytical tools, they obtain data from the short-term price trend and set their position in the market in the same short-term period. Some concluding remarks of the present study can be expressed as follows: – The relationship between energy price returns over different amounts of q is quite variable and, in some markets, shows significant differences. This indicates the existence of multifractal behaviors in all US energy markets. The prevalence of COVID-19 pandemic has increased the multifractal spectrum in almost all markets. Larger fractal degrees mean a wider range of nonlinear behavior of energy price returns. This result confirms the effect of various factors on its dynamic process over time. – The outbreak of the COVID-19 has reduced the efficiency of virtually all energy markets (except PJM). The possibility of storage in the energy markets (excluding the electricity market) and the increase in energy demand during the pandemic outbreak can be a strong reason to reduce efficiency and improve the predictability of these markets. However, like other markets, it is still possible to forecast prices at a relatively high level in the short term. – In general, in all US energy markets after the pandemic outbreak, long-term memory increased in the short run compared to the same period prior to the pandemic outbreak. In other words, there are short-term inefficiencies in the US energy markets. However, in the end, this situation is approximately close to the efficiency situation, and technical analysis of efficiency dynamics fails to have significant predictive power in energy future markets. In other words, the prevalence of the present pandemic and the fluctuations in energy markets have increased the predictability of these markets in the short term and enabled market players to make a profit in these periods.

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Overall, it can be mentioned that COVID-19 was one of the events to be capable of changing the fractality pattern in the US energy market. Inefficiency can bring significant benefits due to the growing demand for energy after the pandemic especially in countries seeking to offset their economic growth. The USA, OPEC, and China are the most significant energy market players thriving to profit from the forecast of oil prices. Acknowledgments Data availability: www.eia.gov Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this chapter. Formatting of Funding Sources This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Fractal Organizations and Employee-Organization Relationship Dynamics Fatemeh Rezazadeh

, Sima Rezazadeh

, and Mina Rezazadeh

1 Introduction In the last two decades, the study of employees’ relationships with each other and with organizations aimed at providing theoretical foundations for understanding the employees’ different views on an exchange as an approach has become an essential and integral part of the employee-organization relationship (EOR) (Ribeiro & Urbano, 2010: 350(. EOR, a broad term to describe, allows the organizations to improve and develop the affairs to achieve sustainable competitive advantage and is a prerequisite for effective organizational performance and the health and cohesion of the organizations. In addition, it is considered a vital stimulus to link human resource management procedures and strategies and organizational behavior to tangible business results such as the quality of customer service, employees’ loyalty, and effective job performance. Accordingly, concentrating on this issue contributes to the managers’ understanding of the possible obstacles and the minor relationship inconsistencies through predicting and identifying the type of relationships and striving to create, sustain, and promote practical and dynamic employment relationships (Rezazadeh et al., 2022c: 75). Today, considering the hierarchical levels and division of responsibilities among frontline members, most organizations increasingly function as living systems in nature. This process may reflect the growth of human consciousness and the awareness of mutual relationships between employees F. Rezazadeh (✉) Organizational Behavior, Allameh Tabataba’i University, Faculty of Management and Accounting, Tehran, Iran e-mail: [email protected] S. Rezazadeh Faculty of Management and Accounting, Islamic Azad University Shiraz Branch, Shiraz, Iran M. Rezazadeh Faculty of Engineering, Islamic Azad University Shiraz Branch, Shiraz, Iran © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Faghih (ed.), Time and Fractals, Contributions to Management Science, https://doi.org/10.1007/978-3-031-38188-1_8

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and organizations (Malone, 2004: 71). On the other hand, the process of using chaos theory and fractals has spread its radiations beyond the field of physical sciences and has provided new research in theorizing and explaining the phenomena of change, evolution, growth, and development in a wide range of behavioral and cognitive sciences. This fact, in turn, can expand the usage of fractal theory in management research and its functions (Faghih, 2006: 18). Fractal organizations may have more meetings and conversations, but due to efficient operating principles, they always do more in less time, referred to as natural hierarchy reflecting various levels of members’ knowledge, skills, and capabilities (Raye, 2014: 65). This is a relatively new idea that the geometry of organizational structure can influence the interpersonal relationships and also can be the basis of systemic behavior. Fractal plans enable democracy, primarily at the team level, as long as everyone has a “vote” in team decisions. However, not all opinions align with the goal and common organization’s values, so the presence of leaders as conversation facilitators seems necessary. Because instead of focusing on specific organizational or employee’s problems, leadership can comprehend the interrelationship between employee and organization (Martens, 2011: 4). Therefore, how people interact with the work environment determines the quality of the results. The present chapter covers topics such as chaos and evolution in management systems, theoretical literature of EOR, theoretical literature of fractal and fractal organization, commonalities between EOR and fractal organization, and the necessity of fractal dynamic behavior in the optimal management of EOR are explained and interpreted. Eventually, the chapter ends with a discussion and conclusion.

2 Chaos and Evolution in Management Systems: An Example of Human Systems The word chaos is equivalent to confusion, mess, and anarchy (Faghih, 2006: 19). The systemic approach is one of the leading aspects of management science, and in this, the approach of systemic dynamics has a fundamental aspect. In dynamic management systems, the variety of distinct elements in the system’s structure and the multiplicity of its relationships can be very complex and complicated. They often consist of nonlinear systems with nonlinear interactions and human factors (with nonlinear functions). Hence, management systems can lead to chaotic situations. The dependence and sensitivity to the initial conditions to the extent of the butterfly effect indicates that seemingly minor changes can be the source of significant changes in the system, which may originate from inside or outside the system. Chaos leads to a new and more complex order with a higher level. This new stability arising from chaos is often achieved due to the effect and consequence of self-organizing internal processes. Such processes are motivated by the organization’s fundamental goals and its leaders’ values and are more dependent on their internal foundations or organizational context than environmental factors. This emerging framework

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establishes a revised behavioral model to guide new relationships and processes in the system. Finally, this systematic renewal modifies, modulates, and evolves the essential characteristics. This process of self-organization can continue indefinitely in the process of organization evolution to establish various balance points over time. Therefore, understanding the dynamic process of innovativeness in the organization is crucial for scientific management (Faghih, 2006: 61–67).

3 Theoretical Literature of EOR The first studies of EOR as the established construct of formal and systematic research date back to the 1980s and are rooted in the classic work of Chester Barnard (1938) under the title of “Resources Exchanged” and the concept of “Exchange of Utilities.” The study of EOR is mainly based on Blau’s social exchange theory (1964), Gouldner’s oppositional norm theory (1960), and March’s and Simon’s inducements-contributions model (1958), and developing the model by Tsui et al. (1997) is considered as the dominant theoretical basis for the study of EOR in the last three decades to describe and classify different individual and organizational relationships and their consequences in desired organizational tendencies and behaviors (Shore et al., 2012: 1; Gillis, 2017: 1). The concept of psychological contract (PC) that was first proposed by Chris Argyris (1960), along with perceived organizational support as the micro level and employment relationship (ER) as the macro level, creates three primary levels for the concept of EOR (Baranova & Ivana, 2019: 201). EOR can be defined as the degree of trust between an organization and its employees (Men & Sung, 2019: 7), and four essential dimensions of EOR, such as mutuality control, trust, satisfaction, and commitment, have been presented by Hon and Grunig (1999).

4 Theoretical Literature of Fractal and Fractal Organization Fractal is derived from the Latin word fractus. Based on Mandelbrot’s finding (1982), fractals, as powerful new mathematical languages, can describe and solve the natural phenomena that were once abandoned. Mandelbrot’s main goal was to find a comprehensive way to explain chaos through information technology. Mandelbrot (1982) introduced fractals as new and more efficient geometric shapes to show the complexity of nature (Nobari, 2009: 73). A fractal is a geometric object that repeats itself in a structure at different scales or times and shows repeating patterns. Indicatively, the fractal is a geometric pattern for the characteristics of complex systems and represents the same structures revealed at different scale levels. Objects with such behavior can appear as artificial

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constructions, and their examples are abundant in nature, such as the arrangement of tree branches, the shape of cauliflower, the surface of clouds, the stream of the river, the structure of galaxies, and the shape of lightning (Mosteanu et al., 2019: 46). The main characteristics of complex systems are the following: • Branching structure (balanced system power) • Existence of relationships and interdependence of performance components (system integration) • The formation of an additional effect that is not natural in the elements of the system • Orientation of the operational target of the system • Performance in the unstable and stochastic external environment (system openness) • The desire of the system to recover continuously, effectively, and sustainably, that is, ensuring balance (the adaptability of the system) (Skydan et al., 2021: 63) In a nutshell, based on complexity theory, fractals are defined by two theoretical and organizational concepts: • Theoretical concept: Natural systems at scale have behavior patterns of selfsimilarity that can be identified and measured through mapping. • Organizational concept: Organizations have self-similar behavior and common values at the individual, group, or organizational levels (Nobari, 2009: 25). Unquestionably, adopting a fractal view of organizations is like using a telescope to observe the night sky. Without a telescope, one can observe the night sky with the naked eye to gain insight into the movement of celestial bodies. New insights, new relationships, and new natures of stars and planets are revealed using a telescope which brings forth new knowledge with a more precise understanding of why objects move and how some of them do. How and why are different here (Malik, 2004:108–109). The architectural model of fractals shows a hierarchical structure made of the elements of a basic fractal unit (BFU), and the design of a basic unit includes a set of related characteristics that can fully represent any level in the hierarchy. This means that the term “fractal” can represent an entire organization at the highest level or a basic unit at the lowest level. Warnecke (1993) defined a fractal as “an independent entity whose purpose and function can be precisely described.” Fractals have many intrinsic characteristics, including self-organization, self-optimization, goal orientation, self-similarity, vitality, and dynamics in a dynamic external environment (Ryu et al., 2003: 722).

4.1

Fractal Patterns

Mandelbrot (1982) defined two fractal patterns: stochastic and deterministic. Stochasticity is one of the characteristics of chaos theory, where “strange attractors” evolve to show pattern order. In fractals such as Cantor set and Sierpinski triangle,

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successive magnifications always produce the same structure: these fractals are selfsimilar (Raye, 2014: 59). Deterministic fractals are the closest geometric equivalent to a top-down hierarchical structure with the disadvantage that they are not symmetrical enough and cannot be uniformly scalable (Mandelbrot, 1982: 205). Overall, stochastic fractals are more efficient because they reflect the beauty of the natural world around us, constantly evolving and adapting as conditions change. In fractal organizations, the stochasticity that is unified by a fixed goal (shared goal) enables us to evolve in real time rather than based on an accounting plan or a five-year plan that becomes obsolete prematurely and limits an organization’s potential. In this way, we can understand the geometry of the organizations we belong to. Organizations with top-down relationship structures limit individual growth because advancement opportunities in these structures are based more on competition than performance. The need to innovate and keep pace with constant changes is a more significant challenge because collective wisdom and the spread of information underlie the desire and need for continuous improvement. Fractal organizations enable uniform scaling because there is no limit to growth as long as attraction remains constant. As a result, they expand by maintaining the integrity of the pattern as long as their product or service meets the needs of their market. As a fractal organization grows, new branches or arms are formed that allow individuals to take on new responsibilities and experience personal growth, which is the natural tendency of each individual. Everything we see in the natural world is based on a fractal pattern, including trees, plants, animals, and insects; geographical formations, such as mountains, valleys, and coastlines; and water formations, such as clouds, storms, waves, eddies, and tornadoes. Integration is the pattern of fractal formula that can evolve toward the best results (continuous growth and regeneration as long as possible) if it is not constrained. Therefore, as long as we try to control anything or anyone, we disturb the pattern integrity of that system (Raye, 2014: 58–59).

5 Commonalities Between EOR and Fractal Organization as the Facilitator of Desirability and Dynamics of Organizational Relationships to Develop Fractal Organizations 5.1

The Requirement to Have a Pattern of Organizational Behavior

EOR forms an emerging process concerning human resource management and organizational behavior through creating and maintaining interpersonal relationships and valuable relationships between employees and the organization. The presence of effective and correct relationships in an organization is always considered one of the crucial components in the success of management because the absence of correct relationships in the organization causes the flow of affairs to be disrupted and things

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Fig. 1 The process of identifying the structure of the complex system (Flake, 2000: 64)

to become chaotic. A comprehensive understanding of organizational behavior requires the study of human behavior in the field of dealing with interpersonal relationships and the organization (Griffin & Moorhead, 2021: 38). Therefore, the realization of a comprehensive understanding of organizational behavior depends on understanding all individuals’ behavior in the organization as well as understanding the individuals’ interactive behaviors in the organizational context (Shore et al., 2012: 16). Thus, research in the field of EOR in order to solve the fundamental problems of effective management of EOR needs to focus on the broad principles of management based on the knowledge of human resources and organizational behavior. As it was said, in fractal patterns, the way of looking at the phenomena to design the organization’s behavioral model is investigated according to the basics of complexity theory. Figure 1 clearly shows the process of identifying the complex structure. Therefore, the flow presented in this figure identifies the focus of the study of organizational behavior and the factors influencing the formation of that behavior. Self-similarity (fractal patterns) is evident in the behavior pattern of the organization. The final behavior of an organization at any point in time is determined by its interaction with the environment (in the general sense), the type of perception of the environment, and the formation of the imposed environment. Therefore, the behavior pattern at any point in time affects the organization’s form and the environment and the type of relationships between these two, and the sum of these behaviors makes the desired fractal pattern. The obtained behavioral pattern is a general pattern for the pathology of the organization’s behavior and provides the basis for gaining knowledge about the apparently unpredictable situation of the organization’s behavior. Assuming that the present is not the result of the difference between the past and the future in the form of a single point and itself is the distance in which individuals’ interactions build the future, interrupting the movement of the pattern and creating a

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change at each stage and setting the intensity of the strategy can be effective on the type of irregularity and the resulting fractal pattern (Nobari, 2009: 187).

5.2

The Integrity of Goals and the Unity of Individuals’ and Organization’s Interests

Alignment of employees’ and organization’s goals and interests paves the path of development and growth of organizational and interpersonal relationships, and both parties of the relationship, whether the employee or the organization, believe that they have a share in desirability, stability, and dynamic of the relationship and are required to meet the expectations of the other party. Since the organization is an abstract concept, providing the individuals’ goals should be a priority in designing the organization’s goals. Because meeting the employees’ expectations and needs makes them dependent on the organization and its goals in such a way that they consider the organization as their own and consider themselves as a part of the organization and they strive for the organization to achieve its goals and also, they have a lasting commitment. On the other hand, in designing the organization, special attention should be given to clarifying both managers’ and employees’ goals, and the process of organizational affiliation and belonging should be facilitated through mutual awareness. This is the first step in forming a good relationship and guaranteeing stability. Since not paying attention to the integrity and alignment of individual’s and organization’s goals leads to consequences such as duality, alienation, and mutual forgetting of the goals, the degree of the organization’s success in determining the goals can put both organization and individuals in the path of development and achievement as a guide, and its weakness damages the path of organizational development. Dimensions such as commitment, satisfaction, trust, and their total level are equivalent to the unification of the employees’ and organization’s goals and interests at different levels. Mutual development and institutionalization of these two dimensions in organizational relationships can guarantee the integrity of the individuals’ and organization’s goals so that individuals consider themselves a part of the organization with a persuasive sense of affiliation. Also, they consider their interests to be dependent on the organization’s interests. As a result of the feeling of achieving their goals, they help the organization achieve its worthy goals, and a desirable and stable relationship with the organization is formed through social identity (Rezazadeh et al., 2022b: 248–249). On the other hand, fractal organizations usually keep members connected by sharing goals and ethics that are “constant and dynamic.” Fractal patterns are based on a formula creating continuous integrated patterns that start with an unchanging and strange attractor and change over time based on environmental conditions. Mandelbrot (1982) made a mega fractal of different formulas, which is now called the “Mandelbrot set.” Based on this iterative equation, Z- < Z2 + C. Z becomes Z2 + C, and squaring it causes to repeat and expand the fractal pattern and ensures

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the integrity of the pattern. In fractal organizations, Z defines each person and is a variable of the equation. Square Z represents the remarkable performance of leadership to promote individual growth and development of Z. C is constant and is an example of a shared goal that preserves the integrity of the pattern and provides the possibility of individual exclusive explanation simultaneously. C, similar to the strange attractor, initiates chaos and is considered a fractal pattern in nature over time. Every fractal pattern must start with a strange attractor, just as any successful modern organization requires a shared goal along with collective effort. The prominent investigator who wrote about the importance of shared goals was Peter Senge (1990), a famous thinker of systems and developer of the concept of “learning organization.” Senge emphasized that “a shared vision changes EOR.” It is no longer “their organization” but becomes “our organization.” A sense of ownership is essential for people who want to be personally accountable for their efforts and relationships with others. Typically, top-down structures prohibit personal ownership because they centralize decision-making at the managers’ levels and delegate tasks and commitments to employees. Senge has dedicated his life to developing and training leaders for learning organizations that are evolving and adapting to changing circumstances. According to Sange, organizations can transform, and “a shared vision is the first step in allowing the individuals who distrust each other to start working together, and this creates a shared identity.” Undoubtedly, “an organization’s shared sense of goal, vision, and operational values creates the most fundamental level of partnership” (Raye, 2014: 56–57). Accordingly, organizations require equilibrium between individual visions and the group’s shared goals to coordinate collective actions for achieving the best results. Since leaders’ opinions often dominate those of subordinates in a top-down hierarchy, aligning members with a common goal and central values is accomplished by leaders trained in using negotiation means to facilitate decision-making (Raye, 2014: 63).

5.3

Requirements of Nucor Corporation

Since managers are the mediators between the organization and employees and the extent of their competency is efficient in directing the organizational relationships, they include a more extensive field than a manager. This is because playing considerable desired roles must agree with the requirements of managers’ competency (requirements such as elitism, the rule of law and ethics, jihadi spirit and will, cognitive capacity for strategic need assessment, playing the role of coordinator in management of the processes, interactive capability and emotional intelligence, ideation as a pattern of value creation in relationships, farsighted and clarified decision-making, manager’s self-awareness to prevent false pride, and performance without behavioral discrimination). These factors determine, develop, or improve the extent of unity and the reconciliation of the employees’ and organization’s goals. In other words, aligning the members with a shared goal and also the principal values in line with a set of requirements of managers’ competency is accomplished by

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leaders who are devoted to inspiring, guiding, monitoring, and empowering the process owners. Therefore, according to the increasing importance of the role of the organization’s manager in forming and linking the relationships, the factors mentioned above are considered critical factors influencing the level of EOR desirability. If these factors are developed and institutionalized in an individual as a manager, it can be promising and optimistic about the resilience and dynamics of EOR following the individual’s management. For example, when leaders or managers guide team members and improve the quality of interpersonal and organizational relationships in their organization, it is as if they spontaneously guide and facilitate innovation development through individual and team achievements (Rezazadeh et al., 2022b: 381). On the other hand, since the power of leadership/management in organizations with top-down hierarchy is often dictatorial and authoritarian, the flow of information is limited in one direction, and decisions are made in a limited way. At the same time, the quality of decision-making in human systems determines whether the results best serve all individuals in the system. Fractal organization, inspired by the factors such as systems theory, fractal geometry, quantum mechanics, information dynamics, sociobiology, epigenetics, cosmology, and evolutionary biology, explains how the natural structure of natural organizational relationships mimics systems in nature and empowers the relationships (Raye, 2014: 52). Ken Ivorson, the leader of Nucor1 corporation, believes that managers need to accept once and for all that staffers are the real progress engines, not managers. They must devote their management career to creating an environment where employees can grow at higher performance levels. The manager should try to encourage the employees to share more of their ingenuity and shape his/her business )from the very beginning (in such a way as to allow employees to identify and show the management the way to achieve goals that once seemed unattainable to the leader/manager (Iverson & Varian, 1998: 91). According to Iverson and Varian (1998), typically, most administrators spend additional time on planning, training and inspecting than listening, and testing and analyzing, while they should reverse this ratio to turn their employees into engines of progress and development. “Motivational Leaders”, Leaders who motivate individuals to take personal accountability for their work quality, and acknowledge their contributions, can enhance their team members’ wellbeing and satisfaction (Pert, 1997: 265). Leaders in top-down hierarchies consider interpersonal relationships the second priority to maximizing production and profits. They reluctantly accept this unexpected notion that perhaps the workforce’s attitudes, perceptions, emotions, and the [top-down] structure of relationships can be related to productivity (Bennis et al., 2001: 277). Accordingly, most leaders need to be trained in situations where they must focus on the personal understanding of the employees under their leadership.

1

Nucor corporation is one of the most successful American steel companies, of industrial materials ranked 138 out of 500 in 2012, and is the largest recycler (www.nucor.com) in North America.

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As the channels for the flow of information to adopt macro decisions, leaders need awareness of what is occurring in their organization. Seemingly, if all organizations operate in a natural hierarchy, the need to assign leadership roles to individuals throughout the organization will disappear. However, most organizations still need leaders to facilitate the negotiations. As Bohm and Nichol (1996) stated, “assumptions and opinions are like computer programs in employees’ minds, but sometimes leaders act against the individuals’ best assumptions and opinions and implement their assumptions and opinions. So, the situations are inevitably organized to make us believe that we cannot do anything without leaders, but perhaps we can.” Nevertheless, we will need leaders as long as most individuals do not have the necessary self-awareness and cannot analyze their main beliefs. Overall, in fractal organizations, developing relationships at the organization levels unite group efforts for a shared goal because leaders are dedicated to inspiring, guiding, and empowering “the process owners” (and all other individuals) (Raye, 2014: 52).

5.4

The Importance of the Individual’s Role

According to Shore et al. (2012), the issue of EOR is partly psychological. Therefore, each individual’s function in an organization differs, depending on employees’ perception of the organization as an abstract concept. These individuals are employed to provide the opportunity to reach the organization’s comprehensive and ultimate goals. Thus, as employees in the organization, individuals are not only passive receivers but also see and interpret the organizational context, the manager’s behavior, and how the organization and the manager organize relationships. Besides, their response is based on their interpretation of what they have seen and under the influence of their characteristics and behavioral background and in the form of the level of interaction and participation in line with the organization’s goals. Therefore, as the most valuable strategic human resources, individuals in the organization monitor the management behavior like an active magnifier. As a result, the dynamism and mutuality of EOR depend on the sustainability of organizational capital (Rezazadeh et al., 2022a: 151). Every individual has a unique point of view and collects information based on it. A person’s lifestyle and his/her interaction with home and community influence his/her perceptions and beliefs, and he/she inevitably brings them into the workplace. So individuals in most organizations have different expertise levels, and fractal organization is a novel and diverse way to visualize the network of relationships and how information flows in different circumstances (Raye, 2014: 58). Notably, the conditions where individuals’ freedom is limited, and others try to control their actions, are inherently unnatural and cause illness and stress, and for these individuals, there is no difference between workplace and prison (Zimbardo, 2007: 221).

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The Structure of Governing Interpersonal and Organizational Relationships

In EOR, the empowering and restrictive structure of governing relationships creates “the extent of unity of individual’s and organization’s goals and interests” as the starting and central point of the EOR process. The structure of relationships in EOR is said to be a set of factors that determine the procedure and process of duties and organizational interactions. The structure of governing relationships can be revealed in two categories: empowering and restrictive. The path of forming the structure of empowering relationships (through valuation of mutual need assessment and eliminating them, creating a balance in informal relationships as an educational medium, positive feedback of performance as a factor of individual’s responsibility, involvement of experts as process owners as a factor of persistence commitment, proportion of individual’s physical and mental health to the job, executive guarantee and mutual monitoring levers, comprehensive and restrictive laws, clarification of individual’s role in the chain of continuous service and training) (Rezazadeh et al., 2022b: 381) or the structure of restrictive relationships (through downward arrangement of the structures of relationships, the institutionalization of factors such as the structures infected by political factionalism, hidden programs, multiple parallel management, hidden decision-making leading to secret discriminations, the rule of malfunctioned behavior due to unconvincing expectations, unilateral control of mafiaism within the system, authoritative management style as a factor if ambiguity and systemic slowness, flight management, the rule of unbalanced informal institution) is manifested with special dimensions and characteristics of each one. Management style governing restrictive relationships is authoritative or top-down. In this style, the mutual feedback process is interrupted, and the manager needs more technical management in designing organizational strategies and participation and acts as a machine for signing and issuing the circulars. This traumatic management style leads to the manager’s unscientific intervention, depriving the process owners of their wills and disrupting the main processes by unnecessary addition of gears, and neglects the process owners’ influential role in facilitating the work of the system that these factors can cause severe problems in the formation of social identity (Rezazadeh et al., 2022b: 289). The structure of a top-down hierarchical relationship is typically characterized by the systems which command and control the power and often cause problems for the organization’s progress by creating harmful stress and internal competition. The overarching notion expresses “limited room at the top,” where positions of power become inadequate resources. Focusing and spending energy on internal competition instead of external competition, members hide or hoard information, create a silo of information, and cause adverse stress that manifests in absenteeism and increased organizational costs. Unforced turnover eliminates talent because creative people are looking for a homogenous work environment. All these factors lead to the formation of the structure of restrictive relationships, causing anger and dispersal of organizations’ members instead of uniting them in a shared goal and eventually

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leading to the separation of goals and interests in organizational relationships (Lipton, 2005: 42). The issue of the structure of the relationship relies on centralized versus decentralized decision-making, and information is accumulated at a central point where the executive managers make decisions to rule over their subordinates (Malone, 2004: 51). A fractal organization can incorporate both characteristics through the decentralized decision-making at the boundaries of the organization and centralized decision-making at the center of the organization. Strategic decisions concerning allocating the organization’s primary resources and orientation for coming development require a great perspective so that the information leaders distribute throughout the organization is best collected at the center. In line with these contents, the book titled Plain Talk (Iverson & Varian, 1998: 93), devotes an entire chapter to destroying hierarchies in the structure of governing relationships and state that relying on the remains of command and control management discourages the extensive bulk of individuals from doing work and other vital contributions. Systemic issues such as internal competition, involuntary turnover, and unhealthy employees are common in top-down hierarchies. In contrast, happy and healthy employees distinguish fractal organizations due to the emphasis on positive information flows and relationship structures that produce the best results. These organizations are frequently identified as “Best Places to Work” because their members have common goals and central values that merge their actions and create an integration pattern or self-similarity that is a hallmark of a fractal organization. Organization members feel admired for their measures and are supported by the organization of their workplace, which naturally increases organizational health (a happy heart is a healthy heart). The repeated information quality flows from the organization’s edges to the center and inside, making it possible to create successful interpersonal and organizational relationships throughout the organization (Raye, 2014: 52). On the other hand, the structural elements of fractal systems have the necessary resources and competences for independent decision-making. In fractal systems, management relationships (the structure of governing relationships) cause the alignment of departments. This means that different fractals do not execute commands from the top level (management) and decide to get the desired effect through risk-taking (Skydan et al., 2021: 66–67). In other words, departments of the fractal system make decisions independently but necessarily take into account the shared goals and interests of all fractals in such a way that the structure of relationships in these organizations will empower and facilitate the path of achieving growth, excellence, and dynamism of human systems.

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Dynamics of Information and Background Knowledge of Dynamics of Relationships in Fractal Organizations

The organization will retain its initial dynamism if the human factors have enough motivation and desire to work and participate in the effort to achieve the goals for any reason. To put it in another way, the staff’s reluctance and effort to participate in organizational activities and procrastination in it, if it becomes widespread, have unfortunate consequences for the organization and endanger the effectiveness and dynamics of interpersonal and organizational relationships. Therefore, EOR is like an umbrella that researchers use to evaluate the scope of employees’ interaction and dynamics with each other on the one hand and the organization on the other. This issue is like an umbrella under which all extensive plans are placed under it through the employment of people and the staff’s interaction with the organization, and ignorance of the adjustment mechanism processes causes severe challenges and problems for the growth and development processes. Mutual feedback of supervisory levers in empowering relationships prevents individual commenting in the hiring process that along with clear job promotion leads to factors such as perception of organizational justice, reduction of tension in organizational relationships, improvement of mutual performance, the efficiency of human resource management, improvement of continuous relationships, and stability and dynamics of EOR. In the structure of restrictive relationships, little attention is paid to research and futurology, and hindsight causes the organization’s decline and lack of dynamism and repetition of past mistakes and prevents knowledge sharing. Optimizing the two parties’ relationships and confirming the effect of different factors on EOR focuses on different perspectives. Employers who expect a high level of employee’s participation and provide extensive incentives actually foster a higher level of knowledge sharing, so improving employees’ motivation can effectively empower and dynamize EOR. Desired performance of human resource management methods helps to coordinate EOR and improve mutual understanding because the model and desirability of EOR are formed based on the competency background of that organization’s human resource management, and it is in this way that the organization’s managers can help the development and dynamics of EOR while clarifying the relationships between employers and employees (Zhang et al., 2019: 71–72). On the other hand, in complex organizations, the knowledge of employees is influenced by the integration of knowledge as a fractal. Knowledge integrity means that each fractal must be constantly aware of all critical events. The centralized alignment of resources among all fractals characterizes this awareness. In addition to adaption them to the capabilities of the system, it is directly responsible for personal aggregative development and specialization in the whole system, which requires understanding the environment as well as the specialized field of the system (Shoham & Hasgall, 2005: 228). According to Custer (2007), frequent information flows specify the quality of the relationships in any process. Top-down hierarchies prevent the information flow from employees to management. Hence, this limits the individuals’ functional

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capability to develop intellectually. At the same time, fractal organizations follow the laws of nature in which information and resources flow in a channel (Raye, 2014: 56). Organizations with top-down relationship structures tend to put management in front of employees and create internal conflicts and battles, which is stressful for many individuals. However, Nucor has central values such as no layoffs and guaranteeing coming chances for its staff’s children, delivering their resume to emphasize innovation. This organization has a flat hierarchy to monitor the information flow and believes that each relationship can develop a “voice” in the situation of the company, so it considers the employees’ interpersonal relationships to be significant (Iverson &Varian, 1998: 84). This company also sees the information feedback importance loops as critical to the growth of stochastic fractal patterns: “If you consider employees to be the key to the success of a business, they will demand more access to information. It is quite natural that they need relevant information. The official information policy at Nucor is to share everything” (Iverson & Varian, 1998: 95). Communicating information reduces uncertainty and broadens all individual’s vision in the feedback loop. In the information flow dynamics, each individual has a unique vision. Increasing information access increases an individual’s ability to see the more excellent picture and juxtapose the puzzle pieces. So an organization’s members feel a sense of belonging and ownership toward the company regardless of whether the employee owns the company, and identity is accordingly created. According to Custer (2007), a lack of organizational attention to the information dynamic quality between staff leads to dread and inconsistency of aims and command errors, causing the reduction of speed (time delay), disorganization, dissipation of time and energy, reduction of financial resources, and generally the governance of negative relationship. Personal health is affected by negative information dynamics because it leads to anxiety and unsafe outcomes. Overall, “excessive work hours (75%), lack of work-family balance (65%), and fear of job loss (64%) are the most important sources of stress affecting employees in most organizations” (Bedell & Kaszkin-Bettag, 2010: 26). Eradicating the causes of stress diminishes healthcare expenses and the demand for intervention programs dramatically. In general, an organization’s costs are not only subject to healthcare, but also the bitter and overworked individuals express their dissatisfactions in different ways and cause problems for themselves and the organization. In general, extracting order from the disorder, as well as creating purposeful chaos in the organization, requires an optimal flow of energy and information to the system, fostering research, development and innovation programs, creation of brainstorms, development of polls, taking advantage of the organization leadership and cultural elements to empower the existing fluctuations, formation of self-organizing groups to resolve the conflicts, creation of a dynamic process, transforming accumulated information into knowledge, establishing an educational organization, and developing educational programs and skills (Faghih, 2006: 72).

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The Importance of Mutual Trust as a Facilitating Factor

The relationship is the basic foundation of EOR that relates individuals to the organization, and as a macro part of EOR, it is based on two foundations of interaction and organizational context. Interaction based on the reciprocity norm appears in the position of organizational performance basis in employment relationships and is empowered and weakened based on the level of trust between the parties of the relationship (Wu et al., 2006: 378). The human organization is the context in which interactions and behavior happen, and the relations between the two are the degrees to which an organization and its staff trust each other and dimensions such as trust, control, satisfaction, and mutual commitment (Men & Robinson, 2018: 476). According to Mayer et al. (1995), organizational trust represents the quality of relationships between institutions and is a necessary factor in maintaining a relationship over time. Individuals trust their real experiences to show the necessary solutions for doing actual work. According to Rentsch (1990), small events contain great messages (Rezazadeh et al., 2022b: 99). In situations where innovative organizations must quickly adapt to changing market or customer needs conditions, the structure of relationships with top-down control has less performance effectiveness. Educated individuals, whose minds have become more aware and capable of making decisions, often object to being told what to do. On the other hand, employees in approvingly competitive markets, where innovation is crucial to survival, involving in top-down hierarchies, tend to store information as an authority or abuse information unfairly to maintain relationships to attain internal progress. As a beneficial resource, this behavior directs competitive capacity inward instead of outward, destroying the organization’s pattern integrity. This issue generally stems from a need for more trust because individuals work toward mutual goals, not the unity of goals. Therefore, resources are reduced, and as a result, ambiguity, uncertainty, health problems, and stress become inevitable. Due to increasing concerns for organizational effectiveness, employees prefer to adopt horizontal and natural hierarchical systems as an alternative. Significant organizational progress occurs when all employees share responsibility, reflecting separately individual abilities. The trust that arises from the shared goal space impacts the inner and outer relationships, attracting resources that facilitate the continuous provision of desired products and services (Raye, 2014: 51). Nevertheless, in human organizations, if the staff does not feel interested in successful outputs, they are fraught with destructive interpersonal relationships, absenteeism, unwanted turnover, and declining fruitfulness and beneficialness, reflecting damaging harmonics within the organization. Undoubtedly, focusing on open, unbiased, obedient, accommodating, and determined relationships is essential to achieve the most satisfactory results. Only with these characteristics, values such as trust and appreciation emerge in the relationships among groups working together (Laszlo, 2004: 150). Whyte and Whyte (1998) believe that the type of organizational relationship formation determines successful results and is the basis for managing a selfregulating team because increasing the level of team relationships creates conditions

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in which the organization can stop supervisory roles and trust its members doing their job while improving its efficiency and dynamism. On the other hand, when individuals with open views are present in the organization, participating in collaborative, innovative actions, they intrinsically flourish and produce the most reasonable results as stakeholders in their positions. Emergent collective behavior includes pattern integrity that creates trust in interpersonal relationships and relationships within the organization. All information required for an adequate decision is unrestricted and flows all over the organization structure, ensuring the optimal use of resources (Raye, 2014: 65). However, in fractal organizations, behavioral characteristics such as openness, honesty, respect, generosity, and commitment do not preclude disagreement about what and how we create. Indeed, each of us has a variety of perspectives on life, entirely wide and potentially intellectual. We can disagree with each other in our alignment. This disagreement allows for the emergence of any idea and makes the conversation richer with this view that the best decisions come from different opinions.

6 The Necessity of Fractal Dynamic Behavior in Optimal Management of Employee-Organization Relationships The best place to start looking for the organizational fractal is the “system” itself, the space in which all the organizations’ components play a role because this issue is the aim of countless objective analyses. The fractal is the concept of essential dynamics, animating the organization. Comprehending these dynamics constructs a renewed and potent basis for managing organizations. Any field of management, such as formulation of strategy, management of change, cost-cutting, redesign of process, or development of a new product, can be done and come up with robust, unique views, very far from management through linear, sequential, and traditional thinking or even different from the approach of linear systematic thinking (Malik, 2004: 108–109). Through making a slight change in the concept of the fractal, “pattern” can be replaced with “system” or “dynamic behavior” to achieve a modified definition of fractal as a dynamic behavior that repeats itself at various scales. “Scale” can be defined as different levels of the organization (individual, team, corporation itself, and the market in which the organization exists). Therefore, we find a revised definition of the organizational fractal. Organizational fractal includes a dynamic behavior of all that exists in the individual and manifests itself at the team level, at the organization level itself, and again at the market or system level in which the organization exists (Malik, 2004: 101). Therefore, the formation of fractal dynamic behavior can facilitate and guarantee the creation, promotion, and dynamics of desired relationships between employees and the organization.

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7 Discussion Since human organizations and systems, like natural organisms and systems, have the characteristics of growth, development, and vital attributes, such attitudes are usually used in the study. Moreover, investigation of organizational and human systems, taking advantage of fractal theory in related studies, can provide powerful instruments to researchers and also provide quantitative criteria for metrics and indicators in evaluating and comparing growth and development processes, strength and coherence of organizations and human systems, simulation, decision-making, and the like. Fractal organization theory identifies an emerging human operating system, following nature in capacity for creativity, adaptation, vitality, and innovation. Characteristics of a fractal organization comprise shared goals and values that create the integrity of pattern, global participation in ideas and solutions for continued advancement, decision-making at functional levels, leadership dedicated to global leadership, and directing power to external competition rather than internal competition. Developing effective interpersonal and organizational relationships enables adequate information flow between individuals and groups. At all fractal organization levels, partners frequently communicate information and collectively make decisions regarding ever-changing situations. In human organizations, maintaining the integrity of the fractal pattern requires a mutual relationship between team members, individuals, leaders, and leaders themselves. Relational structures, encouraging equality in relationship patterns, regardless of their position in the hierarchy, enable each person to play the role of information source. Hence, according to Alvani (2013), in order to integrate individual’s and organization’s goals based on value views and theories such as expectation and probability, management tries to motivate the individual to fulfill the organization’s goals by increasing the amount of expectation and probability of what is desired by them. Here, work is a means that makes the individual achieve their desired result, and the organization’s goals are also realized. The higher the expectation and the probability of the desired result, the higher the individual’s interest in accomplishing the organization’s goals. Therefore, an organization’s effort should be to know the individual’s desired results and increase the probability and expectation of their occurrence for the employees to create an atmosphere in the organization where people consider the fulfillment of their needs possible and probable. Competent managers facilitate the path of futurology by farsighted and transparent decision-making, and they involve process owners in decision-making and on needs and realism to protect the organization’s interests. This involvement makes employees feel more belonged and loyal to the organization. Closeness to the organization aligns the individual’s and organization’s goals and reconciles individual and organizational goals. According to Alvani (2013), as inferred from all theories of expectation and probability, the individual’s and the organization’s goals never become unified, but the effort is to bring these goals as close as possible and reduce the intensity of the conflict between them. The reason for this conflict and irreconcilability of the individual’s and organization’s goals is their values or, in

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other words, their ultimate goals. So, if we identify, clarify, and unify their values and ultimate goals, the organization and the individual will be united, and reconciliation will be possible due to this unity. According to Logan et al. (2008), finding the values that affect a group of employees can bring the whole tribe to the edge of gratitude and a level of positive and effective performance. These results can also seem miraculous from the outside. It also aligns with Tony Hsieh (2010), who advocates the importance of goal integration and says, “Coordinated performance creates passionate will and energy.” Also, “We have actually said “No” to very talented people who we know could immediately impact our policy. Unfortunately, we were willing to sacrifice short-term benefits to protect our culture (our brand) for the long term. In fact, organizations need leaders who are thinkers in addition to having great ideas because most leaders interact with the environment. Therefore, they need ways to encourage personal growth and improve informant flow among their team members. Leaders must comprehend that each person’s mind is designed by opinions and assumptions that can not only affect their capability to develop but also block their ability to effectively negotiate about workplace and product improvement. Modern leaders who focus on analyzing the nuances of interpersonal relationships and guiding their team members toward more remarkable personal growth can help those members overwhelm restricting beliefs and achieve superiority and dynamism.2 As Willis Harman and Sahtouris (1998) stated, “If our belief systems change fundamentally about the path of any process or experience, our perceptions and everything else about our lives will change; this will be true individually or collectively.” Therefore, in EOR, the employees have an influential role because they are considered the organization’s most essential and valuable strategic resources, and organizations’ and managers’ efforts should be designed and directed in such a way that these human resources remain stable and dynamic and also help the organization to achieve its worthy goals. In other words, the organization’s context and the managers’ view should be designed and trained so that they believe that the organization cannot achieve its goals except by providing and persuading the employees’ interests and goals. Adopting the organizations’ fractal view causes a further and more influential body of organizational knowledge to be considered. An organizational dynamism level, far removed from traditional organizational thinking and vision, is disclosed. Such insight is crucial to justify the difference between business success and failure in this rapidly transforming world. According to Faghih (2006), any process or phenomenon that changes and evolves over time is an example of a dynamic system, and the dynamic direction of human systems is not such that managers are required to watch and play a passive role or become the victim in the course of chaos and chaotic developments. Instead, the manager should have the wise insight to use this instrument in integration with the transformative forces to use it on time. They can also foster innovations in the context of existing conditions to strengthen the desired order and emerge from chaos. These things will

2

Here, Myers-Briggs’s assessment is a good instrument for leaders to use.

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be possible by applying structures, organizational systems, work agendas, inspirational programs, managerial ideals, values, principles, and concepts. Therefore, fractal theory paves the way to visualize and navigate multiple unstable domains, multiple layers, and system dynamics.

8 Conclusion The fractal theory has been used in psychology and behavioral sciences to formulate quantitative growth and development models. Thus, fractal theory can also be used in organizational and managerial systems and related research. Therefore, organizational decision-makers can find the position of the organization’s behavior in the fractal pattern by gaining knowledge about the organization’s current situation, the governing strategy, and the extent of ambiguity and uncertainty in the environment. The result of this activity is to increase their power of control and foresight to obtain the best proportion in interpersonal and organizational relationships at any point in time. Besides, according to Faghih (2006), all of these require continuous testing, practicing, and learning cycles because all nature, including humans, consists of fractal organizational patterns. Fractal organizations act like living systems in nature, where the information exchange is continuous and part of the evolutionary process. Pervasive and enduring beliefs about management in human organizations are potent links to old ways of understanding the world and our relationships. Our understanding of the world affects our behavior and how we structure our relationships and communicate. In line with Raye (2014), it can also be acknowledged that in the last few decades, the increase in turnover and the high costs of training the substitute employees may be sufficient motivation to change the organization’s structure from top to bottom and make a fractal structure, although the change in consciousness is also required. Probably, suppose leaders recognize the vital importance of feedback from employees who interact with the organization’s environment and organizational context during their daily performance. In that case, they will be more willing to make changes in their organization so that reflecting this valuable information leads to creating fair and cooperative structures. Therefore, leaders’ performance as the channel of information flow is critical for this approach’s success because the quality and quantity of information exchanged inside and outside the organization are essential to successfully integrating employees and organizational goals and interests. Leaders who work to improve the dynamics of information flows in their organization ensure the best results in a rapidly changing environment. Workforce health directly reflects the information quality streaming in an organization. If groups of employees in an organization share the main goals and values, the result will be a healthy environment in which the staffs flourish and collaborative engagement is appreciated and awarded in this organizational context. These organizations’ fractal nature represents the shared consciousness in the quantum context where information affects energy and material. Conversely, negative stress, incompatible relationships, and poor communication methods lead to physical harm to employees

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Table 1 Common characteristics of EOR and fractal organization to create fractal organizations Number 1 2 3

4 5 6

7 8 9 10 11 12 13

14

15

Common characteristics of EOR and fractal organization Having an integrated pattern of organizational behavior based on the fractal pattern Having an integrated pattern of individuals’ and organization’s shared, stable, and dynamic goals and interests Leader/manager in the role of developer of relationships at all levels of the organization about a shared goal, inspiration, guidance, and empowerment of process owners and all individuals in the organization Importance and special place of individual’s role as the most valuable strategic human resource Paying attention to the sustainability of organizational capital in line with the dynamism and mutuality of EOR in fractal organizations Governance of the structure of empowering relationships based on fair and collaborative relationships through centralized internal and decentralized external decisionmaking Strategic decision-making of human resources with a broad and comprehensive view Governance of the structure of empowering relationships on positive information flow, organizational support, organizational health, and best results Independent decision-making of departments based on common organizational goals and interests Dynamism and knowledge sharing Appreciation of knowledge of employees and integration of knowledge based on the centralized alignment of human resources with the system’s capabilities Importance and place of information feedback loops in line with the growth of fractal patterns Creating purposeful chaos in the organization based on the flow of energy and information, promotion of research and development programs, brainstorms, formation of self-organizing groups to resolve conflicts, establishing an informative organization through accumulated internal information, and promotion and development of individual’s skills Importance and place of mutual trust based on open, honest, respectful, generous, and committed trust in line with the richness of ideas in decision-making and achieving the best results Collaborative participation of leaders and employees in organizational relationships based on common consciousness in the field of quantum

and thus expensive healthcare and reduced productivity. In the end, in Table 1, common characteristics of EOR and fractal organization to create fractal organizations are shown. In summary, characteristics of mutual dynamics of EOR are based on human capital and strategic and optimal EOR decision-making. Besides, characteristics like mutual dynamics based on diversity of options, open information flows, process owners’ participation, and governance of open, generous, and committed relationships facilitate the movement toward fractal organizations and have particular importance.

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Index

A Ambiguity, 5–7, 79–97, 110, 111, 197, 201, 205

C Cognition, 5, 6, 79–97, 101–103, 106, 112, 113 Complexity, 3, 7, 8, 39, 79–82, 87, 88, 92, 93, 95, 105–107, 110, 111, 148, 189 Countries income, 22, 24–26, 44 Cross-correlation, 8, 132, 133, 137, 143, 145, 149, 152–154, 156

D Danger, 101, 105, 106 Decision-making, 63, 65, 71, 79, 80, 86, 87, 95, 107, 194, 195, 198, 203, 206 Detrended moving average (DMA), 134, 137, 147

E Economics, 1–9, 15, 18, 20, 21, 42, 43, 54, 81, 121, 123, 124, 127, 129–132, 135, 138, 139, 153–155, 163–165, 183, 184 Effectiveness, 5, 6, 53–73, 149, 199, 201 Employee-organization relationship (EOR), 8, 53–73, 187–206 Energy economics, 5, 7, 8, 121–156 Energy markets, 8, 121, 122, 130, 134, 135, 137–140, 142–147, 149, 151, 152, 154– 156, 162–184

Energy prices, 5, 8, 121, 122, 131, 134, 137, 139, 143, 145–147, 149, 152, 154–156, 162–184 Entrepreneurial orientation (EO), 6, 15–44, 61 Entrepreneurship, 1–9, 15–17, 19–22, 26, 27, 33, 42–44, 73

F Fat-tailed distribution, 82 Fractal, 1–9, 121–156, 161–184, 187–206 Fractal dimensions, 8, 123, 124, 127, 129–131, 134, 135, 138, 140, 144, 145, 147, 148, 155, 165 Fractal methodology, 8, 121–156 Fractal organizations, 8, 9, 187–206 Fractal structure, 7, 8, 121–123, 127, 130, 134, 135, 137, 139, 140, 143, 145, 149, 153– 155, 164–166, 180, 183, 205 Fractal time series, 123, 124, 130, 131, 135, 140 Fractional-ARIMA, 137

G GEM data, 5, 15–44 Gender, 16, 17, 19–20, 22–24, 26, 27, 29, 39, 41, 42, 44

H Hazard, 104, 105, 107, 109, 111–113 Human systems, 9, 188–189, 195, 198, 203, 204

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Faghih (ed.), Time and Fractals, Contributions to Management Science, https://doi.org/10.1007/978-3-031-38188-1

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210 Hurst exponent, 123, 125, 126, 129, 130, 134, 135, 138–145, 147, 155, 165, 169, 173– 175, 177–179, 181, 182

I Incident, 114–115 Information, 5–7, 9, 42, 44, 62, 79–93, 96, 101– 115, 124, 132, 139, 141, 142, 144, 164, 167, 189, 191, 195–203, 205, 206 Innovativeness, 16–20, 22, 24, 26, 27, 29–31, 33–35, 39, 41–44, 189

Index P Performance improvement, 53, 59, 69–71 Proactiveness, 6, 16–22, 24, 26–34, 39, 41–44 Project management, 6, 80, 81, 86, 92–94, 96

R Risk, 5, 6, 18, 20, 35, 36, 41–43, 80, 81, 85–87, 95, 105–113, 141, 143, 154, 162, 165, 182 Risk-taking, 6, 16–22, 24–30, 34–39, 41–44, 87, 106, 110, 198

J Job satisfaction, 68–71

M Machine learning, 5, 6, 15–44 Management, 1–9, 15, 53–57, 59, 62, 63, 65– 67, 71, 73, 79–81, 85, 87, 88, 90–96, 106, 109, 187–189, 191, 192, 194–200, 202, 203, 205 Market efficiency, 131, 134, 135, 143, 145, 148, 149, 151, 163–166, 182 Modelling, 7, 121–156 Multifractal detrended fluctuation analysis (MF-DFA), 134, 136, 141, 145, 146, 155, 163, 165, 169, 172, 173, 180

N Nonlinear dynamics, 5, 121–156 Nonlinear modeling, 137–155

O Organizational context, 55–58, 61, 64, 188, 192, 196, 201, 205 Overruns, 6, 7, 79–96

S Safety, 5, 7, 101–106, 108–115 Simulation, 7, 80, 89, 96, 97, 203 Stress management, 63, 66–67, 73 Systems, 2, 4, 5, 7–9, 39, 56, 63, 68, 79–85, 88– 90, 92–96, 103–106, 111, 113, 114, 123, 125, 127, 130–132, 134, 138, 141, 148, 153, 187–192, 194, 195, 197–206

T Threat, 5, 7, 90, 95, 101–115 Time, 1, 16, 53, 82, 104, 121, 162, 188 Time management (TM), 2, 5, 6, 53–73 Time series, 5, 8, 16, 21, 30, 36–44, 121–135, 137–145, 147–152, 154–156, 162–184

U Uncertainty, 21, 64, 66, 80, 81, 85, 86, 89, 91, 114, 141, 154, 200, 201, 205 U.S. energy, 5, 8, 162–184