Renminbi Exchange Rate Forecasting 9780367686062, 9780367694937, 9781003141983

Table of contents :
Cover
Half Title
Series Page
Title Page
Copyright Page
Table of Contents
List of figures
List of tables
Preface
Acknowledgments
Chapter 1 Introduction
Chapter 2 Literature review
Chapter 3 The dynamic relationships of the renminbi
Chapter 4 A forecasting approach based on the characteristics of China’s exchange rate
Chapter 5 A forecasting approach based on the domestic economic situation
Chapter 6 A forecasting approach based on the international economic situation
Chapter 7 A forecasting approach based on the public’s expectations
Chapter 8 A comprehensive integrated forecasting approach based on long short-term memory (LSTM)
Chapter 9 Conclusions and future research
References
Index

Citation preview

Renminbi Exchange Rate Forecasting

With the internationalization of renminbi (RMB), the gradual liberalization of China’s capital account and the recent reform of the RMB pricing mechanism, the RMB exchange rate has been volatile. This book examines how we can reliably forecast the exchange rate. It explains how we can do so through a new methodology for exchange rate forecasting. The book also analyzes the dynamic relationship between the exchange rate and exchange rate data decomposition and integration, the domestic economic situation, the international economic situation, and the public’s expectations, and how these interactions would affect the exchange rate. The book also explains why this comprehensive integrated approach is the best model for optimizing accuracy in exchange rate forecasting. Yunjie Wei received her PhD in Management Science and Engineering at the University of Chinese Academy of Sciences, China, in 2017, and also received a PhD in Management Science at City University of Hong Kong in 2018. She is currently Assistant Professor at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China. Her research interests include economic modeling, analysis and forecasting. Shouyang Wang is currently Bairen Distinguished Professor of Management Science at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China, and a Changjiang Chair Professor of Management Science and Engineering at the University of Chinese Academy of Sciences. Kin Keung Lai is currently Distinguished Professor at the College of Economics, Shenzhen University, China, and also Honorary Professor at the Department of Industrial and Manufacturing Systems Engineering, Hong Kong University, Hong Kong.

Routledge Advances in Risk Management Managing Currency Options in Financial Institutions Vanna-Volga Method Yat-Fai Lam and Kin-Keung Lai Gold and International Finance The Gold Market Under the Internationalization of RMB in Hong Kong Haywood Cheung Green Transportation and Energy Consumption in China Jian Chai, Ying Yang, Quanying Lu, Limin Xing, Ting Liang, Kin Keung Lai and Shouyang Wang Chinese Currency Exchange Rates Analysis Risk Management, Forecasting and Hedging Strategies Jiangze Du, Jying-Nan Wang, Kin Keung Lai and Chao Wang Forecasting Air Travel Demand Looking at China Yafei Zheng, Kin Keung Lai and Shouyang Wang Supply Chain Risk Management in the Apparel Industry Peter Cheng, Yelin Fu and Kin Keung Lai Risk Management in Supply Chains Using Linear and Non-linear Models Mohammad Heydari, Kin Keung Lai and Zhou Xiaohu Risk Management in Public-Private Partnerships Mohammad Heydari, Kin Keung Lai and Zhou Xiaohu Renminbi Exchange Rate Forecasting Yunjie Wei, Shouyang Wang and Kin Keung Lai Candlestick Forecasting for Investments Applications, Models and Properties Haibin Xie, Kuikui Fan and Shouyang Wang For more information about this series, please visit www.routledge.com/Routled ge-Advances-in-Risk-Management/book-series/RM001

Renminbi Exchange Rate Forecasting

Yunjie Wei, Shouyang Wang and Kin Keung Lai

First published 2021 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN and by Routledge 52 Vanderbilt Avenue, New York, NY 10017 Routledge is an imprint of the Taylor & Francis Group, an informa business © 2021 Yunjie Wei, Shouyang Wang and Kin Keung Lai The right of Yunjie Wei, Shouyang Wang and Kin Keung Lai to be identified as the authors of this work has been asserted in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record has been requested for this book ISBN: 9780367686062 (hbk) ISBN: 9780367694937 (pbk) ISBN: 9781003141983 (ebk) Typeset in Galliard by Deanta Global Publishing Services, Chennai, India

Contents

List of fgures List of tables Preface Acknowledgments 1 Introduction

vi viii x xiii 1

2 Literature review

18

3 The dynamic relationships of the renminbi

41

4 A forecasting approach based on the characteristics of China’s exchange rate

77

5 A forecasting approach based on the domestic economic situation

88

6 A forecasting approach based on the international economic situation

99

7 A forecasting approach based on the public’s expectations

115

8 A comprehensive integrated forecasting approach based on long short-term memory (LSTM)

123

9 Conclusions and future research

128

References Index

131 145

Figures

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 2.1

2.2 2.3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10

Imports and exports of China and the United States The SDR basket – composition and size The central parity of the RMB against the US dollar, CNY and CNH China’s current account and the growth rate of GDP The fluctuations of China’s foreign exchange reserves PMI of global manufacturing China’s imports and exports 2000–2016 The central parity of RMB/USD and the RMB exchange rate indices Timeline: China’s reform of the RMB exchange rate Book structure Joint density distributions of the Gaussian copula, Student t-copula, Clayton copula and Gumbel copula under different parameters Flowchart of estimating the mode number k of VMD Comparison between three-layer WD and WPD Schematic diagram for the hybrid approach Daily CNH and CNY data from August 23, 2010, to December 31, 2015 IMFs and residue for CNY from August 23, 2010, to December 31, 2015 IMFs and residue for CNH from August 23, 2010, to December 31, 2015 Market impacts from August 2010 to December 2010 Extreme event impacts from August 2010 to December 2010 Market impacts from August 2011 to November 2011 Extreme event impacts from August 2011 to November 2011 Market impacts from August 2015 to December 2015 Extreme event impacts from August 2015 to December 2015

2 2 3 4 5 5 6 7 9 16

25 32 33 44 45 48 49 50 51 51 52 53 53

Figures vii

3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19 3.20 4.1 4.2 4.3 5.1 6.1 6.2 6.3 7.1

The immediate network relation of the risks between various currencies (A) before and (B) after RMB joined the SDR 60 Dynamic variation process of risk input for the SDR currencies 64 Dynamic variation process of risk output for the SDR currencies 65 The amount and annual growth rate of China’s imports and exports 67 The amount and annual growth rate of Japan’s imports and exports 68 The cumulative impact on China’s imports and exports after the 811 exchange rate reform 70 The cumulative impact on China’s processing trade and general trade after the 811 exchange rate reform 71 The cumulative impact on China’s foreign trade with major trading partners 72 The cumulative impact on China’s exports of major products 73 The cumulative impact on China’s imports of major products 74 EEMD-LSSVR decomposition and integrated approach 80 Result of EEMD algorithm of daily central parity of RMB/USD 82 Result of EEMD algorithm of monthly central parity of RMB/USD 84 A forecasting approach based on the domestic economic situation 90 Structure of D-vine copula 101 Structure of C-vine copula 101 Time series of five RMB exchange rates and the returns 107 A forecasting approach based on the public’s expectations 116

Tables

2.1 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 4.1 4.2 4.3 4.4 4.5

Distribution functions of copulas Description of CNH and CNY Correlation test results for CNY and CNH in different periods Results of the Granger causality test for the entire period of CNY and CNH Statistics of CNY and CNH Results of Bry-Boschan algorithm from August 2010 to December 2010 (IMF1–3) Results of Bry-Boschan algorithm from August 2010 to December 2010 (IMF4–7) Results of Bry-Boschan algorithm from August 2011 to November 2011 (IMF1–3) Results of Bry-Boschan algorithm from August 2011 to November 2011 (IMF4–7) Results of Bry-Boschan algorithm from August 2015 to December 2015 (IMF1–3) Results of Bry-Boschan algorithm from August 2015 to December 2015 (IMF4–7) Summary statistics for the real effective exchange rate indices Stationary test for the real effective exchange rate indices Prediction variance decomposition based on DAG results (%, forecast period: 10th) Risk conduction network constitution among the SDR currencies (%) Statistics of central parity of RMB/USD Decomposition of daily central parity of RMB/USD Decomposition of monthly central parity of RMB/USD Sample period of training subset and testing subset Performance comparison of different models for daily and monthly exchange rates: three-step-ahead forecasting results

24 42 46 47 49 50 51 52 52 53 54 59 59 61 62 81 83 85 85 86

Tables ix

5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 7.1 7.2 7.3 7.4 7.5 7.6 7.7 8.1 8.2

Statistics of the domestic economic variables and the exchange rate Results of the Granger causality test Results of the correlation test of RMB/USD and domestic economic variables Results of the grey relational analysis of RMB/USD and domestic economic variables Statistics of RMB/USD and the main domestic economic variables Statistics of the seasonally adjusted data Unit root test of RMB/USD and the main domestic economic variables Results of the Johansen cointegration test Performance comparison of different models for daily and monthly exchange rates: three-step-ahead forecasting results Statistics of five RMB exchange rates Statistics of the return of five exchange rates Results of Student t-copula of C-vine copula Results of Clayton copula of C-vine copula Results of SJC copula of C-vine copula Statistics of four RMB exchange rates Sample period of training subset and testing subset Performance comparison of different models for daily and monthly exchange rates: three-step-ahead forecasting results Keywords for web search data Statistics of RMB/USD and the web search data Results of the Granger causality test of daily data Results of the Granger causality test of monthly data Results of the gray relational analysis of RMB/USD and web search data Sample period of training subset and testing subset Performance comparison of different models for daily and monthly exchange rates: three-step-ahead forecasting results Performance comparison of different models for daily exchange rates: one-step-ahead forecasting results Performance comparison of different models for monthly exchange rates: one-step-ahead forecasting results

91 92 94 95 95 96 96 96 97 108 109 110 111 111 112 112 113 117 117 118 118 119 120 122 125 126

Preface

Due to the deepening of the internationalization of the renminbi (RMB), the gradual opening of the capital account and the further reform of the RMB pricing mechanism, the fluctuation of the RMB exchange rate has had a markedly enhanced trend. Since 2014, the RMB against the US dollar has ended the unilateral appreciation trend and gone into two-way fluctuations. With the high speed of China’s economic development, the international influence of the RMB is increasing, and the international use of the RMB had developed rapidly. In November 2015, the International Monetary Fund announced the RMB joining the Special Drawing Right (SDR) currency basket. The RMB is now at a new stage of internationalization. The role of the exchange rate for the national economy can’t be ignored. Accurately forecasting exchange rate trends and scientific analysis of exchange rate changes are of great significance in both theoretical and practical aspects. A new methodology for exchange rate forecasting is proposed in this book. Firstly, from the perspective of China’s exchange rate data analysis, this book systematically studies the lead–lag relationship between the offshore RMB (CNH) and the onshore RMB (CNY) under the influence of extreme events. From the perspective of the domestic economic situation, this book analyzes the relationship between major domestic economic variables and the exchange rate; specially, we quantitatively measure the impact of renminbi depreciation on China’s imports and exports. From the perspective of the international economic situation, it analyzes the relationship between the RMB and the major foreign exchange assets after exchange rate reforms. We also systemically study the risk spillover networks and examine the dynamic relationship of exchange rates among the SDR currencies. From the perspective of the public’s expectations, this book also analyzes the correlation between web search data, which is related to the public’s expectations, and the exchange rate. Secondly, with the new comprehensive integrated approach, the exchange rate is finally weight integrated from four perspectives: the exchange rate data decomposition and integration, the domestic economic situation, the international economic situation, and the public’s expectations. The main innovations and features of this book are as follows:

Preface xi 1. Theoretical research. This book analyzes the reasons for exchange rate fluctuations and develops a new methodology for exchange rate forecasting from four perspectives: the exchange rate data decomposition and integration, the domestic economic situation, the international economic situation, and the public’s expectations. 2. Basic data. In this book, the research data include not only exchange rate data and macroeconomic variable data, but also daily and monthly web search data, such as the Baidu search volume index and Google search volume index, to forecast exchange rate. The research results show that there is a dynamic relationship between web search data and the exchange rate. Modeling the exchange rate based on web search data can improve the forecasting accuracy. 3. Empirical research. This book analyzes the dynamic relationship between the exchange rate and four aspects, namely exchange rate data decomposition and integration, the domestic economic situation, the international economic situation, and the public’s expectations, and forecasts the exchange rate based on these four aspects. In sum, the main innovations and features of the empirical research are as follows: Firstly, a hybrid approach named the EMD-Bry-Boschan method is proposed to study the lead–lag relationship between the offshore RMB and the onshore RMB under the influence of extreme events. Furthermore, this book analyzes the lead–lag relationship between the CNH spot exchange rate and the CNY spot exchange rate when extreme events are caused by market factors and/or policy factors. Secondly, for evaluating the influence of the RMB joining the SDR basket on RMB’s internationalization, we propose a new hybrid approach by integrating the directed acyclic graph (DAG) and structural vector autoregression (SVAR) to further analyze and assess the risk spillover and the resulting dynamic change between the SDR currencies before and after the RMB joined the SDR basket. Thirdly, after the “811 exchange rate reform”, the renminbi continued to depreciate against the US dollar, with a cumulative depreciation of 8.42% from August 2015 to June 2016. An extended event analysis method is utilized to quantitatively measure the impact of renminbi depreciation on China’s imports and exports. Fourthly, a forecasting approach based on the exchange rate data analysis is proposed. It is the first time that the decomposition and integration approach named EEMD-LSSVR is utilized to forecast the exchange rate. The ensemble empirical mode decomposition (EEMD) algorithm is used to decompose the exchange rate to several different intrinsic mode functions (IMFs) and a residual sequence, and least squares support vector regression (LSSVR) is employed to forecast those different IMFs and the residual sequence respectively. Based on the simple addition ensemble method, the results are aggregated into final integrated results.

xii

Preface Fifthly, a forecasting approach based on the domestic economic situation is proposed. According to the Granger causality test, correlation test and the grey relational analysis, the book studies the correlation between the major domestic economic variables and the exchange rate, and develops a vector error correction model (VECM) to forecast the exchange rate with three variables that are selected by the three correlation analysis methods. Sixthly, a new forecasting approach based on the international economic situation is proposed by integrating the vine copula and a support vector neural network (SVNN). The vine copula is used to study the dependencies between the RMB and the major foreign exchange assets, particularly during exchange rate reforms. Three variables that have high degrees of dependence with RMB/USD are selected to represent the international economic situation to forecast RMB/USD with SVNN. Seventhly, a forecasting approach based on the public’s expectations is proposed by integrating the Granger causality test, grey relational analysis and kernel extreme learning machine (KELM). Daily and monthly web search data, such as the Baidu search volume index and Google search volume index, which are related to the public’s expectations, are used to forecast exchange rates. This book analyzes the dynamic relationship between the web search data and the exchange rate using the Granger causality test and the grey relational analysis, and develops a KELM forecasting approach based on the public’s expectations. Eighthly, a comprehensive integrated approach is proposed for exchange rate forecasting by using long short-term memory (LSTM) to integrate the forecasting results of four aspects, that is, the exchange rate data decomposition and integration, the domestic economic situation, the international economic situation, and the public’s expectations. The empirical results show that the LSTM-integrated forecasting approach outperforms the benchmarks in level forecasting and directional forecasting.

Acknowledgments

This research is supported by the National Natural Science Foundation of China (Project No: 71801213 and Project No: 71988101). The authors extend their sincere thanks to the many people and organizations who provided so much support and understanding, which helped them to complete this book. The authors also express their sincere appreciation to all the researchers and organizations who provided references during the process of writing this book and thus made great contributions to the content of the book.

1

Introduction

Background and motivations Background Foreign exchange rates are always characterized by high complexity and strong nonlinearity, since exchange rates are affected by numerous unstable factors including economic conditions and political events. Developing a highly accurate forecasting method is of great significance since it can provide requisite evidence for investors and policy makers to develop strategies and hedge risks. Currently, how to accurately forecast foreign exchange rates is still an open question with respect to the economic and social organization of modern society. Rapid development of China’s economy has resulted in quick growth in the international use of the renminbi (RMB). China overtook the United States as the world’s biggest exporter in 2007. China’s total imports and exports amounted to US$4.16 trillion and China rose to the largest goods trading nation in 2013 (Figure 1.1). As the Chinese economy expands, the influence of the RMB has been rapidly growing. According to a report from the Society for Worldwide Interbank Financial Telecommunication (SWIFT), the RMB accounted for 2.31% of the global payments and was the fifth most active currency in December 2015.1 In recent years, the international influence of the RMB has increased, and the international use of the RMB developed rapidly. In 2015, the proportion of RMB in cross-border trade increased, and the amount of RMB in the current account was 7.23 trillion yuan, up by 10.4% over the previous year. In November 2015, the International Monetary Fund announced the launch of the new Special Drawing Right (SDR) valuation basket including the Chinese renminbi. Effective October 1, 2016, the RMB officially joined the International Monetary Fund’s SDR basket, along with the US dollar, the euro, the Japanese yen and the British pound sterling. The weight of the RMB is 10.92%, which is more than the Japanese yen (8.33%) and the British pound sterling (8.09%). Please see Figure 1.2 for details. Due to the deepening of the internationalization of the RMB, the gradual opening of the capital account, and the further reform of the RMB pricing mechanism, the fluctuation of the RMB exchange rate has a markedly enhanced trend.

2 Introduction

40,000 30,000 20,000 10,000 2015

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Trade balance of export US_Export

Trade balance of import China_Export

Figure 1.1 Imports and exports of China and the United States

Figure 1.2 The SDR basket – composition and size

Since 2014, the RMB against the US dollar has ended its unilateral appreciation trend and gone into two-way fluctuations. In 2014, the PBOC expanded the floating band of the RMB’s trading price against the US dollar in the interbank foreign exchange market to 2%. On August 11, 2015, the PBOC adjusted and improved the quotation mechanism of the central parity of the RMB against the US dollar (hereinafter referred to as “811 exchange reform”). The central parity of the RMB against the US dollar weakened 1136 basis points and the depreciation rate is 1.9%. From the 811 exchange reform to June 30, 2016, the RMB against the US dollar, the euro and the Japanese yen depreciated 8.42%, 9.70% and 30.47%, respectively. There exist three highly relevant exchange rates in China, named the central parity of the RMB against the US dollar, the China yuan against the US dollar (CNY) and the Hong Kong dollar against the US dollar (CNH) (Figure 1.3). Among them, the volatility of the central parity of the RMB against the US dollar is smallest, followed by the CNY, while the volatility of the CNH is the highest.

Introduction  3

CNY/USD

CNH/USD

2016-04-02

2016-01-02

2015-10-02

2015-07-02

2015-04-02

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2014-10-02

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6.8 6.7 6.6 6.5 6.4 6.3 6.2 6.1 6.0 5.9 5.8

Central parity of RMB/USD

Figure 1.3 The central parity of the RMB against the US dollar, CNY and CNH

The main influencing factors of exchange rate fluctuation Foreign exchange rates are always characterized by high complexity and strong nonlinearity, since the exchange rates are affected by numerous unstable factors including international economic conditions, the domestic economic situation, political events and the public’s expectations. Developing a highly accurate forecasting method is of great significance since it can provide requisite evidence for investors and policy makers to develop strategies and hedge risks. Nowadays, China’s economic situation and the international economic situation are complex, and geopolitical conflicts are ongoing. China’s economy has entered a stage of new normal development, and the volatility of the RMB exchange rate has significantly increased. All these have brought new challenges to theoretical and empirical research. Meanwhile, under the market mechanism, the RMB against the US dollar has gone into two-way fluctuations, and the volatility of the exchange rates are much stronger. The main influencing factors are as follows.

Domestic economic fundamentals The situation of China’s macroeconomics is one of the most important factors that affect the fluctuation of China’s exchange rate. In recent years, faced with structural adjustment problems and affected by economic downward pressure, China’s economic growth slowed (Figure 1.4). Meanwhile, the pace of global economic and global trade recovery is still difficult. China’s imports and exports growth rate has declined a lot; China’s exports growth rate was –14.27% and –5.48% in 2015 and 2016, respectively.

100 millon of the US dollar

4 Introduction 1,500

7.60

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6.40 Current account: balance Balance of payments

Capital and financial account: balance GDP

Figure 1.4 China’s current account and the growth rate of GDP

Second, the balance of payments of one country can directly affect the supply and demand situation of the foreign exchange market; meanwhile the fluctuation in the balance of payments can also reflect the changes in the supply and demand situation of the foreign exchange market. If the balance of payments is surplus, it means the country’s currency is in oversupply. In recent years, China’s current account surplus has been gradually reduced; in 2016 it was $1845.58 billion, and the capital and financial account surplus was $37 billion (Figure 1.4). Third, the level of inflation is one of the most important factors influencing monetary value and purchasing power. If a country’s inflation level is higher than a foreign country, it means the local currency purchasing power has declined, facing devaluation pressure. A rise in the inflation rate will increase the prices of export products, weaken the export competitiveness and further exacerbate the devaluation pressure of the local currency. Fourth, the central bank’s intervention will also affect the fluctuation of the exchange rate. Recently, China’s central bank uses the foreign currency reserve and some other ways to slow the Chinese yuan’s decline against the US dollar, and to keep the RMB basically stable at a reasonable and balance level. When the RMB is faced with devaluation pressure, the central bank can sell foreign currency in the foreign exchange market and buy the local currency. Moreover, usually the movements in foreign exchange reserves can be regarded as an indicator of the central bank’s intervention. As shown in Figure 1.5, since September 2014, and especially since August 2015, China’s foreign exchange reserves have shown a decreasing trend. In June 2016, China’s foreign exchange reserves fell $488.676 billion compared with June 2015, down 13.23% year on year, reflecting the determination of China’s government to keep the RMB basically stable.

Introduction  5

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Foreign exchange reserve: YoY

Figure 1.5 The fluctuations of China’s foreign exchange reserves 53.50 53.00 52.50 52.00 51.50 51.00

2016-05

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PMI of global manufacturing

Figure 1.6 PMI of global manufacturing

International economic situation Faced with strong rebounding trade protectionism and new challenges for globalization, the pace of global economic recovery is difficult. The global manufacturing PMI has remained at 50–51 since December 2015 (Figure 1.6). Global trade is still struggling in a recession phase. From 2008 to 2009, the financial crisis ended the growth rate of more than 10% of global trade, replaced by a low growth rate of 5% or less, and even negative growth in some quarters. From 2012 to 2016, the average annual growth rate of China’s trade was 0.46%. In 2015 and 2016, the growth rate of China’s trade showed two consecutive years of negative growth of –8.1% and –6.78%, respectively (Figure 1.7).

6 Introduction 40

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Figure 1.7 China’s imports and exports 2000–2016

The imbalance of the global economic structure has led to an increase in the potential volatility of global exchange rates. At the same time, the role of monetary policy was weakened, which increased the exchange rate pass-through effect. With the shrinking of economic borders of major countries, the conflicts and fluctuations of exchange rates between countries have increased significantly. The constant rise of the US dollar is one of the most important reasons for the increasing fluctuation in global exchange rates. Since the end of 2015, the RMB against the US dollar has shown a devaluation trend, mainly because the US dollar has been strengthening. However, all of the three RMB exchange rate indices have maintained a steady trend (Figure 1.8).

Public’s expectations The fluctuation of exchange rates is strongly influenced by the public’s expectations of the future exchange rate. If the public’s future expectations of the RMB against the US dollar depreciate, they will sell the RMB and buy US dollars to preserve or increase the value of assets, which will further increase the intensity of the devaluation of the RMB. In summary, exchange rates are influenced by various factors, including the domestic macroeconomics, the international economic situation, the public’s expectations and vice versa. This book estimates the dynamic relationship between China’s onshore and offshore exchange rates, and analyzes the correlation between the exchange rate and the major domestic economic variables, the international economic situation and network search data which can reflect the public’s expectations. Then we can develop a new methodology for exchange rate forecasting from four perspectives: exchange rate data decomposition and integration, the domestic economic situation, the international economic situation, and the public’s expectations.

Introduction  7 6.65

100 millon of the US dollar

105

6.60

103

6.55 101

6.50 6.45

99

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6.35 95

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6.25 93 2015-11-30 2015-12-31 2016-01-31 2016-02-29 2016-03-31 2016-04-30 2016-05-31 2016-06-30 CFETS exchange rate index RMB exchange rate index based on BIS currency basket RMB exchange rate index based on SDR currency basket The central parity of RMB/USD

Figure 1.8 The central parity of RMB/USD and the RMB exchange rate indices

Motivations Forecasting exchange rates accurately is of great importance for investors and policy makers to make strategies and hedge risk. Exchange rates are unstable and complex with high volatility, and are affected by many factors, such as domestic macroeconomics, the international economic situation and the public’s expectations. Therefore, to develop a new methodology to forecast exchange rates accurately and to analyze exchange rates scientifically are of significance for both theoretical and practical aspects.

Significance for theoretical aspects This book develops a new methodology for exchange rate forecasting. Firstly, from the perspective of China’s exchange rate data analysis, this book systematically studies the lead–lag relationship between the offshore RMB and the onshore RMB under the influence of extreme events. From the perspective of the domestic economic situation, it analyzes the relationship between the major domestic economic variables and the exchange rate; specially, we quantitatively measure the impact of renminbi depreciation on China’s imports and exports. From the perspective of the international economic situation, this book analyzes the relationship between the RMB and the major foreign exchange assets following exchange rate reforms. We also systemically study the risk spillover networks and examine the dynamic relationship of exchange rates among the SDR

8

Introduction

currencies. From the perspective of the public’s expectations, this book also analyzes the correlation between web search data, which is related to the public’s expectations, and the exchange rate. Secondly, with the new comprehensive integrated approach, the exchange rate is finally weight integrated from four perspectives: exchange rate data decomposition and integration, the domestic economic situation, the international economic situation and the public’s expectations.

Signifcance for practical aspects First, for the Chinese government, forecasting exchange rates (1) can help to adjust policy decisions in time because it will provide solid evidence for policy adjustment and seize the market trends; (2) can analyze the dynamic relationship between CNY and CNH to help promote internationalization of the RMB; and (3) can help optimize resource allocation and manage inflation through adjusting the exchange rate. Secondly, for investors, it can guide them to timely seize the market signals and predict the exchange rate more accurately to make more profit. Thirdly, for the non-financial enterprises, it can help enterprises reduce the exposure caused by exchange rate fluctuations, foresee trends, make proper development decisions and improve the ability of asset management. This book proposes a new methodology for exchange rate forecasting (1) to estimate the dynamic relationship between China’s onshore and offshore exchange rates, and to analyze the correlation between the exchange rate and the major domestic economic variables, the international economic situation and the network search data that can reflect the public’s expectations; and (2) to develop a comprehensive integrated approach based on long- short-term memory (LSTM) for exchange rate forecasting with four perspectives – exchange rate data decomposition and integration, the domestic economic situation, the international economic situation, and the public’s expectations – to get the final forecasting results.

China’s reforms of the RMB exchange rate regime With China’s economic reform, the RMB exchange rate has been reformed several times, based on the goal of establishing a managed floating exchange rate regime based on market demand and supply with reference to a basket of currencies, and maintaining the RMB exchange rate basically stable at an adaptive and equilibrium level, promoting a balanced BOP account and financial market stability and realizing quality and rapid growth of the economy. (Hu, 2010) In the following sections, we will introduce China’s reforms of the RMB exchange rate regime since 1994 when a managed floating exchange rate regime was in place (Figure 1.9).

Figure 1.9 Timeline: China’s reform of the RMB exchange rate

Introduction  9

10

Introduction

January 1, 1994 From 1979 to 1993, there existed two exchange rates: the RMB’s official exchange rate and the swap market exchange rate. On January 1, 1994, with the unification of dual exchange rates, a managed floating exchange rate based on market supply and demand was officially adopted, and the exchange rate of the RMB to the US dollar was 8.7 yuan to 1 dollar. The exchange rate regime reform also established a unified interbank foreign exchange market and launched the foreign exchange surrender system, which required enterprises to sell their foreign exchange receipts to banks and buy foreign exchange from banks, since the RMB started to play an important role in the allocation of foreign exchange resources.

1997 Asian fnancial crisis When the Asian financial crisis deepened in 1997, many of the Asian currencies depreciated. In order to preserve financial stability in Asia and prevent further contagion of the crisis, China kept the RMB stable around 8.28 yuan to 1 dollar and narrowed the floating range of the RMB exchange rate.

July 21, 2005 In order to further enhance the managed floating exchange rate and increase the importance of market supply and demand, China improved the managed floating exchange rate regime by moving into a managed floating exchange rate regime based on market supply and demand with reference to a basket of currencies, and revalued the RMB by 2.1% on July 21, 2005. In addition, the exchange rate was allowed to move within a wider band, that is, a daily band of 0.3% against the US dollar.

May 21, 2007 From July 21, 2005, to May 21, 2007, the RMB against the US dollar had appreciated 5.48%, from 8.11 yuan to 1 dollar to 7.7752 yuan to 1 dollar. Meanwhile, since the exchange rate reform of 2005, the flexibility of the RMB exchange rate had increased. In order to further increase the flexibility of the RMB exchange rate and improve the RMB exchange rate regime, on May 21, 2007, the exchange rate was allowed to move within a wider band, from a daily band of 0.3% against the US dollar to 0.5%.

July 2008 From May 21, 2007, to June 30, 2008, the RMB against the US dollar had appreciated 10.52%. In July 2008, in order to preserve exchange rate stability in China and to help China’s economy ride through the impact of the US subprime

Introduction 11 mortgage crisis, China’s central bank pegged the RMB against the US dollar at 6.83 and narrowed the floating range of the RMB exchange rate.

June 19, 2010 On June 19, 2010, China’s central bank announced resuming and furthering the reform of the RMB exchange rate regime based on measures taken in 2005 to increase the flexibility of the RMB exchange rate, and continued emphasis would be placed to reflect market supply and demand with reference to a basket of currencies.

April 16, 2012, and March 15, 2014 In order to further increase the flexibility of the RMB exchange rate, beginning April 16, 2012, China’s central bank widened the daily trading band for the RMB against the US dollar from 0.5% to 1%. And on March 15, 2014, the RMB exchange rate was allowed to move within a wider band; the daily trading band for the RMB against the US dollar increased from 1% to 2%.

August 11, 2015 On August 11, 2015, China further improved the quotation mechanism of the RMB’s central parity rate against the US dollar by taking into consideration the previous day’s closing rate on the interbank forex market to reflect the changes of market supply and demand. The People’s Bank of China described this reform as a “one-time correction” in order to bridge previously accumulated differences between the spot market rate and the central parity rate. On that day, the RMB’s central parity rate against the US dollar depreciated sharply by 1136 basis points. On December 11, 2015, China Foreign Exchange Trade System (CFETS) published the CFETS exchange rate index, which is based on a basket of currencies and offeredr a more comprehensive and accurate way to assess market conditions so as to maintain the stability of the RMB exchange rate against a basket of currencies. In 2015, the internationalization of the RMB made much progress:2 1. The RMB gained increased prominence in international economic affairs. On November 30, 2015, the International Monetary Fund announced including the RMB in the currency basket of the SDR. According to SWIFT, the RMB accounted for 2.31% of the global payments and was the fifth most active currency in December 2015. 2. The international use of the RMB rose steadily. By the end of 2015, in Mainland China the RMB bank deposit of nonresidents was 1.54 trillion yuan, in major offshore markets the RMB deposit was RMB 1.45 trillion

12

Introduction

yuan and the outstanding amount of RMB international bonds was RMB 590.07 billion yuan. 3. RMB foreign exchange transactions were more active. In 2015, the average daily trading volume on the onshore RMB exchange market was US$72.8 billion. According to incomplete statistics, the average daily turnover of RMB exchange trading on major RMB offshore markets, e.g., Singapore, Hong Kong and London, exceeded US$210 billion in 2015. 4. International cooperation made remarkable gains. By the end of 2015, 33 overseas central banks or monetary authorities had signed the bilateral local currency swap agreements with the PBOC, whose total size had reached 3.31 trillion yuan. Overseas RMB clearing arrangements were established in 20 countries and regions, including Hong Kong, Macau, Taiwan, Singapore and Switzerland. 5. The reform of the RMB exchange rate regime on August 11, 2015. On August 11, 2015, China further improved the quotation mechanism of the RMB’s central parity rate against the US dollar by taking into consideration the previous day’s closing rate on the interbank forex market to reflect the changes of market supply and demand. On December 11, 2015, CFETS published the CFETS exchange rate index that further strengthened the RMB exchange rate regime on the basis of market supply and demand with reference to a basket of currencies.

Contributions A new methodology for exchange rate forecasting is proposed in this book. Firstly, from the perspective of China’s exchange rate data analysis, this book systematically studies the lead–lag relationship between the offshore RMB and the onshore RMB under the influence of extreme events. From the perspective of the domestic economic situation, it analyzes the relationship between major domestic economic variables and the exchange rate; specially, we quantitatively measure the impact of renminbi depreciation on China’s imports and exports. From the perspective of the international economic situation, this book analyzes the relationship between the RMB and major foreign exchange assets following exchange rate reforms. Meanwhile, we systemically study the risk spillover networks and examine the dynamic relationship of exchange rates among the SDR currencies. From the perspective of the public’s expectations, this book also analyzes the correlation between web search data, which is related to the public’s expectations, and the exchange rate. Secondly, with the new comprehensive integrated approach, the exchange rate is finally weight integrated from four perspectives: exchange rate data decomposition and integration, the domestic economic situation, the international economic situation, and the public’s expectations. The main innovations and features of this book are as follows: 1. Theoretical research. This book analyzes the reasons for exchange rate fluctuations and develops a new methodology for exchange rate forecasting from

Introduction 13 four perspectives: exchange rate data decomposition and integration, the domestic economic situation, the international economic situation, and the public’s expectations. 2. Basic data. In this book, the research data include not only exchange rate data and macroeconomic variable data, but also daily and monthly web search data, such as the Baidu search volume index and Google search volume index, to forecast exchange rate. The research results show that there is a dynamic relationship between web search data and the exchange rate. Modeling the exchange rate based on web search data can improve forecasting accuracy. 3. Empirical research. This book analyzes the dynamic relationship between the exchange rate and four aspects – exchange rate data decomposition and integration, the domestic economic situation, the international economic situation and the public’s expectations – and forecasts the exchange rate based on those four aspects. In sum, the main innovations and features of the empirical research are as follows: Firstly, a hybrid approach, named the EMD-Bry-Boschan method, is proposed to study the lead–lag relationship between the offshore RMB and the onshore RMB under the influence of extreme events. Furthermore, this book analyzes the lead–lag relationship between the CNH spot exchange rate and CNY spot exchange rate when the extreme events are caused by market factors and/or policy factors. Secondly, for evaluating the influence of the RMB joining the SDR basket on RMB’s internationalization, we propose a new hybrid approach by integrating the directed acyclic graph (DAG) and structural vector autoregression (SVAR) to further analyze and assess the risk spillover and the resulting dynamic change between the SDR currencies before and after the RMB joined the SDR basket. Thirdly, after the 811 exchange rate reform, the renminbi continued to depreciate against the US dollar, with a cumulative depreciation of 8.42% from August 2015 to June 2016. An extended event analysis method is firstly utilized to quantitatively measure the impact of renminbi depreciation on China’s imports and exports. Fourthly, a forecasting approach based on exchange rate data analysis is proposed. It is the first time that the decomposition and integration approach named EEMD-LSSVR is utilized to forecast the exchange rate. The ensemble empirical mode decomposition (EEMD) algorithm is used to decompose the exchange rate to several different intrinsic mode functions (IMFs) and a residual sequence, and least squares support vector regression (LSSVR) is employed to forecast those different IMFs and the residual sequence respectively. Based on the simple addition ensemble method, the results are aggregated into final integrated results. Fifthly, a forecasting approach based on the domestic economic situation is proposed. Using the Granger causality test, correlation test and the grey relational analysis, the book studies the correlation between major domestic economic variables and the exchange rate, and develops the vector error correction

14

Introduction

model (VECM) to forecast the exchange rate with three variables that are selected by the three correlation analysis methods. Sixthly, a new forecasting approach based on the international economic situation is proposed by integrating the vine copula and the support vector neural network (SVNN). The vine copula is used to study the dependencies between the RMB and major foreign exchange assets, particularly during exchange rate reforms. Three variables that have higher degrees of dependence with RMB/ USD are selected to represent the international economic situation to forecast RMB/USD with SVNN. Seventhly, a forecasting approach based on the public’s expectations is proposed by integrating the Granger causality test, grey relational analysis and the kernel extreme learning machine (KELM). Daily and monthly web search data, such as the Baidu search volume index and Google search volume index, which are related to the public’s expectations, can be used to forecast exchange rates. This book analyzes the dynamic relationship between web search data and the exchange rate using the Granger causality test and the grey relational analysis, and develops a KELM forecasting approach based on the public’s expectations. Eighthly, a comprehensive integrated approach is proposed for exchange rate forecasting by using LSTM to integrate the four aspects’ forecasting results, that is, the exchange rate data decomposition and integration, the domestic economic situation, the international economic situation and the public’s expectations. The empirical results show that the LSTM integrated forecasting approach outperforms the benchmarks in level forecasting and directional forecasting.

Book structure This book proposes a new methodology for exchange rate forecasting: Firstly to estimate the lead–lag relationship between the offshore RMB and the onshore RMB under the influence of extreme events, and to analyze the correlation between the exchange rate and major domestic economic variables, the international economic situation and network search data which can reflect the public’s expectations; Secondly, through the LSTM network to integrate the forecast results of the four aspects, and to develop a new methodology for exchange rate forecasting from four perspectives – exchange rate data decomposition and integration, the domestic economic situation, the international economic situation, and the public’s expectations – get final forecasting results. The remaining chapters of this book are organized as follows. In Chapter 2, a detailed review of literature on exchange rate analysis and forecasting is provided. Firstly, a detailed review of literature on exchange rate theory is introduced including purchasing power parity theory, interest rate parity theory and exchange rate pass-through theory. Secondly, we summarize the literature of the correlation relationship between economic variables and the exchange rate, and the approaches for correlation analysis. Thirdly, commonly used decomposition algorithms are introduced, including the

Introduction 15 empirical mode decomposition method (EMD), ensemble empirical mode decomposition (EEMD), variational mode decomposition (VMD), wavelet packet decomposition (WPD) and complementary ensemble empirical mode decomposition (CEEMD). Fourthly, we detail the forecasting approaches and divide the approaches into three categories: single forecasting models, hybrid forecasting approaches and ensemble learning approaches. Fifthly, we provide some comments on the existing literature. In Chapter 3, we analyze the dynamic relationships of RMB and other factors, including CNH and CNY, SDR currencies and China’s foreign trade. Firstly, a hybrid approach named the EMD-Bry-Boschan method is proposed to study the lead–lag relationship between the offshore RMB and the onshore RMB under the influence of extreme events. In this part, the EMD algorithm is used to decompose the offshore RMB and the onshore RMB to several different IMFs and a residual sequence, respectively, and the EMD-Bry-Boschan method is employed to analyze the lead–lag relationship between the CNH spot exchange rate and CNY spot exchange rate when the extreme events are caused by market factors and/or policy factors. Secondly, for evaluating the influence of the RMB joining the SDR basket on the RMB’s internationalization, we propose a new hybrid approach by integrating the directed acyclic graph (DAG) and structural vector autoregression (SVAR) to further analyze and assess the risk spillover and the resulting dynamic change between the SDR currencies before and after the RMB joining the SDR basket. Thirdly, after the 811 exchange rate reform, the renminbi continued to depreciate against the US dollar, with a cumulative depreciation of 8.42% from August 2015 to June 2016. Therefore, an extended event analysis method is utilized to quantitatively measure the impact of renminbi depreciation on China’s imports and exports. In Chapter 4, the EEMD-LSSVR–based decomposition and ensemble methodology is utilized to forecast exchange rates. The EEMD-LSSVR decomposition and integrated approach mainly consists of three stages: Firstly, data decomposition. The EEMD algorithm is used to decompose the exchange rate to several different IMFs and a residual sequence. Secondly, single forecasting. LSSVR is employed to forecast those different IMFs and the residual sequence respectively. Thirdly, ensemble forecasting. Based on the simple addition ensemble method, results are aggregated into final integrated results. In Chapter 5, a forecasting approach based on the domestic economic situation is proposed. The proposed VECM-based ensemble learning approach includes the following three steps. First, data extraction. According to the existing literature, 16 macroeconomic variables are selected, including import, export and foreign exchange reserves, which are often selected to study the relationship between the exchange rate and the macroeconomic variables. Secondly, data selection. By integrating the Granger causality test,

16

Introduction

Figure 1.10 Book structure

correlation test and grey relational analysis, we rank the correlation of RMB/ USD with China’s 16 major macroeconomic variables, and then filter the three variables that have the highest degrees of relevance with the exchange rate to represent the domestic situation. Thirdly, data computing. Based on the domestic situation, VECM is used to forecast the central parity of RMB/ USD. Multiple evaluation criteria are employed to comprehensively evaluate the forecasting performance of the proposed approach and benchmarks. In Chapter 6, a forecasting approach based on the international economic situation is proposed by integrating vine copula and SVNN for the first time. In this chapter, major foreign currencies are selected, including the currencies of the SDR currency basket. By considering the particularity of China’s exchange market, the Hong Kong dollar is also taken into consideration. Firstly, the AR-GJR-GARCH is utilized to filter the log yield. Secondly, the vine copula is used to study the dependencies between the RMB and the

Introduction 17 major foreign exchange assets, including the RMB against the US dollar, the RMB against the euro, the RMB against the 100 Japanese yen, the RMB against the Hong Kong dollar and the RMB against the British pound sterling, under the exchange rate reforms. Thirdly, three variables are selected to represent the international economic situation, for they have higher dependencies with the RMB/USD. Fourthly, a vine copula–SVNN hybrid forecasting approach based on the international economic situation is proposed to forecast the central parity of the RMB against the USD. In Chapter 7, a forecasting approach based on the public’s expectations is proposed. With the wide use of the internet, web search data can reflect the public’s attention and expectations. First, data extraction. By using different keywords, the Google search volume index (GSVI) and Baidu search volume index (BSVI) are extracted from Google Trends and the Baidu Index, respectively. These two indices are used to represent the public’s expectations. Secondly, data selection. The Granger causality test and grey relational analysis are utilized to analyze the dynamic relationship between the RMB exchange rate and the web search data, including GSVI and BSVI. Thirdly, data computing. The KELM forecasting approach based on web search data to present the public’s expectations is proposed, by integrating GSVI, BSVI and KELM to forecast the daily and monthly central parity of the RMB against the US dollar. And multiple evaluation criteria are employed to comprehensively evaluate the forecasting performance of the proposed approach and benchmarks. In Chapter 8, a comprehensive integrated approach based on LSTM is proposed to forecast the exchange rate. LSTM is used to integrate the four aspects’ forecasting results, that is, exchange rate data decomposition and integration, the domestic economic situation, the international economic situation, and the public’s expectations, to get the final forecasting results. The empirical results show that the LSTM-integrated forecasting approach outperforms the benchmarks in level forecasting and directional forecasting. Chapter 9 presents the conclusions and discusses future research issues. The structure of the book is shown in Figure 1.10.

Notes 1 https://www.swift.com. 2 2016 RMB internationalisation report published by PBOC.

2

Literature review

In this chapter, first, a detailed review of literature about exchange rate theories is introduced including purchasing power parity theory, interest rate parity theory and exchange rate pass-through theory. Secondly, we summarize the literature of the correlation relationship between economic variables and the exchange rate, and approaches for correlation analysis. Thirdly, multiple commonly used decomposition algorithms are introduced, including the empirical mode decomposition method (EMD), ensemble empirical mode decomposition (EEMD), variational mode decomposition (VMD), wavelet packet decomposition (WPD) and complementary ensemble empirical mode decomposition (CEEMD). Fourthly, we analyze the forecasting approaches and divide the approaches into three categories: single forecasting models, hybrid forecasting approaches and ensemble learning approaches. Fifthly, we provide some comments on the existing literature.

Exchange rate theories In a market-oriented economy, the foreign exchange rate is one of the most important economic variables. It can connect and coordinate the various macroand microeconomic variables, and affect one country’s balance of domestic and foreign economy. To analyze foreign exchange rates, Cassel (1918) and Keynes (1923) proposed purchasing power parity (PPP) and interest rate parity (IRP) from the perspective of international commodity markets and the balance of asset markets, respectively. Meanwhile, the exchange rate pass-through (ERPT) is often used to analyze the pass-through effect of exchange rates to the macroeconomic variables (Goldberg and Knetter, 1997; Campa and Goldberg, 2002; Jiang and Kim, 2013).

Purchasing power parity theory The purchasing power parity (PPP) theory states that the exchange rate between two currencies is equal to the ratio of the currencies’ respective purchasing power (Cassel, 1918). The concept is based on the law of one price, where in the absence of transaction costs and official trade barriers, identical goods will have the same price in different markets when the prices are expressed in the same currency.

Literature review 19 No consensus has been reached among the empirical literature that has studied PPP. Mark (1990), Grilli and Kaminsky (1991), Doganlar (1999), Coe and Serletis (2002) proved PPP can’t hold. However, the empirical studies of Taylor (1995), Taylor and Sarno (1998), Sarno and Taylor (2002), MacDonald (1993), Lothian and Taylor (2000, 2008), and Cuestas (2009) showed that PPP can hold. Lee and Chou (2013) analyzed the possibility of nonlinear adjustment and unknown smooth breaks in the stationarity of real exchange rates in the Group of 20 (G-20) countries and the results implied that PPP was valid for all in the G-20. Bahmani-Oskooee et al. (2016) used a panel stationary test with both sharp and smooth breaks to test PPP in 11 emerging countries and the results provided strong support for PPP in these emerging countries.

Interest rate parity theory Interest rate parity is a theory in which the interest rate differential between two countries is equal to the differential between the forward exchange rate and the spot exchange rate. The interest rate parity can be divided into uncovered interest rate parity (UIRP) and covered interest rate parity (CIRP). There are many empirical studies based on interest rate parity. Flood and Rose (2002) investigated UIRP using daily data for 23 developing and developed countries during the crisis-strewn 1990s, and the empirical results showed that UIRP works better on average in the 1990s than in previous eras. MacDonald and Nagayasu (2000) studied the long-run relationship between real exchange rate and real interest rate (RERI) differentials of 14 industrialized countries, and the empirical results implied that the long-run relationship between RERI differentials is consistent with the interest rate parity. PPP and IRP are widely used in exchange rate forecasting (Hoffman and Rasche, 1996; Cuestas, 2009; Lee and Chou, 2013). Lots of literature have demonstrated that the PPP and IRP are effective in long-time exchange rate forecasting (Bahmani-Oskooee et al., 2016; Ma et al., 2017).

Exchange rate pass-through theory Exchange rate pass-through (ERPT) refers to the degree to which exchange rate changes are passed through to price level changes (Goldberg and Knetter, 1997; Campa and Goldberg, 2002; Jiang and Kim, 2013). Much literature has studied the impact of incomplete ERPT on macroeconomic variables, including inflation, monetary policy, foreign trade and balance of payments (Taylor, 2000; Gueorguiev，2003; Gagnon and Ihrig, 2004; Pollard and Coughlin, 2004; Sutherland, 2005; Campa and Goldberg, 2002; Pennings, 2017). According to the existing literature, we can conclude that (1) exchange rate movements can partially be transmitted into prices, that is, the pass-through is incomplete and thus lies between zero and one (Goldberg and Knetter, 1997; Campa and Goldberg, 2002, 2005; Ihrig et al., 2006); (2) the ERPT is bigger

20

Literature review

in developing countries and emerging economies than in developed countries (Campa and Goldberg, 2002; Choudhri and Hakura, 2001); (3) over the last decades, the ERPT has substantially declined in several advanced and industrial economies, and likewise in some developing countries (Campa and Goldberg, 2005; Civcir and Akçaglayan, 2010). In general, when the ERPT is low, the central bank is less concerned about the inflation impact of exchange rate changes on domestic prices and, consequently, the freedom of the monetary policy implementation is bigger. The previous literature on estimating the short-run and long-run ERPT often utilized the following approaches: (1) univariate model, (2) vector autoregression (VAR) model, (3) vector error correction (VEC) model and (4) time-varying parameter model. Many authors have used time series data or panel data to estimate the impact of nominal exchange rate changes on domestic prices (Campa and Goldberg, 2002; Jiang and Kim, 2013; Pennings, 2017). The VAR is often utilized to investigate the effect of ERPT (McCarthy, 2000; Ito and Sato, 2008). McCarthy (2000) employed quarter data to investigate the pass-through of exchange rates and import prices to domestic inflation in selected economies. Jiang and Kim (2013) used a structural vector autoregression (SVAR) model to estimate the impact of the nominal exchange rate changes on domestic price under the current monetary policy of China, and the results showed that the ERPT to the producer price index (PPI) and retail price index (RPI) is relatively rapid and incomplete, and the ERPT to the PPI is higher than that to the RPI. Some authors regard the exchange rate as a key macroeconomic determinant for the degree of ERPT (McCarthy, 2000; Campa and Goldberg, 2005; Ghosh, 2013; Ozkan and Erden, 2015; Jiménez-Rodríguez and Morales-Zumaquer, 2016), but no consensus has been reached about the role. Some authors found evidence that in the countries with lower volatility in exchange rates, the ERPT is lower (McCarthy, 2000). Whereas some authors suggested that countries with lower ERPT have higher volatility in exchange rates (Corsett et al., 2008). The degree of ERPT is mainly influenced by the following variables: inflation volatility, degree of openness, output gap, exchange rate regime and expectations (McCarthy, 2000; Jiménez-Rodríguez and Morales-Zumaquer, 2016).

Correlation analysis of the exchange rate market Correlation analysis of exchange rates and other macroeconomic variables Stock price On the dynamic relationship between stock price and the exchange rate market, there is not any unified conclusion (Abdalla and Murinde, 1997; Nieh and Lee, 2002; Caporale and Hunter, 2014; Sui and Sun, 2016). Granger et al. (2000) used Asian flu data to analyze the relationship between exchange rates and stock prices in Hong Kong, Indonesia, Japan, Korea,

Literature review 21 Malaysia, Philippines, Singapore, Thailand and Taiwan. The results indicated that (1) in Korea, the exchange rate led the stock price; (2) the stock prices led exchange rates to some extent in Hong Kong, Malaysia, Singapore, Thailand and Taiwan; (3) there existed no relation between the stock price and the exchange rate market in Japan and Indonesia. Doong et al. (2005) estimated the dynamic relationship between stocks and exchange rates for six Asian countries and areas including Indonesia, Malaysia, Philippines, South Korea, Thailand, and Taiwan. Aydemir and Demirhan (2017) employed the panel Granger causality to estimate the dynamic relationship between stock price and exchange rate for six selected Middle East and North Africa (MENA) countries – Bahrain, Lebanon, Morocco, Pakistan, Qatar and Saudi Arabia – in the sample period of January 2005 to December 2013. The empirical study showed that there was a unidirectional causality from exchange rate to stock prices in the MENA countries. Phylaktis and Ravazzolo (2005) estimated the dynamic relationship between stock prices and the exchange rate. There is a substantial amount of literature that focuses on the dynamic relationship between the stock prices of America and the exchange rate (Roll, 1992; Chow et al., 1997). For China, Zhao (2010) utilized VAR and generalized autoregressive conditional heteroscedasticity (GARCH) to study the dynamic relationship between the RMB real effective exchange rate and stock price. The results showed that there was not a stable long-term equilibrium relationship between the RMB real effective exchange rate and stock prices, and there existed the bidirectional volatility spillovers effects between the two markets, indicating that the past innovations in the stock market had great effect on the future volatility of the foreign exchange market and vice versa.

Infation Based on the exchange rate pass-through theory, the changes of exchange rate can pass-through to the changes of price level (Jiménez-Rodríguez and Morales-Zumaquer, 2016; McCarthy, 2000). Jiménez-Rodríguez and MoralesZumaquer (2016) estimated the exchange rate pass-through to domestic prices and to import prices for Group of Seven (G-7) countries. Goldberg and Campa (2010) studied the relative importance of the different channels that underpin consumer price index (CPI) responsiveness to exchange rates and import prices across the 21 industrialized economies. Edwards (2006) investigated the relationship between inflation targeting and exchange rates. The empirical results found that the inflation-targeting countries have experienced a decline in the pass-through from exchange rate changes to inflation. Aizenman et al. (2011) estimated the inflation targeting in emerging markets, and they mainly focused on the role of the real exchange rate and the distinction between commodity and non-commodity exporters. In this book, we not only focus on the impact of the exchange rate changes on inflation, but also estimate whether the inflation changes will influence the exchange rate.

22

Literature review

Import and export According to the exchange rate pass-through theory, when the pass-through is complete, the response of import prices to the exchange rate movements is one for one. Many empirical studies show that the exchange rate pass-through plays an important role on import prices (Obstfeld and Rogoff, 2000; Choudhri et al., 2005; Ito and Sato, 2008). Arize et al. (2000) estimated the impact of real exchange rate volatility on the export flows of 13 less developed countries. The empirical study results showed that an increase of the real effective exchange rate volatility, in other words, the exchange rate approximated uncertainty, would exert a significant negative effect on export demand in both the short run and the long run in each of the 13 less developed countries. Aristotelous (2001) investigated the impact of exchange-rate volatility and exchange-rate regime on British exports to the United States, and the results showed that there was no evidence that any of the exchange rate regimes of the late 19th and 20th centuries had any impact on the volume of British exports to the United States. A lot of literature is focused on studying the impact of exchange rate movements on imports and exports (Bini, 1991; Chowdhury, 1993; Doğanlar, 2002; Romero, 2017).

Web search data With the wide use of the internet, web search data can reflect the public’s attention and expectations, and provide data for macroeconomic and financial research. More and more researchers begin to develop models using web search data. Economic forecasting using web search data is always based on an assumption, that is “that movements in financial markets and movements in financial news are intrinsically interlinked” (Alanyali et al., 2013). Nardo et al. (2016) revised the literature linking changes in stock returns and trade volumes to measures of web buzz and found that although the web can anticipate financial movements to some extent; the gain seldom exceeds 5%. There is a substantial mass of literature investigating the dynamic relationship between web search data (Weibo, Twitter, financial news and so on) and stock returns and trade volumes (Das and Chen, 2001; Antweiler and Frank, 2004; Gloor et al., 2009; Schumaker and Chen , 2009; Bordino et al., 2012; Alanyali et al., 2013; Karabulut, 2013; Nardo et al. 2016; Wysocki, 1998; Gilbert et al., 2010). Web search data have been applied to predict many macroeconomic variables and can significantly improve forecasting performance. Li et al. (2015) used the weekly Google Trends index for inflation forecasting, and the study found that the search data were strongly correlated with the CPI and the mixed-data sampling (MIDAS) model, and the search data outperformed the benchmark models, with the average reduction of root mean square error (RMSE) by 32.9%.

Literature review 23

Approaches for correlation analysis Copula In probability theory and statistics, a copula is a multivariate probability distribution for which the marginal probability distribution of each variable is uniform. Copulas can capture the dependence between random variables, which are widely used in financial and economic analysis. Embrechts (1999) was the first to introduce copulas to capture the dependency of financial markets. Rodriguez (2007) employed a copula approach to estimate the financial contagion between the stock market returns of countries in Asia and Latin America during the Asian and Mexican crises. Doman and Doman (2013) investigated changes in the dynamics of linkages between selected national stock markets during the period 1995–2009, and focused on the possible effects of globalization and differences between crisis and non-crisis periods. Frequently used copulas include Gauss copulas, Student t-copulas, Archimedean copulas and extreme-value copulas. Most important Archimedean copulas include Gumber copulas, Clayton copulas and Frank copulas (Table 2.1). Figure 2.1 displays the joint density distributions of the Gaussian copula, Student t-copula, Clayton copula and Gumbel copula under different parameters.

Vine copula Traditional copulas can capture the dependency between financial markets, however they don’t perform well in higher-dimensional cases. Joe (1996) proposed pair-copula construction, and was extended by Bedford and Cooke (2001, 2002), which can be used to compute a multivariate distribution as the product of d(d – 1)/2 bivariate copulas. Kurowicka and Cooke (2006) and Aas et al. (2009) proposed C-vine and D-vine pair-copula constructions. Vine copula has been widely used to study foreign exchange markets. Maya et al. (2015) used the vine copula methodology to estimate the level of contagion among the exchange rates of six Latin American countries (Argentina, Brazil, Chile, Colombia, Mexico and Peru). The empirical results showed that during periods of large appreciations, there existed contagion in Latin American exchange rates. However during the periods of currency depreciation, there was no evidence of contagion. Czado et al. (2012) introduced the class of mixed C-vine copulas and provided sequential and ML estimation procedures for the unknown parameters, and the mixed C-vines were used to model the dependencies among some US exchange rates. Min and Czado (2014) utilized the semiparametric copula–based dynamic (SCOMDY) models based on pair-copula constructions to estimate the dependencies among exchange rates.

Granger causality test Granger (1969) proposed the Granger causality test based on the assumption of linear relationships between variables. A time series x is said to Granger-cause another time series y if the predication error of current y declines by using past

24

Literature review

Table 2.1 Distribution functions of copulas Name

Distribution function

Gauss copula

C (u1, u 2 , ˜,uN ; r ) = fr f -1 (u1 ) , f -1 (u 2 ) ,˜, f -1 (uN )

Student t-copula

C (u1, u 2 , ˜,uN ; r , v )

(

(

= T r ,v Tv-1 (u1 ) ,Tv-1 (u 2 ) ,¼,Tv-1 (uN )

ò

Tv-1 (u1 ) -¥

ò

Tv-1 (u 2 ) -¥

˜

1 æ -1 ö ç 1 + v x¢r x ÷ è ø

ò

v +N 2

Tv-1 (uN ) -¥

)

æ v + N ö - 12 Gç ÷r è 2 ø N æv ö G ç ÷ ( vp ) 2 è2ø

dx1dx 2 ˜dxN

(

Archimedean copula

C (u1, u 2 , ˜,uN ) = j -1 j (u1 ) + j (u 2 ) + ˜ + j (uN )

Extreme-value copula

C u1t , u 2t , ˜,uNt = C t (u1, u 2 , ˜ ,uN )

Gumbel copula

Clayton copula

(

)

a ì éN 1ù ü ï C (u1, u 2 , ˜,uN ; a ) = exp í- ê ( - ln un )a ú ïý ê ûú þï îï ë n =1

å

æ N ö C (u1, u 2 , ˜,uN ; q ) = ç un-q - N + 1÷ ç ÷ è n =1 ø æ 1 ç C (u1, u 2 , ˜,uN ; l ) = - ln ç 1 + l ç è

)

"t > 0

å

Frank copula

)

-

1 q

Õ (e N

n =1

(e

-l

a Î ( 0, 1 1ùû

q Î ( 0, ¥ )

)

ö -1 ÷ ÷, N -1 -1 ÷ ø - lun

)

l ¹ 0,N ³ 3, l Î ( 0, ¥ )

values of x in addition to past values of y. The Granger causality test has been widely used to analyze the correlation of economic and financial variables. Let y and x be stationary time series. To test the null hypothesis that x does not Granger-cause y, one finds the proper lagged values of y to include in a univariate autoregression of y:

y t = a 0 + a1 y t -1 + ¼ + am y t -m + e t

Literature review 25

Figure 2.1 Joint density distributions of the Gaussian copula, Student t-copula, Clayton copula and Gumbel copula under different parameters

Next, the autoregression is augmented by including lagged values of x:

y t = a 0 + a1 y t -1 + ¼ + am y t -m + b p x t - p + ¼ + bq x t -q + e t One retains in this regression all lagged values of x that are individually significant according to their t-statistics, provided that collectively they add explanatory power to the regression according to an F-test (whose null hypothesis is no explanatory power jointly added by the x’s). In the notation of the preceding augmented regression, p is the shortest and q is the longest lag length for which the lagged value of x is significant. The null hypothesis that x does not Granger-cause y is accepted if and only if no lagged values of x are retained in the regression. The Granger causality test has been widely used to analyze the relationship of economic and financial variables. For further details on this method, please refer to Granger (1969).

26

Literature review

Narayan and Smyth (2005) used the Granger causality test to estimate the dynamic relationship among electricity computation, employment and real income. Akinboade and Braimoh (2010) applied the Granger causality test to study the dynamic relationship between international tourism and economic development in South Africa. The approach has also been applied in other areas, including energy consumption (Narayan and Prasad, 2008; Chiou et al., 2008; Bozoklu and Yilanci, 2013), foreign trade (Bini, 1991; Chowdhury, 1993; Konya, 2004), economic growth (Chang et al., 2014; Hsueh et al., 2013) and the stock market (Ajayi et al., 1998; Granger et al., 2000; Chu et al., 2016). Many researchers used the Granger causality test to study foreign exchange rates (Ajayi et al., 1998; Abdalla, 1997; Ibrahim, 2000; Granger et al., 2000; McCarthy, 2000; Doğanlar, 2002; Kim, 2003; Ito and Sato, 2008; Bhattacharya et al., 2011; Aydemir and Demirhan, 2017; Romero, 2017).

Grey relational analysis The Grey relational analysis is employed to solve problems with complicated interrelationships between multiple factors and variables, which is a measurement method to determine the relationship between sequences using limited amounts of data. The grey relational coefficient and grey relational degree can be formulated as follows:

m + x maxmax x 0¢ ( k ) - xi¢ ( k )

r0i ( k ) =

i

k

x 0¢ ( k ) - xi¢ ( k ) + x maxmax x 0¢ ( k ) - xi¢ ( k ) i

k

x Î ( 0, 1) ; k = 1, 2,˜, n; i = 1, 2,˜,m r0i =

1 n

n

år

0i

(k )

i = 1, 2,˜,m

k =1

The fundamental idea of grey relational analysis is that the closeness of a relationship is judged based on the similarity level of the geometric patterns of sequence curves. Then the variables are ranked by the degree of relevance. The higher the degree of geometric similarity, the greater the degree of correlation (Tan and Deng, 1997).

Spillover index The spillover index approach developed by Diebold and Yilmaz (2012, 2014) is usually utilized to analyze the spillover effects between the exchange rate market

Literature review 27 and macroeconomic variables (Reboredo, 2012; Leung et al., 2017; Mensi et al., 2017). This spillover index approach is the generalized form of Diebold and Yilmaz (2009) and is based on the forecast error variance decomposition under the VAR framework of Koop et al. (1996) and Pesaran and Shin (1998), which is invariant to the ordering of the variables in the model. The basic objective of this spillover index methodology is to examine the spillover contribution “to” and “from” other variables in the model through a simple and intuitive forecast of the error variance decomposition under the VAR model. Moreover, in order to capture the magnitude and direction of spillovers, this methodology also uses a rolling window estimation that determines whether a particular variable is a net transmitter or a receiver of the spillovers at each point in time. This approach is widely used to examine the linkage between, for example, exchange rate and equity markets (Grobys and Heinonen, 2017; Leung et al., 2017), exchange rate and oil markets (Chen and Chen, 2007; Reboredo, 2012; Chou and Tseng, 2016; Mensi et al., 2017), exchange rate and inflation (Jordan, 2016), and exchange rate and stock markets (Sui and Sun, 2016). Mensi et al. (2017) identified and selected the currencies that were the most significant net contributors/receivers of returns from/to the oil/currency markets by using the spillover index and network diagrams. Jordan (2016) analyzed the impact of the international spillover effect on Swiss inflation and the exchange rate. The specifications of the spillover index measures start with the following equation of the pth order for the stationary N-variable VAR: p

xt =

åF x

i t -i

+ et

i =1

where xt is a vector of endogenous variables, Φi denotes the N×N matrix of the parameters to be estimated, t = 1, …, T is the time index and i = 1, …, p is the variable index. In addition, ε~(0,∑) is a vector of the error terms that are distributed independently and identically over time. Following Diebold and Yilmaz (2012, 2014), the generalized VAR framework of Koop et al. (1996) and Pesaran and Shin (1998) is usually utilized to produce a forecast of the error variance decompositions that are invariant to the variable ordering. The H-step-ahead generalized forecast error variance decomposition is given by g ij

q

(H ) =

å (e A Se ) å (e A SA e )

s jj-1

H -1

h =0 H -1

h =0

’ i

’ i

h

h

2

j

’ h i

where ∑ denotes the variance matrix of the error vector ε, σjj is the standard deviation of the error term for the jth equation and ei is a selection vector, with one as the ith element and zeros otherwise. This yields the N×N matrix θ(H) = [θij(H)]i,j=1,...,N, where each entry gives the contribution of variable j to the forecast

28

Literature review

error variance of variable i. The main diagonal elements of the θ(H) matrix represent the own shock contributions, whereas the off-diagonal elements represent the contributions “to” other and “from” other variables in the forecast error variance decomposition. The sum of the variance contributions by own- and crossvariables is not equal to one under the generalized variance decomposition, i.e., N

åq

g ij

( H ) ¹ 1 because the shocks to each variable are statistically independent.

j =1

Therefore, each entry of the θ(H) matrix is normalized by dividing by the row sum as

q˜ijg ( H ) =

with

å

N j =1

qijg ( H )

å

N j =1

qijg ( H )

q˜ijg ( H ) = 1 and

å

N i , j =1

q˜ijg ( H ) = N by construction.

As mentioned by Fengler and Gisler (2015), the preceding equation is the representation of approximate fraction of the H-step-ahead forecast error variance of variable i coming from variable j. By using a statistically independent variance contribution, we can construct several spillover measures that would justify the degree of independence of the variables’ ordering in the system. The total spillover index that measures the average contribution of the spillover effect to the variance decomposition of all variables is written as follows:

S

g

å (H ) = å

N g i , j =1 ij i¹j N g ij i , j =1

q˜

(H )

q˜

(H )

=

å

N

q˜

g i , j =1 ij i¹j

(H )

N

The spillover index in this equation measures the average contribution of spillovers to the forecast error variance. Specifically, the directional spillovers transmitted from the i variables to the j variables can also be calculated. For more information, please refer to Diebold and Yilmaz (2012, 2014).

Decomposition algorithms There are many decomposition algorithms, which can decompose the sequence into many subsequences according to the characteristics of the data. It is a completely localized and adaptive algorithm for stationary data and nonstationary data. Due to the high volatility and irregularity nature of foreign exchange rates, the “decomposition and ensemble” principle is especially used to deal with the difficulties in modeling and forecasting foreign exchange rates. Based on the principle

Literature review 29 of decomposition and ensemble, the ensemble learning approach has proved to be an effective and efficient way to improve forecasting performance. And many decomposition models are used to analyze and forecast financial data (Plakandaras et al., 2015; Sun et al., 2020). The forecasting process of the decomposition ensemble learning approach includes the following parts: firstly, decomposition of the original sequence into several modes; secondly, each mode is forecast respectively; and thirdly, the forecasting results of each mode are ensembled to generate final forecasting results. The decomposition strategy is very important for decomposition ensemble learning approaches; a better decomposition algorithm may enhance the forecasting performance. In the following, the empirical mode decomposition method (EMD), ensemble empirical mode decomposition (EEMD), variational mode decomposition (VMD), wavelet packet decomposition (WPD) and complementary ensemble empirical mode decomposition (CEEMD) are introduced.

Empirical mode decomposition (EMD) Huang et al. (1998) proposed a new method for analyzing nonlinear and nonstationary data, named the empirical mode decomposition method (EMD). Based on the principle of local scale separation, it decomposes the original series x(t) into several intrinsic mode functions (IMFs) and a residual sequence r(t). It is different from traditional decomposition methods (e.g., wavelet transform, Fourier transform). It is a completely localized and adaptive algorithm for stationary data and nonstationary data (Zhang et al., 2009b). EMD was initially proposed for studying ocean waves and is now broadly applied in natural science, engineering and social sciences. In economic areas, EMD has been used to examine the changeability of stock markets (Huang et al., 2003), to analyze financial records from the mortgage market (Huang et al., 2003) and to estimate the impact of extreme events on crude oil prices (Zhang et al., 2009a). The EMD algorithm has been applied in exchange rate forecasting. Lin et al. (2012) proposed the EMD-LSSVR model to forecast the exchange rate, which outperformed EMD-ARIMA, LSSVR and ARIMA. Premanode and Toumazou (2013) proposed differential EMD-SVR for exchange rate forecasting. The empirical results showed that the proposed model performed better than the Markov regime switching model and MS-GARCH model. Fu (2010) proposed the EMD-SVR model to forecast the RMB against the euro and the results showed that the forecasting performance of EMD-SVR is better than SVR. Some integrated models have been proposed, including EMD and some neural network models, and the integrated models can improve the forecasting accuracy (Yu et al., 2008b; Yang et al., 2011).

Ensemble empirical mode decomposition (EEMD) To overcome some drawbacks of the EMD algorithm, Wu and Huang (2004 & 2009) extended the EMD algorithm and proposed the EEMD algorithm

30

Literature review

(ensemble empirical mode decomposition), which can be used to analyze the sequence effectively and to reduce the influence of mode mixing of the EMD algorithm. The EEMD algorithm is utilized to decompose the original series x(t) into several IMFs and a residual sequence. The EEMD algorithm decomposes the sequence according to the characteristics of the data. It is a completely localized and adaptive algorithm for stationary data and nonstationary data (Zhang et al., 2009b). However, the EEMD algorithm differs from the EMD algorithm, which is based on a hypothesis that “observations are made up of the real sequence and white noise”. Therefore, the EEMD involves an additional step of adding white noise, which can help to extract the real IMFs. The EEMD algorithm is widely used in complex system analysis, and those results further validate the effectiveness of the EEMD method (Tang et al., 2015; Yu et al., 2016). Meanwhile the EEMD algorithm was utilized to integrate with some artificial neural network algorithms and the integrated models perform good in wind forecasting, port container throughput forecasting and air travel demand forecasting (Wang et al., 2011; Xie et al., 2013; Yu et al., 2014; Hu et al., 2013; Ren et al., 2015). There is less literature about the EEMD algorithm applied in exchange rate forecasting, except for Plakandaras and Papadimitriou (2015) who proposed an SVR and neural network (NN) algorithm based on EEMD to forecast exchange rate.

Variational mode decomposition (VMD) The VMD is a novel signal filtering method originally introduced by Dragomiretskiy and Zosso (2014). In comparison to the traditional EMD algorithm, it has strong robustness for sampling and denoising. VMD is a completely nonrecursive decomposition method in which the modes are extracted simultaneously. The model looks for a set of patterns and their respective center frequencies such that the patterns collectively reproduce the input signal, and each mode is smooth after demodulation to baseband. Lahmiri (2016) utilized the VMD to analyze the stock price, and a new hybrid predictive model was proposed to forecast stock price by using VMD and the backpropagation neural network. He et al. (2018) proposed a new approach to forecast the exchange rate by integrating the VMD and entropy theory, and the empirical results showed that the forecasting performance outperformed the benchmarks. Each mode μk is required to be mostly compact around a center pulsation ωk determined along with decomposition. Moreover, VMD requires the sum of the bandwidth of each mode, which is estimated through the H1 Gaussian smoothness of the demodulated signal, i.e., the squared L2-norm of the gradient is the least, under the constraint that the sum of the modes is equal to the original signal. Hence, for the time series f, the decomposition issue is equivalent to solving the constrained variational issue as follows:

Literature review 31

éæ j ¶t êç d (t ) + pt ëè

å

min

{mk },{wk }

k

åm

s .t .

k

ù - j wk t ö ÷ * mk (t ) ú e ø û

2

2

f

k

where {μk}:={μ1, μ2, …, μk} and {ωk}:={ω1, ω2, …, ωk} are shorthand notations for the set of K modes and their center frequencies, respectively. δ denotes the Dirac distribution, t denotes the time script, j2 = –1 and * is the convolution operator. To render the problem unconstrained, a quadratic penalty term and Lagrangian multipliers λ are introduced. Then, the augmented Lagrangian function is as follows:

L ( mk , wk , l ) = a

å k

éæ ù j ö ¶t êç d (t ) + * mk (t ) ú e ÷ pt ø ëè û

+ l (t ) , f (t )

2 j wk t 2

+ f (t )

å m (t )

2

k

k

2

å m (t ) k

k

where α is the balancing parameter of the data-fidelity constraint. Then, the preceding equation is addressed by the alternate direction method of multipliers. The mode μk(ω) in the frequency domain is updated by the following equation, and the mode μk(t) in the time domain is calculated by the real part of the inverse Fourier transform of μk(ω) in the following equation:

mˆkn +1 (w ) =

fˆ (w ) -

å

i ¹k

mˆi (w ) +

1 + 2a (w - wk )

2

lˆ (w ) 2

The updated equation of center frequencies ωk is provided in the following equation: ¥

wˆ

n +1 k

ò w mˆ (w ) dw = ò mˆ (w ) dw 0

2

k

¥

0

2

k

And the λ is updated by the following equation:

æ ö lˆn +1 (w ) = lˆn (w ) + t ç fˆ (w ) - å mˆ kn +1 (w ) ÷ k è ø

32

Literature review

For further details on the VMD method, please refer to Dragomiretskiy and Zosso (2014). In the VMD framework, the mode μ with high order k represents low-frequency components. Before the VMD method, the number of modes k should be predetermined. In this study, to address this problem regarding optimal selection of the parameter k, a mode number fluctuation method is proposed to determine the number of modes k. The flowchart is displayed in Figure 2.2. The detailed process is as follows: Step 1 – The initial value of mode number is k = k0. Step 2 – When the number of modes is k0, determine whether the central frequencies of mode overlap. Step 3 – If the central frequencies of mode overlap, decrease the mode number and perform VMD until the central frequencies do not overlap. Return k. Step 4 – If the central frequencies of mode do not overlap, increase the mode number and perform VMD until the central frequencies overlap. Return k – 1.

Figure 2.2 Flowchart of estimating the mode number k of VMD

Literature review 33 Wavelet packet decomposition (WPD) is an improved wavelet decomposition (WD) method (Wang et al., 2015), used to decompose the nonlinear and nonstationary signals into various frequencies. The structure of WPD is similar to WD. However, WD only can decompose low-frequency components, whereas the high-frequency components remain unchanged. Part (a) in Figure 2.3 shows a schematic diagram for WD. The result of the decomposition is xt = D1 + D2 + … + Dj + Lj where the original sequence xt is decomposed into the low-frequency component Aj and many high-frequency components Di(i = 1, 2, …, j). As shown in part (b), WPD generates both low-frequency and high-frequency decomposition, and effectively overcomes the limitations of WD. The decomposition result of the original sequence is define as follows:

xt = AAA3 + AAD3 + ADA3 + ADD3 + DAA3 + DAD3 + DDA3 + DDD3 There are two finite impulse filters for wavelets: a high-pass filter h(k) and a lowpass filter l(k). The sequence of recursive functions is defined as follows: 2M -1 12

W2m (t ) = 2

å h(k)W (2t - k) m

k =0

2M -1

W2m +1(t ) = 21 2

å l (k)W (2t - k) m

k =0

ìW0 = f (t ) , ϕ(t) and φ(t) are the scaling function and waveîW1 = j (t )

When m = 0, that is í

let function, respectively. The form of wavelet packet is given by the following:

W j ,m,k (x ) = 2- j 2Wm (2- j x - k)

Figure 2.3 Comparison between three-layer WD and WPD

34

Literature review

Then, the wavelet packet coefficients can be computed by

Skj ,m (x ) =

ò

+¥

-¥

x (t )W j ,m,k (x )dt

where x(t), j, k and m are the signal, scale, position and surge parameter, respectively.

Complementary ensemble empirical mode decomposition (CEEMD) Complementary ensemble empirical mode decomposition (CEEMD) is a modified EMD algorithm developed by Yeh et al. (2010). The EMD algorithm is an empirical, intuitive, direct and self-adaptive processing technique and especially effective when applied to nonlinear dynamical patterns (Yu et al., 2008b; Tang et al., 2012). The CEEMD method adds white noise in pairs to improve the decomposition effect. Hence, CEEMD is adopted in this chapter as another decomposition technique to further decompose the high-frequency components generated by the WPD. The decomposition procedure is as follows: 1. Obtain a positive mixture xp(t) and a negative mixture xn(t) through adding white noise in pairs (ωm(t)) to the original sequence x(t).

x p (t ) = x (t ) + wm (t ) x n (t ) = x (t ) + wm (t ) 2. Decompose the mixtures of added white noise into IMFs utilizing the EMD procedure. 3. Repeat step 1 and step 2 iteratively, and obtain the ensemble IMFs with positive noise and their complementary IMFs with negative noise as the final results. For details, please refer to Yeh et al. (2010).

Forecasting approaches Foreign exchange rates are always characterized by high complexity and strong nonlinearity, since exchange rates are affected by numerous unstable factors including economic conditions and political events. Developing a highly accurate forecasting method is of great significance since it can provide requisite evidence for investors and policy makers to develop strategies and hedge risks. Currently, how to accurately forecast foreign exchange rates is still an open question with respect to the economic and social organization of modern society. To tackle this challenge, a lot of research work has been devoted to exploring the high volatility, nonlinearity, complexity and noisiness nature of foreign exchange rates

Literature review 35 and to developing specific nonlinear approaches to improve the performance of exchange rate forecasting. These forecasting approaches can be divided into three major categories: single forecasting models, hybrid forecasting approaches, and ensemble learning and combination forecasting approaches. Each category is detailed in the following.

Single forecasting models In a variety of single forecasting models, many types of different econometric methods have been proposed for forecasting foreign exchange rates, such as the autoregressive integrated moving average (ARIMA) model (Xiong et al., 2017; Chortareas et al., 2011), generalized autoregressive conditional heteroscedasticity (GARCH) model (West and Cho, 1995; Cai et al., 2012; Chortareas et al., 2011; Wan et al., 2016), vector autoregression model (VAR) (Sarantis and Stewart, 1995; Joseph, 2001; Carriero et al., 2009; Jiang et al., 2018), cointegration model (Moosa and Vaz, 2016; McCrae et al., 2002), error correction model (ECM) (Moosa and Vaz, 2016) and Bayesian theory (Byrne et al., 2016). McCrae et al. (2002) employed the ARIMA model with error correction to forecast the daily Japanese yen (JPY), Malaysian ringgit (MYR), Philippine peso (PHP), Thai bahat (THB) and Singapore dollar (SGD) against the US dollar (USD). Cai et al. (2012) modeled a GARCH-type model with a policy dummy variable to consider the conditional mean and volatility of the USD/ CNY exchange rate. The econometric and statistical methods perform better with stationary data. Sims (1980) proposed a VAR model, which can be used to model the stationary sequence and capture the linear dependencies among multiple time series. The VAR model has proved especially useful for describing the dynamic behavior of economic and financial time series and for forecasting (Sims, 1986; Blanchard and Watson, 1986; Bernanke, 1986; Korobilis, 2013; Trevor and Thorp, 1988; Reinsel and Ahn, 1992; Marcellino and Stock, 2003). In addition to data description and forecasting, the VAR model is also used for structural inference and policy analysis. In structural analysis, certain assumptions about the causal structure of the data under investigation are imposed, and the resulting causal impacts of unexpected shocks or innovations to specified variables on the variables in the model are summarized. The vector error correction model (VECM) can be applied to model the nonstationary data including the cointegration relationship, which is widely used to analyze the “short-run” and “long-run” relationship between variables and forecasting (Nieh and Lee, 2002; Asari et al., 2011; Kuo, 2016). Mukherjee and Naka (1995) employed the VECM to estimate the dynamic relationship between macroeconomic variables and the Japanese stock market. The empirical study found that the Japanese stock market is cointegrated with a group of six macroeconomic variables, and the VECM consistently outperforms VAR model in forecasting ability. The econometric methods perform better with stationary data. However, the conventional econometric methods cannot capture the complexity and nonlinearity of the foreign exchange rates data, leading to weak forecasts. Therefore, it

36

Literature review

is very necessary for exchange rate forecasting to explore more effective forecasting models with sufficient learning ability. Hence, to deal with the nonlinearity and nonstationary data, some advanced artificial intelligence (AI) techniques are proposed for forecasting exchange rates, such as support vector regression (SVR) (Huang et al., 2010), artificial neural networks (ANNs) (Kuan and Liu, 1995; Zhang and Hu, 1998; Özkan, 2013; Galeshchuk, 2016) and deep learning techniques (Shen et al., 2015). Zhang and Hu (1998) applied the artificial neural network to forecast the daily and weekly Great British pound (GBP)/USD exchange rate. Hu et al. (2007) found that the multilayer perceptron neural network is better than the random work model in forecasting the monthly GBP/USD exchange rate. Leung et al. (2000) developed a new general regression neural network to forecast the monthly GBP, Canadian dollar (CAD) and JPY against the USD. Shen et al. (2015) used several deep learning algorithms, such as the deep belief network, continuous restricted Boltzmann machines and conjugate gradient method to forecast the weekly GBP, Brazilian real (BRL) and Indian rupee (INR) against USD exchange rates. Vapnik (1995) proposed a support vector machine (SVM) based on the principle of structural risk minimization, which performs better and has been widely used in classification and prediction (Tay and Cao, 2001). However, it takes a long time for SVM to train and analyze huge data. To reduce the computational time, Suykens and Vandewalle (1999) further proposed the least squares support vector machine (LSSVM). In general, LSSVM can be categorized into least squares support vector regression (LSSVR) and least squares support vector classifier (LSSVC) for the purpose of regression and classification, respectively, and LSSVM is a very effective method of forecasting (Wang et al., 2011; Xie et al., 2013; Tang et al., 2015). LSSVR has been widely used in oil price forecasting, port container throughput forecasting, air travel demand forecasting and hydropower generation (Wang et al., 2011; Xie et al., 2013; Yu et al., 2014). Extreme learning machine (ELM) outperform the traditional computational intelligence techniques, since it can get better generalization performance at a much faster learning speed and with least human intervene (Huang et al., 2011). Huang et al. (2012) future extended the ELM and proposed the kernel extreme learning machine (KELM). ELM is a single-layer feedforward neural network (SLFN) architecture. The main drawbacks of ELM are that it has random initialization and its prediction precision is very sensitive to the noise and the number of hidden layer nodes, which lead to a poor robustness. Therefore, the KELM is proposed to overcome the disadvantages of basic ELM with faster convergence speed, multi-output, better stability and generalization ability. Wang and Han (2014) utilized multiple KELM to forecast multivariate time series. The multivariate time series is reconstructed in phase space. By testing of the Lorenz chaotic time series, the effectiveness of the proposed model is demonstrated. Shamshirband et al. (2015) used KELM to forecast the daily global solar radiation of Iran. KELM is widely used in global solar radiation prediction, illumination correction and wind forecasting (Shamshirband et al.,

Literature review 37 2015; Zhou et al., 2016). However, KELM has not been used in exchange rate forecasting. The aforementioned nonlinear artificial intelligence techniques have better forecasting performance than the conventional econometric models and statistical methods, but also have many issues, such as parameter optimization, local optimal problem and overfitting.

Hybrid forecasting approaches Exploring a more effective predictive model with sufficient learning ability is very necessary for exchange rate forecasting. In practice, it is rare that an individual model is capable of obtaining the best performance in all cases. Each model has its own strengths and shortcomings. If various individual forecasting models are available, they can be combined to create a forecasting approach that takes advantage of each model’s strengths. In their seminal article on combining forecasts, Betas and Granger (1969) showed that a linear combination of component forecasts would lead to smaller error variances than any individual component methods. Since then, research on combining forecasts has expanded dramatically, and includes simple averaging methods (Yu et al., 2005; Yu et al., 2008a), simple mean square error (MSE) methods (Benediktsson et al., 1997; Yu et al., 2008a), and variance-based weighted averaging methods (Yu et al., 2008a). The basis of combining forecasts is to take advantage of each component model. Generally, the combination of different models can be regarded as an effective and efficient way to improve forecasting performance via both theoretical and empirical analysis. However, previous linear combination forecasting methods suffer from two main drawbacks. First, the combination of these methods has been restricted to linear combinations, which may not necessarily be suitable for all situations. In addition, the characteristics of the component forecast error may vary over time. This leads to a second drawback. The use of fixed weights to combine forecasts performs poorly. Therefore many hybrid forecasting approaches are used to solve the problem of time series prediction (Chen and Leung, 2004; Yu et al., 2005; Wright, 2008; Yu et al., 2008a; Yu et al., 2010; Sermpinis et al., 2012; Sermpinis et al., 2013; Garratt et al., 2014; Sermpinis et al., 2015; Mostafa and El-Masry, 2016; Bellalah et al., 2016). The hybrid forecasting approaches mainly consist of three parts: data preprocessing, forecasting model formulation and parameter optimization. Examples of such approaches include Bayesian models with shrinkage techniques (Wright, 2008); rolling genetic algorithm-based SVR (Sermpinis et al., 2015); Kalman filters combined with artificial neural networks (Sermpinis et al., 2012); adaptive radial basis functions neural network optimized by the particle swarm optimization algorithm (Sermpinis et al., 2013); machine learning models combined with decomposition algorithms and variable selection methods (Plakandaras et al., 2015); recurrent, higher-order and Psi sigma neural networks with confirmation filter leverages (Dunis et al., 2011); dynamic stochastic general

38

Literature review

equilibrium (DSGE) models combined with Bayesian vector autoregressive (Zorzi et al., 2017); and improved ant colony optimization-based SVR (Hung and Hong, 2009). In these previous studies, Sermpinis et al. (2015) found that SVR optimized by the rolling genetic algorithm is more accurate than other benchmark models in forecasting and trading daily exchange rates between the USD and three other major currencies – EUR, GBP and JPY. Sermpinis et al. (2012) applied artificial neural networks with Kalman filters to forecast and trade the daily EUR/USD exchange rate. Sermpinis et al. (2013) developed adaptive radial basis functions neural networks optimized by the particle swarm optimization algorithm to find the best neural network configuration to forecast and trade the daily USD, GBP and JPY against the EUR. Other previous studies utilizing hybrid approaches in exchange rates forecasting include Clarida et al. (2003) and Zhang (2003).

Ensemble learning approaches Ensemble learning approaches have been demonstrated to obtain better performance than single forecasting models and some hybrid forecasting approaches in foreign exchange rates forecasting. Ensemble learning approaches include weak forecasters and ensemble strategies. Examples of such approaches include the clustering-based nonlinear ensemble learning approach (Sun et al., 2020), timevarying weights combination forecasting approach (Kouwenberg et al., 2017), bootstrap-based kitchen-sink regression approach (Ribeiro, 2017), decomposition and ensemble with variable selection learning approach (Plakandaras et al., 2015), neural network–based ensemble learning approach (Zhang and Berardi, 2001) and decomposition ensemble learning approach (Yu et al., 2008b; Tang et al., 2012; Niu et al., 2017; Sun et al., 2019; Wei et al., 2019). The forecasting process of the decomposition ensemble learning approach includes the following parts: firstly, decomposition of the original sequence into several modes; secondly, each mode is forecast respectively; thirdly, the forecasting results of each mode are ensembled to generate the final forecasting results. The decomposition strategy is very important for decomposition ensemble learning approaches; a better decomposition algorithm may enhance the forecasting performance. Wang et al. (2004, 2005a) proposed the TEI@I methodology, which reflected the idea of decomposition and ensemble. Based on the principle of decomposition and ensemble, the ensemble learning approach has proved to be an effective and efficient way to improve forecasting performance. Following Wang’s methodology, Yu et al. (2008b) proposed a decomposition ensemble learning approach for forecasting of crude oil spot price series. In this learning approach, the original time series is decomposed into many submodels, which are easier to model and predict than the original time series. Then the subcomponents are modeled separately. Finally, the ensemble learning tool is used to generate the final results by combining the subcomponents’ forecasts. At present, ensemble learning approaches have been widely used in time series forecasting, such as

Literature review 39 financial time series forecasting (Yu et al., 2009; Hadavandi et al., 2010; Lin et al., 2012; Plakandaras et al., 2015; Sun et al., 2020), crude oil price forecasting (Wang et al., 2005b; He et al., 2012; Tang et al., 2012; Yu et al., 2015; Zhang et al., 2015), nuclear energy consumption forecasting (Tang et al., 2012) and PM2.5 concentration forecasting (Niu et al., 2016; Niu et al., 2017). In these ensemble learning forecasting approaches studies, Sun et al. (2020) originally proposed a novel clustering-based nonlinear ensemble learning approach to forecast daily and monthly EUR, GBP, JPY and CNY against the USD. The empirical results indicate that the forecasting performance of the clustering-based nonlinear ensemble approach is far superior to other benchmarks used in the study. Yu et al. (2009) used an NN-based nonlinear meta-learning approach to design a system of financial time series forecasting. Kouwenberg et al. (2017) employed a novel time-varying weights combination forecasting approach to find the best combination weights for forecasting quarterly CAD, Australian dollar (AUD), New Zealand dollar (NZD), BRL, JPY, Mexican peso (MXN), Norway kroner (NOK), Russian ruble (RUB), Czech Republic koruna (CHK) and GBP against USD foreign exchange rates.

Conclusions In this chapter, first, the literatures of traditional theories of exchange rate are reviewed, including purchasing power parity, interest rate parity and exchange rate pass-through. Secondly, we reviewed the correlation analysis approach in the literature, including two parts: (1) the correlation relationship between economic variables and exchange rate; and (2) the approaches for correlation analysis. According to the existing literature, 16 macroeconomic variables are selected including import, export and foreign exchange reserves, which are often selected to study the relationship between the exchange rate and the macroeconomic variables in the literature. In Chapter 5, based on the existing literature, 16 macroeconomic variables are selected including import, export and foreign exchange reserves, and the Granger causality test and the grey relational analysis are utilized to further filter out the three variables that have the highest degrees of relevance with the exchange rate to represent the domestic economic situation. Based on the domestic economic situation, the VECM is proposed to forecast the exchange rate. Thirdly, in this chapter, multiple commonly used decomposition algorithms are introduced, including the empirical mode decomposition method (EMD), ensemble empirical mode decomposition (EEMD), variational mode decomposition (VMD), wavelet packet decomposition (WPD) and complementary ensemble empirical mode decomposition (CEEMD). Fourthly, we analyzed the forecasting approaches and divided the approaches into three categories: single forecasting models, hybrid forecasting approaches and ensemble learning approaches. Fifthly, we provide some comments on the existing literature.

40

Literature review

From the review of literature about forecasting approaches, we can conclude, for the single forecasting model, that econometric methods perform better with stationary data. However, the conventional econometric methods cannot capture the complexity and nonlinearity of foreign exchange rates data, leading to weak forecasts. Nonlinear artificial intelligence techniques have better forecasting performance than the conventional econometric models and statistical methods, but also have many issues, such as parameter optimization, local optimal problems and overfitting. Therefore, it is very necessary for exchange rate forecasting to explore more effective forecasting models with sufficient learning ability. In practice, it is rare that an individual model is capable of obtaining the best performance in all cases. Each model has its own strengths and shortcomings. If various individual forecasting models are available, they can be combined to create a forecasting approach which takes advantage of each model’s strengths. Ensemble learning approaches have been demonstrated to obtain better performance than single forecasting models and some hybrid forecasting approaches in foreign exchange rates forecasting. Based on the principle of decomposition and ensemble, the ensemble learning approach has proved to be an effective and efficient way to improve forecasting performance. Therefore, in this book, a comprehensive integrated approach is proposed for exchange rate forecasting by using LSTM to integrate the forecasting results of four aspects, that is the exchange rate data decomposition and integration, the domestic economic situation, the international economic situation, and the public’s expectations.

3

The dynamic relationships of the renminbi

Introduction In this chapter, we mainly analyze the dynamic relationships of the renminbi (RMB) and other factors including the lead–lag relationship between China’s onshore and offshore exchange rates, the impact of the RMB joining the Special Drawing Right (SDR) basket, and the impact of exchange rate fluctuations on China’s foreign trade. First, a hybrid approach named the EMD-Bry-Boschan method is proposed to study the lead–lag relationship between the offshore RMB (CNH) and the onshore RMB (CNY) under the influence of extreme events. Furthermore, this chapter analyzes the lead–lag relationship between the CNH spot exchange rate and CNY spot exchange rate when the extreme events are caused by market factors and/or policy factors. Secondly, for evaluating the influence of the RMB joining the SDR basket on RMB’s internationalization, we proposed a new hybrid approach by integrating the directed acyclic graph (DAG) and structural vector autoregression (SVAR) to further analyze and assess the risk spillover and the resulting dynamic change between the SDR currencies before and after the RMB joined the SDR basket. Thirdly, after the “811 exchange rate reform”, the renminbi continued to depreciate against the US dollar, with a cumulative depreciation of 8.42% from August 2015 to June 2016. An extended event analysis method is utilized to quantitatively measure the impact of renminbi depreciation on China’s imports and exports.

The lead–lag relationship between China’s onshore and offshore exchange rates considering the impact of extreme events Background Since China started to manage the RMB with reference to a basket of currencies in July 2005, instead of pegging the exchange rate to the US dollar, the movements of the RMB have begun to play a growing role and now have had

42

Dynamic relationships of the renminbi

significant impact on regional currencies (Fratzscher and Mehl, 2011; Henning, 2012; Prasad and Ye, 2012; Subramanian and Kessler, 2012; Xie and Wang, 2013). In 2009, the RMB trade settlement pilot was kicked off, followed by the launching of the offshore RMB products platform in August 2010. In 2011 the People’s Bank of China launched the RMB Overseas Direct Investment and formally announced the RMB Foreign Direct Investment. In 2014 the daily trading band against the US dollar was widened to ±2%. A description of CNH and CNY is shown in Table 3.1. Capturing the lead–lag relationship between CNH and CNY is of great importance in both theoretical and practical aspects, since the exchange market is strongly connected with people’s daily lives, and the relationship impacts the government’s macroeconomic policy decisions and a lot of enterprises. For the government, it can help with (1) adjusting policy decisions because it will provide solid evidence for policy adjustment and seizing the market trends in a timely manner; (2) analyzing the dynamic relationship between CNY and CNH to steadily promote RMB internationalization; and (3) optimizing resource allocation and managing inflation through adjusting the exchange rate. For investors, it can guide them in seizing the market signals timely and predicting the exchange rate more accurately to make more profit. For nonfinancial enterprises, it can help to reduce the exposure caused by the exchange rate fluctuation, foresee trends, make proper development decisions and improve the ability of asset management. There are several ways to study the lead–lag relationship between the two variables. The most widely used methods are the Granger causality test (Granger, 1969) and the cross-correlation function (de Jong and Nijman, 1997). A recent study by Owyong et al. (2015) used the Granger causality test to examine the onshore and offshore exchange markets, which found that the causality from the onshore spot market to the offshore counterpart is stronger, while there was a more balanced bidirectional causality in the forward market. The thermal optimal path (TOP) is also a nonparametric method to test the dynamic evolution of the lead–lag relationship between two time series. Gong et al. (2016) applied it to study the lead–lag relationship between the China Securities Index 300 (CSI 300), Hang Seng Index (HSI), Standard and Poor 500 (S&P 500) Index and the associated futures to reveal the variance of their relationships over time. Some other studies applied the generalized autoregressive conditional heteroscedasticity (GARCH) model, vector autoregressive (VAR) model or the error correction Table 3.1 Description of CNH and CNY

Definition Price limit Pricing mechanism

CNY

CNH

Code for onshore trade RMB ±2% Managed float

Code for offshore trade RMB None Free float

Dynamic relationships of the renminbi

43

model (ECM) to detect the dependence between the two series over a certain period of time, but they could not capture the variance of correlation over time. There is a substantial amount of literature that focuses on lead–lag relationships between financial market variables, such as spot and futures markets, as shown in Ghosh (1993), Shyy et al. (1996), Judge et al. (2014) and Gong et al. (2016). When it comes to the onshore and offshore markets, there are quite a few studies on the lead–lag relationship. Owyong et al. (2015) examined the interaction between the onshore and offshore markets. They studied the cointegration and lead–lag effects between the onshore and offshore spot and forward markets, and showed that there was a long-term equilibrium relationship between any pair of them (namely, CNY, CNH and nondeliverable forwards) based on linear and nonlinear Granger causality. Cheung et al. (2014) found that the onshore and the offshore exchange rates exhibited both long-term and short-term interactions. The Bry-Boschan business cycle dating algorithm, proposed by Bry and Boschan (1971), is often used in macroeconomic variables to detect the business cycle and turning points. Some researchers were focused upon the role of fundamentals, global factors and policies related to the RMB internationalization in driving variations between the onshore and offshore exchange rates using extended GARCH models (Funke et al., 2015). The traditional methods have some drawbacks: firstly, the traditional economic theory does not focus on the lead–lag relationship of CNH and CNY; secondly, the typical time series regression models involve data sampled at low frequency; thirdly, some forecast methods convert high-frequency currency data to low frequency. In this chapter, the empirical mode decomposition (EMD) algorithm is employed with daily data to estimate the lead–lag relationship between CNH and CNY. Huang et al. (1998) proposed the EMD method for analyzing nonlinear and nonstationary data. EMD was initially proposed for studying ocean waves and is now broadly applied in natural science, engineering and social sciences. In economic areas, EMD has been used to examine the changeability of the stock markets (Huang et al., 2003), to analyze the financial records from the mortgage market (Huang et al., 2003) and to estimate the impact of extreme events on crude oil price (Zhang et al., 2009). This chapter documents the lead–lag relationship between CNH and CNY from August 23, 2010, to December 31, 2015, using the EMD algorithm, the Granger causality test and the Bry-Boschan business cycle dating algorithm. Firstly, to understand the relationship, it is useful to examine whether the two series have a lead–lag relationship during the entire period. Thus, the correlation test and Granger test are applied to the whole period to find whether CNH and CNY have a dynamic relationship. Secondly, if there exists a dynamic relationship between CNH and CNY, then how do CNY and CNH interact with each other? Then the EMD algorithm is used to decompose those time series into several intrinsic mode function (IMF) components and a residual sequence, from the highest frequency to the lowest frequency. Then the IMFs are combined into three components: one is the short-term fluctuation, caused by the market activities; another is the medium-term fluctuation influenced by the extreme events, such as global

44

Dynamic relationships of the renminbi

economic recessions and policy adjustments by central banks; and the third one is the long-term trend, which is highly related with the original series. In this chapter a hybrid approach combining the EMD algorithm and BryBoschan algorithm is proposed, and the schematic diagram is shown in Figure 3.1. Through the hybrid approach, when fluctuations are caused by market-forced extreme events such as global economic recessions, which factor is the lead one, CNH or CNY? On the contrary, once a shock is caused by a policy adjustment, which factor is the lead one? In these two situations, will the results remain the same? The innovative features of the hybrid approach can be summarized as follows: (1) It is the first time that the EMD algorithm is used to study the lead–lag relationship of CNH and CNY, and the IMFs are combined into three components based on fine-to-coarse reconstruction. Thus, the exchange rate sequence is decomposed to three components, that is, short-term fluctuation caused by the market activities, medium-term fluctuations influenced by the extreme events and long-term trends. (2) The EMD-Bry-Boschan method is proposed to study the lead–lag relationship between the offshore RMB and onshore RMB under the influence of extreme events. (3) We further analyze the lead–lag relationships of CNH and CNY when the extreme events are caused by different kinds of factors.

The model The EMD algorithm was proposed by Huang et al. (1998) and can be used with nonlinear and nonstationary data. Based on the principle of local scale separation, it decomposes the original series into several IMFs and a residual sequence.

Figure 3.1 Schematic diagram for the hybrid approach

45

Dynamic relationships of the renminbi

It must satisfy two conditions: firstly, the number of extreme and zero-crossings should be the same, or differ at the most by one; secondly, they should be symmetric with respect to the zero mean. The algorithm is organized as follows: 1. 2. 3. 4.

Identify all the maxima and minima of the original time series x(t). Its upper and lower envelopes are generated, named emin(t) and emax(t). From the emin(t) and emax(t), calculate the point-by-point mean named m(t). Calculate d(t) from the difference of x(t) and m(t):

d (t ) = x (t ) - m(t ) 5. Check the properties of d(t). a. If it is an IMF, denote d(t) as the ith IMF and replace x(t) with the residual r(t) = x(t) – d(t). Then denote ith IMF as ci(t) and call i its index. b. If not, replace x(t) with d(t). Repeat steps 1–5 until the residual satisfies the stopping criterion. For further details on this method, please refer to Huang et al. (2003) and Zhang et al. (2009).

Empirical analysis The EMD algorithm is applied to study the lead–lag relationships between CNH and CNY. For Figure 3.2, the daily trading data were downloaded from Bloomberg, excluding weekends and holidays, from August 23, 2010, to December 31, 2015. There are 1397 observations. Since resumption of the managed floating exchange regime on June 19, 2010, the value of the RMB has steadily appreciated, and its movement resembles an

6.9

Shortage of liquidity 2010/08-2010/12

6.8

811 Exchange rate reform From 2015/08/11

6.7 6.6 6.5 6.4 6.3 6.2

CNY

8/23/2015

11/23/2015

5/23/2015

2/23/2015

11/23/2014

8/23/2014

5/23/2014

2/23/2014

8/23/2013

11/23/2013

5/23/2013

2/23/2013

11/23/2012

8/23/2012

5/23/2012

11/23/2011

8/23/2011

5/23/2011

2/23/2011

11/23/2010

8/23/2010

6

2/23/2012

European debt crisis 2011/08-2011/12

6.1

CNH

Figure 3.2 Daily CNH and CNY data from August 23, 2010, to December 31, 2015

46

Dynamic relationships of the renminbi

upward crawl against the US dollar. During the sample period, the RMB appreciated by more than 8% against the US dollar. The CNH exchange rate is more volatile than the CNY exchange rate and the central parity rate. While the CNH and CNY exchange rates usually track each other quite well, there have three obvious large disparities of CNH and CNY from August 23, 2010, to December 31, 2015. 1. CNH had a large premium over CNY in the third quarter of 2010. The premium is usually attributed to a liquidity squeeze due to a stronger-thanexpected demand for CNH for cross-border trade settlement. The premium subsided when the Hong Kong Monetary Authority activated its CNH liquidity provision through the swap arrangement with the People’s Bank of China. 2. The CNH suffered the second largest discount to CNY from August 2011 to November 2011, especially in September 2011. The sell-off of CNH was associated with the surge in the global market risk. Due to the European debt crisis, investors were unwilling to hold emerging market currencies including CNH. These two periods of disparities were caused by the market factors. 3. The third large disparity was in August 2015, named the “811 exchange rate reform”. China further improved the quotation mechanism of the RMB’s central parity rate against the US dollar by taking into consideration the previous day’s closing rate on the interbank forex market to reflect the changes of market supply and demand. This policy change necessitated the renminbi a onetime devaluation of 1.9%, because the midpoint had been diverged from the market rate for some time. This period of disparity was caused by policy reform.

Dynamic relationship for all periods In this section, the correlation test and Granger causality test are used to find whether CNH and CNY have a lead–lag relationship in all periods (Tables 3.2 and 3.3). Table 3.2 displays the results of the correlation test between the onshore and the offshore exchange rates. As shown in the table, in all periods, CNY and CNH are highly correlated, with a correlation coefficient of 0.99. However, the coefficient of correlation in 2015 is bigger than that of the whole period. After the 811 exchange rate reform, the correlation between CNH and CNY declined, because the fluctuation of CNH was more intensive than that of CNY. Table 3.2 Correlation test results for CNY and CNH in different periods Data

Correlation coeffcient

2010/8/23–2015/12/31 2015/01/01–2015/12/31 2015/01/01≠2015/08/10 2015/08/11–2015/12/31

0.98706 0.98748 0.96271 0.92301

Dynamic relationships of the renminbi

47

Table 3.3 Results of the Granger causality test for the entire period of CNY and CNH Null hypothesis

Observations

F-statistic

P-value

CNY does not Granger-cause CNH CNH does not Granger-cause CNY

1397 1397

9.091 16.564

0.0001 0.000

The results of the Granger causality test are displayed in Table 3.3. The null hypothesis that no Granger causality from CNY to CNH is rejected with P-value equal to 0.0001. The null hypothesis that CNH does not Granger-cause CNY is also rejected (P-value equals 0.000). Thus, we can conclude that in the sample period, there is strong causality running from CNY to CNH and vice versa.

Lead–lag relationships under different circumstances DECOMPOSING DATA WITH THE EMD ALGORITHM

Since there exists a significant dynamic relationship between CNH and CNY in the sample period, in this chapter a hybrid approach combining the EMD algorithm and Bry-Boschan algorithm is proposed to examine whether there exists a lead–lag relationship under different circumstances, such as when the deviation of CNH from CNY is caused by market factors or policy factors. The EMD algorithm is applied to decompose those time series into several IMF components and a residual sequence, from the highest frequency to the lowest frequency (Figures 3.3 and 3.4). Figures 3.3 and 3.4 are the time series data of CNY and CNH decomposed into several IMFs and a residual sequence, respectively. INTEGRATING DATA WITH DIFFERENT FREQUENCIES

Each IMF has a different meaning and presents one part of the original time series. The key to understanding the meaning of each IMF is to look at its mean frequency, and then it can be integrated with other IMFs that have the same frequency (Zhang et al., 2009). Table 3.4 implies that IMF1, IMF2 and IMF3 represent frequencies of 3 days, 17 days and 22 days, respectively, which are shorter than one month. IMF1 to IMF3 are integrated and named the short-term composition, which is mainly affected by market factors. The frequencies of IMF4, IMF5, IMF6 and IMF7 are 46 days, 77 days, 233 days and 466 days, respectively, and named the medium-term components and are mainly influenced by the extreme events. The residue is often regarded as long-term composition, representing the trend of the original series. LEAD–LAG RELATIONSHIPS DURING THREE EXTREME EVENTS

Extreme event 1: Liquidity squeeze, from August 2010 to December 2010 The first time CNH deviated from CNY significantly was from August 2010 to December 2010, because of a stronger-than-expected demand for CNH. From

48

Dynamic relationships of the renminbi

Figure 3.3 IMFs and residue for CNY from August 23, 2010, to December 31, 2015

Figure 3.5, through the short-term composition, it cannot be found that CNH obviously leads CNY in the movements. The Bry-Boschan algorithm is employed to analyze the lead–lag relationship of CNH and CNY considering the impact of market impacts; the results are displayed in Table 3.5. Table 3.5 shows the short-term composition (IMF1 to IMF3) of CNY and CNH at the turning points, including the peak and the trough. The results of this algorithm show that CNH leads CNY 0.25 of the peak and 0.5 of the trough. The extreme event is caused by the market behavior since the unexpected demand of CNH during August 2010 to December 2010. Figure 3.6 implies that when it comes to the medium-term composition, CNY leads CNH. The observations in Figure 3.6 can be confirmed by the results of Bry-Boschan algorithm in Table 3.6 that is CNY leads CNH 5 of the peak and 1 of the trough. Extreme event 2: European debt crisis, from August 2011 to November 2011 Figure 3.7 plots the market terms of CNH and CNY during the second deviation caused by the European debt crisis (market behavior) from August 2011 to November 2011. Then the Bry-Boschan algorithm is used to test the lead– lag relationship between CNH and CNY of the short-time marked driven parts

Dynamic relationships of the renminbi

49

Figure 3.4 IMFs and residue for CNH from August 23, 2010, to December 31, 2015 Table 3.4 Statistics of CNY and CNH CNY

CNH Mean period

Correlation Standard coeffcient deviation

IMF1 3.4039 0.0208 IMF2 17.9359 0.0205 IMF3 22.5645 0.0318 IMF4 46.6333 0.0675 IMF5 77.7222 0.1150 IMF6 233.1667 0.3682 IMF7 466.3333 0.2063

0.0049 0.0059 0.0085 0.0097 0.0166 0.0500 0.0193

Mean period

Correlation Standard coeffcient deviation

IMF1 4.3856 0.0237 IMF2 14.5729 0.0776 IMF3 23.7119 0.0325 IMF4 48.2414 0.2283 IMF5 77.7222 0.1715 IMF6 174.8750 0.2705 IMF7 466.3333 0.3813

0.0065 0.0075 0.0084 0.0168 0.0260 0.0352 0.0364

during this deviation as shown in Table 3.7, which implies that CNH leads CNY 0.2 of the peak and 0.2 of the trough. The extreme event is caused by the market bevavior namded European debt crisis. And the Figure 3.8 implies that when it comes to the medium-term composition, CNY leads CNH. To be specific, from Figure 3.8 and Table 3.8, it can be concluded that CNY leads CNH 6 of the peak and 5.5 of the trough.

50

Dynamic relationships of the renminbi

Figure 3.5 Market impacts from August 2010 to December 2010 Table 3.5 Results of Bry-Boschan algorithm from August 2010 to December 2010 (IMF1–3)

Peak Trough Peak Trough Peak Trough Peak Trough

CNY_IMF1-3

CNH_IMF1-3

2010/9/8 2010/9/22 2010/10/5 2010/10/19 2010/10/29 2010/11/11 2010/11/15 2010/12/7

2010/9/9 2010/9/21 2010/10/5 2010/10/19 2010/10/27 2010/11/11 2010/11/15 2010/12/6

From Table 3.6 and Table 3.8 it is confirmed that when the extreme event is caused by market behavior, e.g., global recessions or other market activities, CNY leads CNH. Extreme event 3: 811 exchange rate reform, from August 2015 to December 2015 The policy factor caused the third instance of significant deviation between CNH and CNY, from August 2015 to December 2015, named the 811 exchange rate reform. Figure 3.9 and Table 3.9 display CNH leads CNY 0.4 at the peak and 0.5 at the trough and provide evidence that when it comes to the short-term part, which is driven by market factors, CNH always leads CNY. Figure 3.10 and Table 3.10 show that when devaluation is caused by an extreme event affected by policy changes, CNH leads CNY, which is different from the market-forced devaluation. The results of the Bry-Boschan algorithm show that CNH leads CNY 3 of the peak and 1 of the trough. The reason is that the 811 exchange reform caused pessimistic expectations of China’s exchange market, and CNH is allowed to free float and is much more flexible.

51

Dynamic relationships of the renminbi

6.9

0.25

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0.15

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0.1

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0

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6 5.9

-0.05

CNY_IMF4-7 (Left axis)

CNH_IMF4-7 (Left axis)

CNY Curncy (Right axis)

CNH Curncy (Right axis)

Figure 3.6 Extreme event impacts from August 2010 to December 2010 Table 3.6 Results of Bry-Boschan algorithm from August 2010 to December 2010 (IMF4–7)

Peak Trough Peak Trough Peak

CNY_IMF4-7

CNH_IMF4-7

2010/8/26 2010/10/12 2010/10/29 2010/11/16 2010/12/3

2010/9/1 2010/10/13 2010/11/8 2010/11/18 2010/12/10

0.12

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6.1

-0.02 6

-0.04 -0.06

5.9 CNY_IMF1-3 (Left axis)

CNH_IMF1-3 (Left axis)

CNY Curncy (Right axis)

CNH Curncy (Right axis)

Figure 3.7 Market impacts from August 2011 to November 2011

52  Dynamic relationships of the renminbi  Table 3.7 Results of Bry-Boschan algorithm from August 2011 to November 2011 (IMF1–3)

Peak Trough Peak Trough Peak Trough Peak Trough Peak Trough

CNY_IMF1-3

CNH_IMF1-3

2011/8/5 2011/8/16 2011/8/23 2011/8/31 2011/9/12 2011/9/21 2011/9/26 2011/10/10 2011/10/21 2011/11/9

2011/8/5 2011/8/16 2011/8/23 2011/8/31 2011/9/12 2011/9/21 2011/9/23 2011/10/10 2011/10/21 2011/11/8

0.12

6.6 6.5

0.07 6.4 0.02

6.3 6.2

-0.03

6.1 -0.08 6 -0.13

8/1/2011

8/16/2011

8/31/2011

CNY_IMF4-7 (Left axis)

9/15/2011

9/30/2011

CNH_IMF4-7 (Left axis)

10/15/2011

10/30/2011

CNY Curncy (Right axis)

11/14/2011

CNH Curncy (Right axis)

Figure 3.8 Extreme event impacts from August 2011 to November 2011

Table 3.8 Results of Bry-Boschan algorithm from August 2011 to November 2011 (IMF4–7)

Peak Trough Peak

CNY_IMF4-7

CNH_IMF4-7

2011/8/24 2011/9/21 2011/10/14

2011/9/6 2011/9/29 2011/10/18

5.9

11/29/2011

Dynamic relationships of the renminbi 0.12

53 6.8

0.1 6.6

0.08 0.06

6.4

0.04 0.02

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0 6

-0.02 -0.04

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2015/8/11

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2015/11/9

2015/11/24

CNY Curncy (Right axis)

2015/12/9

2015/12/24

5.6

CNH Curncy (Right axis)

Figure 3.9 Market impacts from August 2015 to December 2015 Table 3.9 Results of Bry-Boschan algorithm from August 2015 to December 2015 (IMF1–3)

Peak Trough Peak Trough Peak Trough

CNY_IMF1-3

CNH_IMF1-3

2015/8/13 2015/9/2 2015/9/24 2015/10/12 2015/10/28 2015/12/24

2015/8/13 2015/9/1 2015/9/23 2015/10/12 2015/10/27 2015/12/25 6.7

0.25

6.6 0.2 6.5 6.4

0.15

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0.05 6 0 8/11/2015

8/26/2015

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CNY_IMF4-7 (Left axis)

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CNH_IMF4-7 (Left axis)

11/9/2015

11/24/2015

CNY Curncy (Right axis)

12/9/2015

12/24/2015

5.9

CNH Curncy (Right axis)

Figure 3.10 Extreme event impacts from August 2015 to December 2015

54

Dynamic relationships of the renminbi

Table 3.10 Results of Bry-Boschan algorithm from August 2015 to December 2015 (IMF4–7)

Peak Trough Peak

CNY_IMF4-7

CNH_IMF4-7

2015/9/1 2015/11/2 2015/12/23

2015/8/27 2015/10/30 2015/12/18

Implications and conclusions In this part, a new hybrid approach, the EMD-Bry-Boschan method, is proposed to study the lead–lag relationship between the offshore RMB and onshore RMB under the influence of extreme events. The main results show that (1) there exists a dynamic relationship between CNH and CNY, that is, CNY Granger-causes CNH, and vice versa; (2) CNH always leads CNY when it comes to short-term market activities; (3) the lead– lag relationships between CNY and CNH may alternate when the medium-term impact is caused by different kinds of extreme events. CNY leads CNH when the deviations are caused by extreme events caused by global recessions or some other market activity. However, CNH leads CNY when the deviations are caused by some policy changes, e.g., the 811 exchange reform. The main innovations and features of the EMD-Bry-Boschan method are as follows. (1) It is the first time the EMD algorithm has been used to study the lead–lag relationship of CNH and CNY, and the IMFs are combined into three components based on fine-to-coarse reconstruction. Thus, the exchange rate sequence is decomposed to three components: short-term fluctuation caused by market activities, the medium-term fluctuation influenced by extreme events and long-term trends. (2) The EMD-Bry-Boschan method is proposed to study the lead–lag relationship between the offshore RMB and onshore RMB under the influence of extreme events. (3) We further analyze the lead–lag relationship of CNH and CNY when the extreme events are caused by different kinds of factors.

Impact of the RMB joining the SDR basket on its internationalization from the perspective of risk spillover Background On December 1, 2015, the International Monetary Fund announced that the RMB would be included in the Special Drawing Right (SDR) basket, making it possible for the International Monetary Fund’s 188 members to take out or repay loans in RMB. After official acceptance as one of the SDR currencies, on October 1, 2016, the RMB accounted for 10.92% of the total weighting, becoming the third largest reserve currency in the International Monetary Fund’s SDR basket,

Dynamic relationships of the renminbi

55

right behind the US dollar (USD) and the European Union euro (EUR). This move would become an important milestone in the RMB’s internationalization progress and exert far-reaching impact on the international currency system, even on the global economy. With the internationalization of the RMB, more monetary authorities are choosing the RMB as one of their reserve assets, leading to the growing demand for the RMB’s exchange circulation, thus causing a certain degree of shock on the existing financial system. The financial volatility is highly correlated to the exchange rate market due to the risk aversion of currency investors and the change of risk expectation of the investment. In turn, the fluctuation and risk spillover of exchange rates could profoundly affect portfolio and risk management decisions, and noticeably influence imports and exports, trade balance, and even the entire economic pattern. Consequently, extensive and intensive study for the risk transmission and control mechanism among RMB and the other SDR currencies is of great significance in both theoretical and practical aspects. An increasing number of works have paid attention to exchange rate fluctuations and risk transmission (Peter and Steven, 1978; Abdur, 1993; Enrique, 1995; Sun et al., 2012). Jose and Linda (2005) provided cross-country and time series evidence to manifest the influence of exchange rate transmission on the import prices of 23 countries of the Organization for Economic Cooperation and Development (OECD). However, Silvana (2007) presented a new perspective that nominal exchange rate variability has no obvious impact on trade flows. Likewise, the relevant studies about exchange rate conduction, trade integration and spillover effect have also been reported in succession (Jordi and Tommaso, 2005; Mohsen and Scott, 2007; Joshua and Daniel, 2008; Gust et al., 2010; Galagedera and Kitamura, 2012; Du and Lai, 2017). In view of the complex and diverse correlations, the interaction among the five currencies in the SDR basket could be regarded as a network. The measurement of the network model focuses on the studies of the relationships among different parts in a system to emphasize the recognition of the internal structure of the system. The existing network models can be roughly divided into three types. The first one is a matrix network model based on the balance sheet information. The network model can be developed on the relationship between the assets and the liabilities of like institutions, calculated via the maximum entropy and likelihood estimation (Drehmann and Tarashev, 2011; Meng et al., 2011; Upper, 2011; Lee, 2013; Greenwood et al., 2015). The second and the third network models are based on topology theory (Nier et al., 2007) and market information (Gai and Kapadia, 2010; Pesaran and Pesaran, 2010), respectively. Diebold and Yilmaz suggested a network model based on time series variance decomposition, evaluating the dynamic network association among multiple financial institutions in America by combining it with the conditional value at risk (CoVaR) and marginal expected shortfall (MES) model (Diebold and Yilmaz, 2012), and analyzing the volatility spillover relationship between different financial markets (Diebold and Yilmaz, 2011). Yang and Zhou (2017) improved the variance decomposition network model in studying the volatility

56

Dynamic relationships of the renminbi

spillover effect of global financial markets. However, due to neglect for the correlations between different asset prices and only consideration for the interbank balance sheet in the process of risk transmission, the existing network models and related evaluation methods are still far from perfect, and the results obtained are also inexact. Therefore, according to the network model proposed by Yang and Zhou (2017), we integrate the directed acyclic graph (DAG) and structural vector autoregression (SVAR) into a new model to further analyze and assess the risk spillover and the resulting dynamic change between the SDR currencies before and after the RMB joined the SDR basket. The newly proposed network model involves the following parts: (1) The DAG method is used to calculate the short-term network structure among the SDR currencies. (2) By using the variance decomposition based on DAG prediction, the long-term risk spillover relationships between the SDR currencies are depicted. (3) For investigating the dynamic changes of risk spillover among the SDR currencies in different samples, the recursive prediction variance decomposition is attempted and the corresponding dynamic risk spillover changes are analyzed. (4) Based on identifying and analyzing the dynamic variation among the currencies within different samples, the interplay between the SDR currencies during the internationalization progress of the RMB is also briefly discussed.

Methodology The network model, mainly based on prediction variance decomposition of the SVAR system, is selected to systematically analyze the risk spillover effect among the SDR basket currencies and to evaluate the contribution of each currency for risk conduction. The influences of the RMB on other SDR currencies after its inclusion in the SDR basket are also assessed, so as to monitor and control the process of the RMB’s internationalization, and to predict the risk potential among the SDR currencies.

SVAR model based on DAG To analyze and evaluate the risk spillover between the SDR currencies, we establish the following SVAR model: N

Yt =

åf Y i

t -1

+ m + et

i =1

where Yt is the expected loss (i.e., the risk); and μ and ϕi, respectively, stand for the SVAR system intercept vector and coefficient matrix. The traditional SVAR model is mainly based on Cholesky decomposition to identify the immediate causality between variables. However, since the Cholesky

Dynamic relationships of the renminbi

57

decomposition is highly sensitive to the order of endogenous variables, the diverse sequence settings will lead to completely different results. And the result obtained by the Granger causality test commonly used between economic and financial variables is not the causality in the significance of economics. Therefore, the impulse response and prediction variance decomposition results obtained by this approach are not consistent with reality. Thus, when using the SVAR model to study the interaction between variables, we should add some constraints obtained by proper economic principles for the immediate or longterm relationship. Without sufficient economic theories to support, we can only find the immediate relationship from the subjective experience or data as the constraints. DAG is essentially a method of determining immediate causality between variables by using the unconditional correlation coefficient and partial correlation coefficient. It calculates the immediate causality among variables with the PC algorithm and uses the directed edges to indicate whether there is causality between variables in each pair. Since the DAG method does not need to add a subjective or a priori theoretical hypothesis to determine causality, this method has been used by many scholars in the field of economic and financial research (Yang and Zhou, 2017). Based on this, we use the PC algorithm-based DAG method to determine the immediate causality among variables in the SVAR system.

Network analysis based on prediction variance decomposition The prediction error analysis and impulse response function based on the SVAR model play a key role in accurately understanding the dynamic relation between variables to depict the coefficient matrix (ϕi). In order to visually identify the deeper netlike cross-linked structure among liquidity risks, the systemic analysis for the SVAR prediction variance decomposition is quite necessary, contributing to the evaluation of the network constitution of risk spillover between the SDR currencies. The calculation formula for the overall correlation degree of the SVAR system based on DAG could be expressed (Yang and Zhou, 2017):

å S (H ) = å N

qi , j ( H )

i , j =1, i ¹ j N

qi , j ( H )

´ 100

i , j =1

here, θi,j(H) denotes the effect of currency j on currency i within the H step predictive variance decomposition. The influence of other currencies on currency i could be calculated as follows:

å S (H ) = å

N

i×

qi , j ( H )

j =1, i ¹ j N

qi , j ( H )

i , j =1

´ 100

58

Dynamic relationships of the renminbi

Similarly, the calculation of the impact of currency i on other currencies is as follows:

å S (H ) = å

N

×i

q j , i (H )

j =1, i ¹ j N

q j , i (H )

´ 100

i , j =1

According to the preceding two formulas, the net effect of currency i on all the other currencies can be obtained as

Si ( H ) = S×i ( H ) - Si× ( H ) The net influence between currency i and currency j could be considered as the difference of both interplays, as shown:

æ ç Sij ( H ) = ç ç è

q j , i (H )

å

N

qi , k ( H )

i ,k =1

-

å

ö ÷ ÷ ´ 100 N q j , k (H ) ÷ j ,k =1 ø

qi , j ( H )

Hence, the network model of risk spillover between the SDR currencies before and after the RMB’s inclusion into the SDR basket was evaluated. Meanwhile, in order to further investigate the dynamic changes of risk spillover between the SDR currencies in different samples, a one-month fixed rolling window is selected to make a recursive prediction variance decomposition for each currency, which helps to make clear the dynamic change of the risk spillover between each other.

Empirical results Data The data of real effective exchange rate index of the Chinese renminbi (CNY), Great British pound (GBP), European Union euro (EUR), Japanese yen (JPY) and US dollar (USD) are taken from the Wind Database (www.wind.com.cn), and the sampling time ranges from January 1, 2015, to July 30, 2018, with a total 933 observations. For contrasting and analyzing the risk spillover between the RMB and the other currencies before and after the RMB’s inclusion in the SDR basket, the data sets were divided into two subsamples: subsample 1, from January 1, 2015, to September 30, 2016; and subsample 2, from October 1, 2016, to July 30, 2018. Table 3.11 lists the summary statistics for the real effective exchange rate indices in each subsample. As Table 3.11 shows, the JarqueBera test reveals serious deviations for the unconditional normality, which are consistent with the numerical values from skewness and kurtosis for each currency. Therefore, before conducting the data analysis, the selected data should be standardized.

Dynamic relationships of the renminbi

59

Table 3.11 Summary statistics for the real effective exchange rate indices Subsample 1 (before the RMB joined the SDR)

Mean Standard deviation Skewness Kurtosis Jarque-Bera Probability Observations

CNY

GBP

JPY

USD

EUR

123.4806 3.3296 −0.6890 2.4051 42.8982 0.0000 457.0000

110.2023 5.8634 −0.8683 2.7545 58.5699 0.0000 457.0000

81.5057 6.4865 0.7107 2.1528 52.1354 0.0000 457.0000

117.0603 3.2220 −0.3704 2.2824 20.2554 0.0000 457.0000

96.6400 2.4380 −0.6823 2.3407 43.7370 0.0000 457.0000

Subsample 2 (after the RMB joined the SDR)

Mean Standard deviation Skewness Kurtosis Jarque-Bera Probability Observations

CNY

GBP

JPY

USD

EUR

118.6440 2.7292 0.8871 2.7018 64.2002 0.0000 476.0000

97.2865 1.7475 –0.6034 3.2509 30.1354 0.0000 476.0000

85.5718 2.3432 1.3897 5.3869 266.2173 0.0000 476.0000

120.3626 3.2207 0.1054 1.9803 21.5036 0.0000 476.0000

101.8216 3.4199 −0.1610 1.5479 43.8745 0.0000 476.0000

Table 3.12 Stationary test for the real effective exchange rate indices Subsample 1 (before the RMB joined the SDR) CNY Significant level (1%) T-statistic P-value

GBP

JPY

USD

EUR

−3.4445 −3.4445 −3.4445 −3.4445 −3.4445 −19.1478 −18.5798 −21.3195 −20.0703 −21.3166 0.0000 0.0000 0.0000 0.0000 0.0000

Subsample 2 (after the RMB joined the SDR) CNY Significant level (1%) T-statistic P-value

GBP

JPY

USD

EUR

−3.4439 −3.4439 −3.4439 −3.4439 −3.4439 −19.9776 −23.3070 −22.6758 −21.5461 −22.2651 0.0000 0.0000 0.0000 0.0000 0.0000

The results of the stationary test for each standardized index are listed in Table 3.12. It is shown that the null hypothesis can be rejected at the 1% significance level for all of the original data. Thus, the vector autoregressive model can be developed directly with these data.

Short-term network structure According to the criteria about sequential modified likelihood ratio (LR) test statistic, final predication error (FPE) and Hannan-Quinn (HQ) values, the best lag

60

Dynamic relationships of the renminbi

Figure 3.11 The immediate network relation of the risks between various currencies (A) before and (B) after RMB joined the SDR

order is selected, and consequently the VAR model with two lag periods is adopted. Via estimating the model, the resulting perturbation correlation matrix among the variables is imported into the TETRAD III computational system to obtain the immediate causality of variables at 1% significance level using the PC algorithm. As shown in Figure 3.11A, before the RMB joined the SDR basket, there really exists various degrees of risk spillovers among the CNY, GBP, EUR, JPY and USD, but the directions of the spillovers are evidently different. Among them, there are some one-way risk spillovers (e.g., USD to CNY and CNY to EUR) and also some reversible two-way risk spillovers (e.g., CNY and JPY, GBP and EUR, and GBP and JPY). Moreover, in the immediate network, only the USD is not affected by other currencies, but all remaining currencies are reciprocally influenced. As displayed in Figure 3.11B, after the RMB joined the SDR basket, the risk spillover relationships and directions among the currencies have greatly changed. In this case, there exists only one-way, and no two-way risk spillovers. The JPY and GBP only have one-way risk spillover to the CNY and EUR, respectively, but both are not impacted by the risks from the other currencies. As for the EUR, it receives three one-way risk spillovers from three currencies (USD, GBP and CNY) at the same time. In addition to the risk spillover to CNY, the risk of the USD can also overflow to the EUR. For the case of CNY, the situation is even more peculiar. It not only gets risk from both the USD and JPY, but also outputs risk to the EUR. From the foregoing, it’s not hard to know that the DAG approach can only solve the immediate causality and direction of the risks, and cannot clarify the size of specific impact between the SDR currencies.

Long-term network structure By referring to related study results (Fan et al., 2013; Yang and Zhou, 2017), we set the lag period as two weeks, namely ten forecast periods. Table 3.13

Dynamic relationships of the renminbi

61

Table 3.13 Prediction variance decomposition based on DAG results (%, forecast period: 10th) Before the RMB joined the SDR CNY CNY GBP JPY USD EUR

0.0548 0.5140 40.7056 0.0039 3.5078

GBP

JPY

0.7959 0.1479 0.3845 0.0008 89.2361

2.4339 26.0581 0.1778 0.0096 0.8367

USD 29.5861 72.2673 58.2695 99.9850 6.3835

EUR 67.1294 1.0126 0.4647 0.0007 0.0359

After the RMB joined the SDR CNY CNY GBP JPY USD EUR

85.8147 0.1838 0.0424 0.3213 5.6249

GBP

JPY

0.3291 98.5960 1.8785 0.2416 6.3246

4.8601 0.3767 96.1918 0.7219 0.5921

USD 7.2114 0.2895 0.5942 94.2865 5.8288

EUR 1.7847 0.5540 1.2930 4.4286 81.6276

shows the variance decomposition of the tenth forecast period based on the DAG results. As shown in Table 3.13, from the perspective of a long-term network structure, before the RMB joined the SDR basket, almost all the risk on the CNY was from the other SDR currencies, and the currency with the greatest impact on the CNY was the EUR (67%), followed by the USD (29%). The risk spillover from the CNY to the JPY held a majority (40%). Contrary to the immediate causality, after the RMB’s inclusion in the SDR basket, most of the risk spillover CNY comes from itself (86%), and only a small part of risk comes from the USD (7%) and the JPY (5%). The risk spillover of CNY to other currencies is notably weakened, only to the EUR (5%). The USD holds a strong spillover effect on the other four currencies before the RMB joined the SDR, but after the RMB’s inclusion the risk spillover from USD to the CNY and the EUR is reduced to the degree of 7% and 5%, respectively. Most of the risk spillover to the EUR comes from GBP (89%), and a small proportion comes from the USD (6%) in subsample 1. However, in subsample 2 the risk fluctuations of the EUR are mostly from itself (81%), and the rest derives from other currencies, i.e., CNY (5%), GBP (6%) and USD (5%). According to the predictive variance decomposition of the SVAR system (Yang and Zhou, 2017), the constitution of the risk spillover network among the SDR currencies are obtained (see Table 3.14). As clearly shown in Table 3.14, before the RMB joined the SDR basket, each currency except the USD suffered quite high-risk spillovers (greater than 99%). After the RMB’s inclusion in the SDR basket, the risk spillover effect on the CNY from other currencies, i.e., GBP, JPY,

62

Dynamic relationships of the renminbi

EUR and USD, are 14%, 1%, 3% and 18%, respectively. By comparison, the risk spillover effect on the USD from other currencies has risen from 0% to 5%. In Table 3.14, “From” and “To” denote the risk spillover “from” one currency “to” the other four currencies. Prior to the RMB’s inclusion in the SDR, the risk spillover of USD to the other four currencies is up to 166%, much higher than that of each of the other currencies, but the received risk from the other four currencies is just a paltry 0.015%; the net value of the risk conduction (i.e., output minus input) comes up to a peak of 166.49%, which is the only positive difference for the five currencies. The intensity of the risk output for the other currencies, in descending order is GBP (90%), EUR (69%), CNY (45%) and JPY (29%), but their net values of risk conduction are all negative. From this sense, the USD could be known as the risk exporter, or as a dominator, and the other four currencies are regarded as risk receivers, or subordinates. However, after the RMB’s inclusion in the SDR, the risk spillover from the USD substantially fell to 14%, though it is still higher than that of the other currencies. On balance, the risk output and net values of risk conduction for the five currencies tend to be average under this case. As for the CNY, its previous risk mainly came from the USD and EUR, but gradually transferred to itself after joining the SDR, indicating that it is gradually stable during the international process. Along with the CNY integrating to the SDR system, the net risk spillovers among the SDR currencies tend to be average, which further testifies that the CNY’s inclusion makes the SDR currency system more stable to some extent. The significant reduction of the net values of risk conduction (from –55.21% to –8.01%) after the CNY’s inclusion in the SDR gives profound proof of its great impact on the international monetary system.

Dynamic network structure By using recursive prediction variance decomposition, we further investigate the dynamic changes of risk spillover between the SDR currencies in different Table 3.14 Risk conduction network constitution among the SDR currencies (%) Before RMB joined the SDR CNY From To Net

99.9453 44.7313 −55.2140

GBP 99.8520 90.4173 −9.4347

JPY 99.8243 29.3383 −70.4860

USD 0.0150 166.5064 166.4914

EUR 99.9641 68.6074 −31.3567

After RMB joined the SDR CNY From To Net

14.1853 6.1724 −8.0129

GBP

JPY

1.4040 8.7738 7.3698

3.8081 6.5508 2.7427

USD 5.7134 13.9239 8.2105

EUR 18.3704 8.0603 −10.3101

Dynamic relationships of the renminbi

63

samples. In the base period from January 1, 2015, to July 31, 2016, the collected data is used to make the first variance decomposition; the relative data from January 1, 2015, to August 31, 2016, serves to conduct the second variance decomposition; and the rest can be done in the same manner until coverage of the entire sample interval. Base on the prediction variance decomposition results in the ten sampling periods and the corresponding data listed in the preceding tables, the related diagrams are drawn, as shown in Figures 3.12 and 3.13. As shown in Figure 3.12 the risk input from the other currencies for the CNY clearly presents a significant declining trend in 2017, but somewhat recovers in 2018 (less than 1%). In Figure 3.13, the risk spillover of the CNY to the other currencies increases from October 2016 to early 2017, and partly declines between 2017 and 2018, then begins to rise from January 2018 until the end of the sampling period. The trend of both GBP and USD is similar, and their risk spillover to other currencies is degressive. The risk output of the JPY to the other currencies remains stable after January 2017, but notably increases thereafter. As a whole, the CNY could indeed exert a considerable impact on the USD, GBP, EUR and JPY after its inclusion in the SDR basket.

Implications and conclusions For evaluating the influence of the RMB joining the SDR basket on RMB’s internationalization, we proposed a new hybrid approach by integrating the DAG and SVAR to further analyze and assess the risk spillover and the resulting dynamic change between the SDR currencies before and after the RMB joined the SDR basket. The newly proposed network model involves the following parts: (1) The DAG method is used to calculate the short-term network structure among the SDR currencies. (2) By using the variance decomposition based on DAG prediction, the long-term risk spillover relationships between the SDR currencies are depicted. (3) For investigating the dynamic changes of risk spillover among the SDR currencies in different samples, the recursive prediction variance decomposition is attempted and the corresponding dynamic risk spillover changes are analyzed. (4) Based on identifying and analyzing the dynamic variation among the currencies within different samples, the interplay between the SDR currencies during the internationalization progress of the RMB is briefly discussed. Based on the network model of variance decomposition of the SVAR system, we analyzed the network constitution of risk conduction between the SDR currencies, evaluated the contribution of every currency in the risk contagion process, and summarized the dynamic network configuration before and after the RMB’s inclusion in the SDR basket. The empirical study demonstrates the following: (1) The USD holds the strongest competition superiority relative to the other currencies before and after the RMB joined the SDR owing to its top ability of risk conduction. (2) The risk spillover effect between the CNY and the other SDR currencies has visibly changed before and after the RMB joined the SDR. The risk source of the CNY mainly comes from itself, indicating the gradual

2017/9/30

2017/4/30

Date

99.0

99.2

99.4

99.6

99.8

GBP

2017/9/30

2017/4/30

Date

99.5

99.6

99.7

99.8

99.9

JPY

2017/4/30 Date

2017/9/30

0.008

0.010

0.012

0.014

0.016

0.018

0.020

0.022

USD

Date

2017/4/30

100.0

2017/9/30

100.0

2018/2/28

2016/11/30

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Figure 3.12 Dynamic variation process of risk input for the SDR currencies

99.0

99.2

99.4

99.6

99.8

CNY

98.8

99.0

99.2

99.4

99.6

99.8

100.0

EUR

Date

2017/4/30

100.0

2017/9/30

64 Dynamic relationships of the renminbi

2018/2/28

2016/11/30

2018/2/28

2016/11/30

Date

CNY

82

84

86

88

90

92

Date

GBP

10

20

30

40

50

60

70

80

Date

JPY

100

120

140

160

180

200

220

Figure 3.13 Dynamic variation process of risk output for the SDR currencies

40

50

60

70

2016/11/30 2017/4/30 2017/9/30 2018/2/28

2016/11/30 2017/4/30 2017/9/30 2018/2/28

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USD

2017/4/30 2017/9/30 2018/2/28

0

10

30

20

40

50

60

70

2016/11/30

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EUR

2017/4/30 2017/9/30 2018/2/28

Dynamic relationships of the renminbi

65

66

Dynamic relationships of the renminbi

stability of the RMB after its inclusion in the SDR. (3) The net risk conduction between the SDR currencies tends to be average after the RMB’s inclusion in the SDR, which also verifies that the RMB’s inclusion makes the SDR currency system more stable to some extent. The RMB’s inclusion in the SDR basket could exert a sizable impact on the risk conduction among the currencies, and the risk received by the CNY is largely reduced, and the net risk spillover of the RMB to the other currencies grows a little. This further verifies that the RMB’s inclusion in the SDR can reduce the risk in the international exchange rate market.

The impact of exchange rate fuctuations on macroeconomic variables; taking China’s foreign trade as an example Background China overtook the United States as the world’s biggest exporter in 2007. China’s total imports and exports amounted to US$ 4.16 trillion and has risen to the largest goods-trading nation in 2013. Since the beginning of 2014, the fluctuations of the RMB against the US dollar have ended the unilateral appreciation, which started with the exchange rate reform in 2005, and entered into a two-way fluctuation range. These seemingly unrelated events are actually deeply related: the development of China’s economy has gradually improved China’s status on the international stage, meanwhile the world’s largest trading nation in goods means that China takes the lead in international trade in goods. As the Chinese economy expands, the influence of the RMB has been rapidly growing and the RMB internationalization is steadily promoted. Therefore, with the construction of the RMB offshore market and the gradual opening of China’s capital account, international capital began to short the offshore market to affect the RMB exchange rate. Especially since April 2014, the Federal Reserve System has taken successive advantage of ending quantitative easing and other austerity policies such as hiking interest rates to create expectations for the appreciation of the US dollar. Under this circumstance, the price of offshore RMB against the US dollar has continued to decline, driving the onshore price against the US dollar to devaluation. Therefore, the current depreciation of the renminbi against the US dollar actually reflects the resistance to the rise of China’s economy and the internationalization of the renminbi under the potential changes in the global economic and trade pattern after the financial crisis. Influenced by the international capital, the RMB against the US dollar has continuously depreciated. But more important, the “base” of the Chinese economy has shown signs of “weakness”. For the gradual opening of China’s economy, foreign trade is one of the most important indicators. Statistics show that China’s foreign trade has plummeted to single-digit growth since 2012 (Figure 3.14). In 2015, there was a “double decline” in the import annual growth rate and export

Dynamic relationships of the renminbi   67

1 billion of the US dollar

2,500

50 40

2,000

30 1,500

2 200 10

1,000

0 500 0

-10

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

-20

Amount of China's Export (Left)

Amount of China's Import (Left)

Amount of China's Export: YOY (Right)

Amount of China's Import: YOY (Right)

Figure 3.14 The amount and annual growth rate of China’s imports and exports

annual growth rate of –14.27% and –2.94%, respectively. Although the foreign trade surplus is as high as US$593.9 billion, the scale of imports and exports has shrunk by 8.1%. In the first half of 2016, the cumulative growth rate of imports and exports denominated in US dollars decreased by 7.78% and 10.17%, respectively. The continued decline in the scale of foreign trade has had a significant impact on China’s economy. More important, the decline in foreign trade may further increase expectations of RMB depreciation.

The impact of China’s exchange rate fluctuations on China’s imports and exports Traditional international trade theory and international financial theory point out that currency devaluation will improve one country’s terms of trade, which will help to enhance the country’s overseas competitiveness and promote exports; conversely, currency appreciation will be detrimental to the country’s exports. However, the establishment of those theories require many rigid assumptions, which are not necessarily true in the real economy. Since the start of the exchange rate reform in 2005, despite the continuous appreciation of the renminbi, China’s exports have maintained rapid growth, with an average growth rate of 13.92%, and the share of China’s exports in the global market has continued to increase. The theory of “appreciation inhibits export” is invalid for China in this period. Similarly, the theory of “devaluation promotes export” has also been proven to be not true by history. International experience shows that when one country’s currency depreciates significantly, it will have adverse effects on the country’s imports and exports. For

68  Dynamic relationships of the renminbi  example, at the beginning of 2012, Japan began to implement quantitative easing policies, which led to the continued sharp depreciation of the Japanese yen. From 2012 to 2014, the annual depreciation rates of the Japanese yen against the US dollar were 12.55%, 21.48% and 13.87%, respectively. At the same time, the annual growth rate of Japan’s imports and exports was 0.35%, with a 14.32% decrease compared to the annual growth rate of 2011. The annual growth rate of Japan’s imports and exports in 2013, 2014 and 2015 were –8.08%, 2.96% and –15.24%, respectively, and the share of Japan’s foreign trade in the global market continued to decline (Figure 3.15). Under the current economic situation, the devaluation of the renminbi can’t help improve China’s exports, but also bring certain negative effects on China’s exports. The main reasons include (1) the current decline in China’s exports is the result of global economic rebalancing and the adjustment of global trade patterns. Due to the aggregate impacts of weak overseas demand caused by the weak global economic recovery and rising labor costs in China, the devaluation of the renminbi cannot change those factors in a short time. (2) The processing trade is still an important mode of China’s foreign trade. The depreciation of the renminbi may raise the price of imported raw materials and equipment, increase the cost of processing trade enterprises, and reduce the competitiveness of their products. (3) Despite the devaluation of RMB against the US dollar may benefit some price-sensitive and labor-intensive industries, such as the textile industry, the companies of these industries have weak bargaining power in the international market, and the benefits of the depreciation of the renminbi exchange rate may be obtained by foreign customers through price reduction. (4) In 2015, China’s exports to Asia countries accounted for 50.25% of China’s total exports. Under the current economic situation, the currencies of many Asian countries have depreciated successively, and these devaluations 1,000

5

1 billion of the US dollar

900

0

800 700

-5

600 500

0 -10

400

-15

300 200

-20

100 0

2012

2013

Amount of Japan's Export (Left) Amount of Japan's Export: YOY (Right)

2014

2015

-25

Amount of Japan's Import (Left) Amount of Japan's Import: YOY (Right)

Figure 3.15 The amount and annual growth rate of Japan’s imports and exports

Dynamic relationships of the renminbi

69

will weaken the stimulus effect of RMB exchange rate devaluation on China’s exports. The devaluation of one country’s currency usually has a serious negative impact on the country’s imports. The devaluation of the renminbi exchange rate increases the cost of China’s imports, which is not conducive to increase China’s imports: (1) The current sharp decline in China’s imports is mainly due to the sluggish international commodity prices and weak external demand. As a result, the import price index has kept falling, and the volume and price of some imported products fell. The devaluation of the renminbi exchange rate not only cannot change those factors, but also may cause the currencies to depreciate successively and further deteriorate external demand. (2) After the global financial crisis, the international division of industries has readjusted. Affected by the increase of labor costs in China, some low-end manufacturing industries have shifted to low-cost countries, which has led to a decline in China’s imports, and the devaluation of the renminbi exchange rate is unable to reverse this process in the short term. (3) For importing companies, the devaluation of the renminbi against the US dollar can increase import costs, reduce corporate profits and increase operating pressure of companies, which will lead to a decline in the amount of their imported products and further weaken China’s imports. (4) Due to the previous loose monetary policy of the Federal Reserve, some foreign trade companies in China have borrowed many debt which is priced in dollars. The continuous and rapid depreciation of the RMB against the US dollar will increase the financial burden of the enterprises, which is not conducive to the development of foreign trade enterprises.

Empirical study After the 811 exchange rate reform, the renminbi continued to depreciate against the US dollar, with a cumulative depreciation of 8.42% from August 2015 to June 2016. Therefore, an extended event analysis method is utilized to quantitatively measure the impact of renminbi depreciation on China’s imports and exports. First, econometric models (including univariate autoregressive integrated moving average [ARIMA] models, multivariate autoregressive distributed lag [ADL] models and vector error correction models [VECMs]) are established to characterize the changes in China’s imports and exports before the 811 exchange rate reform. The explanatory variables include multiple international and domestic economic variables (except the RMB exchange rate). Specifically speaking, the domestic indicators include industrial value-added, the PMI of manufacturing and the consumer confidence index. Meanwhile the international economic indicators include the Baltic Dry Bulk Index, US Consumer Confidence Index, EU Consumer Confidence Index and Japan’s Trend Trends Composite Index. Second, based on the hybrid forecast approach, the imports and exports from August 2015 to June 2016 are forecasted. By comparing the predicted value with the real value after the 811 exchange rate reform, the impact of the 811 exchange rate reform on China’s imports and exports is calculated.

70  Dynamic relationships of the renminbi 

Impact on the amount of China’s imports and exports Based on the empirical results, since the 811 exchange rate reform, the depreciation of the RMB against the US dollar has had a negative impact on China’s total exports and total imports. As shown in Figure 3.16, from August 2015 to June 2016 the devaluation of the RMB against the US dollar led to a cumulative decrease of US$98.39 billion in exports, accounting for 4.93% of total exports during this period, with an average monthly decrease of US$8.95 billion; the cumulative decrease in imports is US$106.26 billion, accounting for 7.35% of the total imports during this period, with an average monthly decrease of US$9.66 billion. The scale of China’s foreign trade has been greatly affected by the depreciation of the RMB against the US dollar. From August 2015 to June 2016, there is a cumulative decrease of US$204.65 billion, accounting for 5.94% of the actual trade scale during this period. In 2015, the amount of China’s was only US$144 billion higher than the United States. From the perspective of trade methods, the devaluation of the RMB against the US dollar has had a negative impact on the imports and exports of processing trade, and a small negative impact on the exports of general trade, but a significant negative impact on the imports of general trade. As shown in Figure 3.17, from August 2015 to June 2016, the depreciation of the renminbi exchange rate led to a 10.41% decrease in the exports of China’s processing trade, with a cumulative decrease of US$70.93 billion, and led to a 8.64% decrease in the imports of China’s processing trade, with a cumulative decrease of US$32.36 billion. Meanwhile the depreciation of the renminbi exchange rate also led to a 1.24% decrease of the exports of China’s general trade, with a cumulative decrease of US$13.59 billion, and led to a 9.04% decrease of the imports of China’s general trade, with a cumulative decrease of US$72.34 billion.

1 billion of the US dollar

20

2015-08 2015-09 2015-10 2015-11 2015-12 2016-01 2016-02 2016-03 2016-04 2016-05 2016-06

0 -20 -40 -60 -80 -100 -120

Impact on exports

Impact on imorts

Figure 3.16 The cumulative impact on China’s imports and exports after the 811 exchange rate reform

Dynamic relationships of the renminbi   71

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2015-08 2015-09 2015-10 2015-11 2015-12 2016-01 2016-02 2016-03 2016-04 2016-05 2016-06

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1 billion of the US dollar

0 -10 -20 -30 -40 -50 -60 -70 -80

Impact on the exports of processing trade Impact on the exports of general trade

Impact on the imports of processing trade Impact on the imports of general trade

Figure 3.17 The cumulative impact on China’s processing trade and general trade after the 811 exchange rate reform

Impact on China’s foreign trade with major trading partners The United States, European Union, and Japan are China’s major trading partners. In 2015, China’s total exports to the United States, European Union and Japan accounted for 17.97%, 15.61% and 5.96%, respectively. Based on the empirical results, from August 2015 to June 2016 the depreciation of the RMB against the US dollar had a significant negative impact on the imports and exports between China and United States, and a certain negative impact on the imports between China and European, and had a positive impact on the exports between China and European. Meanwhile, the devaluation of renminbi exchange rate had a certain negative impact on the imports and exports between China and Japan. As shown in Figure 3.18, from August 2015 to June 2016, the fluctuations of renminbi exchange rate has caused a cumulative decrease of US$27.52 billion in exports to the United States, accounting for 7.73% of exports to the United States during this period, with an average monthly decrease of US$2.50 billion and caused a cumulative decrease of US$12.69 billion in imports from the United States, accounting for 9.97% of imports from the United States during this period, with an average monthly decrease of US$1.15 billion. The cumulative amount of China’s trade with the United States decreased by US$40.21 billion, accounting for 8.32% of the actual trade volume during this period. Meanwhile, the devaluation of the RMB against the US dollar led to a cumulative increase of US$0.85 billion of the exports to the European Union, accounting for 0.27% of exports to the European Union, and led to a cumulative decrease of US$7.56 billion imports from the European Union, fell by 4.06% of imports from European Union. The devaluation of RMB exchange rate also caused the exports to Japan to fall by 1.45%, with a cumulative decrease of US$1.75 billion

72  Dynamic relationships of the renminbi 

10

2015-08 2015-09 2015-10 2015-11 2015-12 2016-01 2016-02 2016-03 2016-04 2016-05 2016-06

1 billion of the US dollar

5 0 -5 -10 -15 -20 -25 -30

Impact on the export to US Impact on the export to EU Impact on the export to Japan

Impact on the import from US Impact on the import from EU Impact on the import from Japan

Figure 3.18 The cumulative impact on China’s foreign trade with major trading partners

and caused the imports from Japan to fall by 2.94%, with a cumulative decrease of US$3.74 billion.

Impact on China’s foreign trade of major products The 811 exchange rate reform has had different impacts on China’s foreign trade of major products. Based on the empirical results, the depreciation of RMB against the US dollar has a certain pulling effect on China’s textile yarns, fabrics and products; clothing and accessories; footwear; and automatic data processing equipment and its components, but this positive impact is very limited. The results show that from August 2015 to June 2016, the cumulative increase in the export volume of these four types of products caused by the devaluation of the RMB against the US dollar are US$1.64 billion, US$4.40 billion, US$0.79 billion and US$1.01 billion, respectively, accounting for 1.65%, 2.86%, 1.72% and 0.77%, respectively, of the export volume of these four types of products in this period. However, the devaluation of the renminbi exchange rate has also had a significant negative effect on the exports of high-tech products, and mechanical and electrical products. From August 2015 to June 2016, impacted by the devaluation of the RMB against the US dollar, the total export volume of these two types of products decreased by US$33.87 billion and US$59.14 billion, respectively, accounting for 5.81% and 5.09%, respectively, of the export volume of these two types of products in this period (Figure 3.19). From the perspective of China’s imports of major products, the devaluation of the renminbi exchange rate has had a significant negative impact on the imports

Dynamic relationships of the renminbi   73

1 billion of the US dollar

10

2015-08 2015-09 2015-10 2015-11 2015-12 2016-01 2016-02 2016-03 2016-04 2016-05 2016-06

0 -10 -20 -30 -40 -50 -60 -70

Texle yarns, fabrics and products Clothing and accessories Footwear Automac data processing equipment and its components High-tech product Mechanical and electrical products

Figure 3.19 The cumulative impact on China’s exports of major products

of major raw materials, including crude oil, iron ore and its concentrates, primary shape plastics, and unwrought copper. The empirical results show that from August 2015 to June 2016, impacted by the devaluation of the RMB against the US dollar, the total import volume of these four types of products decreased by US$9.22 billion, US$2.12 billion, US$2.31 billion and US$1.42 billion, respectively, accounting for 9.07%, 4.37%, 6.14% and 5.39%, respectively, of the import value of these four types of products in the period. Meanwhile, the devaluation of the renminbi exchange rate also has a significant negative impact on the imports of high-tech products and mechanical and electrical products. From August 2015 to June 2016, impacted by the devaluation of the RMB against the US dollar, the total import volume of these two types of products decreased by US$36.93 billion and US$50.65 billion, respectively, accounting for 7.57% and 7.11% of the import volume of these two types of products in this period (Figure 3.20). In summary, although the devaluation of the renminbi exchange rate has had a certain positive effect on the exports of consumer goods such as textile yarns, and clothing and accessories, it has a significant negative impact on the exports of mechanical and electrical products and high-tech products, resulting in a negative impact on China’s total exports. The negative impact is mainly due to the fact that mechanical and electrical products and high-tech products are technologyintensive processing trade products. The devaluation of the RMB against the US dollar has increased the import price of intermediate components and weakened the export advantage. Affected by the devaluation, the imports and exports of China’s processing trade have dropped significantly, while imports of mechanical and electrical products and high-tech products have also dropped significantly.

74  Dynamic relationships of the renminbi 

10

2015-08 2015-09 2015-10 2015-11 2015-12 2016-01 2016-02 2016-03 2016-04 2016-05 2016-06

0

1 billion of the US dollar

-10 -20 -30 -40 -50 -60

Crude oil Plastic in primary shape High-tech product

Iron ore and its concentrate Unwrought copper Mechanical and electrical products

Figure 3.20 The cumulative impact on China’s imports of major products

Implications and conclusions After the 811 exchange rate reform, the renminbi continued to depreciate against the US dollar, with a cumulative depreciation of 8.42% from August 2015 to June 2016. Therefore, an extended event analysis method is utilized to quantitatively measure the impact of renminbi depreciation on China’s imports and exports. First, econometric models (including univariate ARIMA models, multivariate ADL models and VECMs) are established to characterize the changes in China’s imports and exports before the 811 exchange rate reform. The explanatory variables include multiple international and domestic economic variables (except the RMB exchange rate). Specifically speaking, the domestic indicators include industrial value-added, the PMI of manufacturing and the consumer confidence index. Meanwhile the international economic indicators include the Baltic Dry Bulk Index, US Consumer Confidence Index, EU Consumer Confidence Index and Japan’s Trend Trends Composite Index. Second, based on the hybrid forecast approach, the imports and exports from August 2015 to June 2016 are forecasted. By comparing the predicted value with the real value after the 811 exchange rate reform, the impact of the 811 exchange rate reform on China’s imports and exports is calculated. The empirical results show that the devaluation of the renminbi exchange rate has had a significant negative effect on China’s imports and exports, which led to a cumulative decrease of US$98.39 billion and US$ 106.26 billion in imports and exports, respectively.

Conclusions In this chapter, we analyzed the dynamic relationship of the RMB to other factors, including CNH and CNY, SDR currencies, and China’s foreign trade. The empirical results show the following.

Dynamic relationships of the renminbi

75

Firstly, we proposed the EMD-Bry-Boschan method to study the lead–lag relationship between the offshore RMB and the onshore RMB under the influence of extreme events. The main results show that (1) there exists a dynamic relationship between CNH and CNY, CNY Granger-causes CNH, and vice versa; (2) CNH always leads CNY when it concerns short-term market activities; and (3) the lead–lag relationships between CNY and CNH may alternate when the medium-term impact is caused by different kinds of extreme events. CNY leads CNH when the deviations are caused by extreme events that are caused by global recessions or some other market activities. However, CNH leads CNY when the deviations are caused by policy changes, e.g., the 811 exchange reform. The main innovations and features of the EMD-Bry-Boschan method include that it is the first time the EMD algorithm has been used to study the lead–lag relationship of CNH and CNY, and the IMFs are combined into three components based on fine-to-coarse reconstruction. Thus, the exchange rate sequence is decomposed to three components, i.e., the short-term fluctuation caused by market activities, the medium-term fluctuation influenced by extreme events and long-term trends. Also the EMD-Bry-Boschan method is proposed to study the lead–lag relationship between the offshore RMB and the onshore RMB under the influence of extreme events. We further analyzed the lead–lag relationship of CNH and CNY when the extreme events are caused by different kinds of factors. Secondly, for evaluating the influence of the RMB joining the SDR basket on RMB’s internationalization, we proposed a new hybrid approach by integrating the DAG and SVAR to further analyze and assess the risk spillover, and the resulting dynamic change between the SDR currencies before and after the RMB joined the SDR basket. The newly proposed network model involves the following parts: (1) The DAG method is used to calculate the short-term network structure among the SDR currencies. (2) By using the variance decomposition based on DAG prediction, the long-term risk spillover relationships between the SDR currencies are depicted. (3) For investigating the dynamic changes of risk spillover among the SDR currencies in different samples, the recursive prediction variance decomposition is attempted and the corresponding dynamic risk spillover changes are analyzed. (4) Based on identifying and analyzing the dynamic variation among the currencies within different samples, the interplay between the SDR currencies during the internationalization progress of RMB is also briefly discussed. The empirical results demonstrate that the USD takes a dominant position and holds the biggest risk spillover to other currencies, and the RMB’s inclusion to the SDR basket makes the risk spillover average, giving rise to a more stable SDR currency system. The inclusion of the RMB in the SDR not only can reduce the systematic risk of the SDR, but also has a certain impact on international exchange rate markets. Nowadays, in front of the growing trade friction, more research could help to effectively deal with currency disputes. Thirdly, after the 811 exchange rate reform, the renminbi continued to depreciate against the US dollar, with a cumulative depreciation of 8.42% from August 2015 to June 2016. Therefore, an extended event analysis method is utilized to

76

Dynamic relationships of the renminbi

quantitatively measure the impact of renminbi depreciation on China’s imports and exports. By comparing the predicted value with the real value after the 811 exchange rate reform, the impact of the 811 exchange rate reform on China’s imports and exports is calculated. The empirical results show that the devaluation of the renminbi exchange rate has a significant negative effect on China’s imports and exports, which led to a cumulative decrease of US$98.39 billion and US$106.26 billion in imports and exports, respectively.

4

A forecasting approach based on the characteristics of China’s exchange rate

Introduction There are many factors that can affect the fluctuations of exchange rates, especially extreme events. From the analysis of Chapter 3, it can be concluded that the original time series can be decomposed into different intrinsic mode functions (IMFs) by using the empirical mode decomposition (EMD) algorithm. Based on the different data characteristics of each IMF, the EMD can be used to predict the exchange rate separately and to get integrated forecasting results to improve the prediction accuracy. Wang et al. (2004, 2005a) proposed the TEI@I methodology, which reflected the idea of “decomposition and ensemble” and can significantly improve forecasting accuracy (Wang et al., 2011; Lin et al., 2012; Tang et al., 2012; Xie et al., 2014). The effectiveness of the idea of decomposition and ensemble has been confirmed. Yu et al. (2008) proposed an EMD-based neural network ensemble learning paradigm to predict crude oil prices. Lin et al. (2012) utilized EMD and least squares support vector regression (LSSVR) for forecasting foreign exchange rates. The results showed that EMD-LSSVR outperformed the EMD-ARIMA model and LSSVR model. Wang et al. (2014) combined the EMD algorithm and Elman neural network model to predict wind speed. To overcome some drawbacks of the EMD algorithm, Wu and Huang (2009) extended the EMD algorithm and proposed the ensemble empirical mode decomposition (EEMD) algorithm, which can be used to analyze the sequence effectively and to reduce the influence of mode mixing of the EMD algorithm. Based on the idea of decomposition and ensemble, a series of decompositionand-ensemble learning paradigms based on the EEMD algorithm and other artificial neural network algorithms also perform better in prediction. Tang et al. (2011) utilized EEMD to decompose the sequence and used the LSSVR model to predict the decomposed IMFs. An EEMD-LSSVR–based decomposition and ensemble methodology is proposed to predict nuclear power consumption. Lu and Shao (2012) used EEMD and ELM models to predict computer product sales. Tang (2015) proposed an EEMD-based EELM model for crude oil price forecasting.

78

A forecasting approach

The EEMD-based LSSVR approach has been barely used in previous literature of forecasting. But the LSSVR model has been widely used in some forecasting areas, such as oil price forecasting, port container throughput forecasting, hydroelectric power consumption forecasting and air travel demand forecasting (Wang et al., 2011; Xie et al., 2013; Yu et al., 2014). In this chapter, based on the characteristic of the central parity of the renminbi (RMB) against the US dollar (USD), an EEMD-LSSVR decomposition and integrated approach is proposed for exchange rate forecasting, which mainly consists of three stages: Firstly, data decomposition. The EEMD algorithm is used to decompose the exchange rate to several different IMFs and a residual sequence. Secondly, single forecasting. LSSVR is employed to forecast those different IMFs and the residual sequence. Thirdly, ensemble forecasting. Based on the simple addition ensemble method, the results are aggregated into final integrated results.

Related methodologies In this section, the EEMD-LSSVR decomposition and integrated approach is introduced.

EEMD Wang et al. (2004, 2005a) proposed the TEI@I methodology, which reflected the idea of decomposition and ensemble. It is different from traditional decomposition methods (e.g., wavelet transform, Fourier transform). The EMD algorithm and EEMD algorithm decompose the sequence according to the characteristics of the data. It is a completely localized and adaptive algorithm for stationary data and nonstationary data (Zhang et al., 2009b). The EEMD algorithm is widely used in complex system analysis, and the results further validate the effectiveness of the EEMD decomposition method (Tang et al., 2015; Yu et al., 2016). The EEMD algorithm is utilized to decompose the original series x(t) into several IMFs and a residual sequence. The IMF must satisfy two conditions: firstly, the number of extreme and zero-crossings should be the same, or differ at the most by one; secondly, they should be symmetric with respect to the zero mean (Huang et al., 2003; Wu and Huang, 2009). The original series x(t) can be formulated as follows:

x (t) =

N

åIMF (t ) + r (t ) i

t = 1, 2,¼, T

i =1

where N is the number of IMFs, and r(t) is the residual sequence.

A forecasting approach 79 The EEMD algorithm differs from the EMD algorithm, which is based on a hypothesis that “observations are made up of the real sequence and white noise”. Therefore, EEMD involves an additional step of adding white noise, which can help to extract the real IMFs. The steps are as follows: (1) the white noise sequence is added to the target sequence; (2) the sequence including white noise is decomposed into several IMFs and a residual sequence; (3) the preceding two steps are repeated with different white noise sequences added; and (4) the ensemble average of each IMF is obtained by the decomposition of different times as the final results (Wu and Huang, 2009).

LSSVR Vapnik (1995) proposed the support vector machine (SVM) based on the principle of structural risk minimization, which performed better and had been widely used in classification and prediction. However, it takes a long time for SVM to train and analyze huge data. To reduce the computational time, Suykens and Vandewalle (1999) further proposed the least squares support vector machine (LSSVM). In general, LSSVM can be categorized into LSSVR and LSSVC for the purpose of regression and classification, respectively. LSSVM is a very effective method for forecasting (Wang et al., 2011; Xie et al., 2013; Tang et al., 2015). The basic idea of LSSVR is to map the training set (y, x) into the high-dimensional feature space through a nonlinear mapping function φ(∙), and then to make linear regression in the high-dimensional feature space. LSSVR can be formulated as follows:

y ( x ) = wT j ( x ) + q where φ(x) is the nonlinear mapping function, ω is a coefficient, and q is a deviation. According to the principle of structural risk minimization, the regression problem can be transformed into the following optimization problem:

min

1 T 1 w w+ g 2 2

T

åe

2 t

t =1

s.t. y t = wT j ( x t ) + q + et where γ is the penalty parameter, and et is the slack variable. By introducing the Lagrangian function and the Karush-Kuhn-Tucker (KKT) conditions, the original problem can be represented into the following form:

y (x) =

T

åw K ( x, x ) + q t

t =1

t

80

A forecasting approach

where K(∙) is the kernel function. In this section, the Gaussian radius basis function (RBF) is utilized, that is, K (x,xt) = exp (–∥x–xt∥/2σ2), where σ is the width of the kernel function. For more information, please refer to Vapnik (1995).

EEMD-LSSVR decomposition and integrated approach In this section, based on the characteristic of the central parity of the RMB against the US dollar, the EEMD-LSSVR decomposition and integrated approach is proposed for exchange rate forecasting, which is mainly consists of three stages: Firstly, data decomposition. The EEMD algorithm is used to decompose the exchange rate to several different IMFs and a residual sequence. Secondly, single forecasting. LSSVR is employed to forecast those different IMFs and the residual sequence. Thirdly, ensemble forecasting. Based on the simple addition ensemble method, the results are aggregated into final integrated results, as illustrated in Figure 4.1.

Data In July 2008, in order to preserve the exchange rate stability in China and help China’s economy ride through the impact of the US subprime mortgage crisis,

Figure 4.1 EEMD-LSSVR decomposition and integrated approach

A forecasting approach 81 China’s central bank pegged the RMB against the US dollar at 6.83 and narrowed the floating range of the RMB exchange rate (see Chapter 1, Figure 1.9). In June 19, 2010, China’s central bank announced resuming and furthering the reform of the RMB exchange rate regime based on measures taken in 2005, to increase the flexibility of the RMB exchange rate, and continued emphasis would be in place to reflect market supply and demand with reference to a basket of currencies. The reforms of the exchange rate mechanism would have a significant impact on the exchange rate market. Therefore, for the daily forecast, the data after the 811 exchange rate reform are utilized, which are the daily data of the central parity of the RMB against the US dollar from August 11, 2015, to June 30, 2016, with a total of 216 observations of each variable. For the monthly data forecast, the sample data after the 811 exchange reform are too short for modeling. Therefore, the monthly data from July 2010 to June 2016, with a total of 72 observations of each variable, are used to forecast the exchange rate. The sample data are obtained from the Wind Database (www .wind.com.cn/) and the statistics are showed in Table 4.1.

Empirical study Decomposing data with the EEMD algorithm In this section, the EEMD algorithm is applied to decompose daily and monthly central parity of RMB/USD data into several IMF components and a residual sequence.

Decomposition of daily data Figure 4.2 shows the decomposition of the daily central parity of RMB/USD. The original series is decomposed into six IMFs and a residual sequence. From Table 4.2, it can be concluded that IMF1, IMF2 and IMF3 represent the frequency of 4 days, 9 days and 18 days, respectively. IMF1–IMF3 can be aggregated together and represent the short-term composition. The frequencies of IMF4 and IMF5 are each 108 days, which represent the medium-term

Table 4.1 Statistics of central parity of RMB/USD Variable

Mean Standard Skewness Kurtosis P-value Observations deviation

Central parity of 6.47 RMB/USD (daily) Central parity of 6.33 RMB/USD (monthly)

0.08

–0.15

1.93

0.00

216

0.19

0.72

2.58

0.03

72

Figure 4.2 Result of EEMD algorithm of daily central parity of RMB/USD

82 A forecasting approach

A forecasting approach 83 Table 4.2 Decomposition of daily central parity of RMB/USD

IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 Residual

Mean period (daily)

Var.

4.41 8.64 18 108 108 216 216

0.51 0.51 0.63 2.41 12.41 0.03 68.28

components. And IMF6 represents the low frequency sequence with the frequency of 216 days. The residue is often regarded as long-term composition, representing the trend of the original series.

Decomposition of monthly data Figure 4.3 shows the decomposition of the monthly central parity of RMB/ USD, and the EEMD algorithm decomposes the original series into five IMFs and a residual sequence. From Table 4.3, it can be concluded that IMF1 represents the high-frequency sequence with a frequency of 5 months. The frequencies of IMF1 and IMF2 are 9 months and 36 months, respectively, which represent the medium-term components. And IMF4 and IMF5 represent the low-frequency sequence with frequencies of 72 months each. The residue represents the trend of the original series. For all the IMFs and the residual sequence, decomposed from the original series via EEMD (as illustrated in Figure 4.2), LSSVR is employed to forecast those different IMFs and the residual sequence. Then based on the simple addition ensemble method, those results are aggregated into final integrated results of daily and monthly central parity of RMB/USD, respectively.

EEMD-LSSVR decomposition and integrated approach Daily and monthly central parity of RMB/USD are obtained from the Wind Database. The daily data covers the period of August 11, 2015, to June 30, 2016, with a total of 216 observations, excluding weekends and holidays. The monthly data covers the period of July 2010 to June 2016, with 72 observations. For modeling and validation purposes, the sample data are divided into two subsets, an in-sample subset and out-of-sample subset, which are shown in Table 4.4. The in-sample subset is used for model training, and the out-of-sample subset is used for model testing.

Figure 4.3 Result of EEMD algorithm of monthly central parity of RMB/USD

84 A forecasting approach

A forecasting approach 85 Table 4.3 Decomposition of monthly central parity of RMB/USD

IMF1 IMF2 IMF3 IMF4 IMF5 Residual

Mean period (monthly)

Var.

5.14 9 36 72 72 131

0.30 0.39 1.78 2.97 0.69 15.91

Table 4.4 Sample period of training subset and testing subset

Central parity of RMB/ USD (daily) Central parity of RMB/ USD (monthly)

In-sample subset

Out-of-sample subset

2015.08.11–2016.05.13

2016.05.16–2016.06.30

2010.07–2015.09

2015.10–2016.06

In this section, LSSVR is employed to forecast the different IMFs and the residual sequence. Then based on the simple addition ensemble method, the results are aggregated into final integrated results of daily and monthly central parity of RMB/USD. To confirm the effectiveness of the idea of decomposition and ensemble, the LSSVR is also utilized to forecast the original series for comparing with the forecasting performance of the EEMD-LSSVR approach.

Evaluation criteria To assess the forecasting accuracy of the proposed EEMD-LSSVR decomposition and integrated approach from different perspectives, such as level forecasting and directional forecasting, two evaluation criteria are employed. For assessing the performance of level forecasting, the mean absolute percentage error (MAPE) is employed. The directional change (DS) is utilized to assess the directional forecasting accuracy. The specific formulas are as follows (Sun et al., 2017):

MAPE =

DS =

1 n

100 n

n

å t =1

Yt - Yˆt Yt

(

)

ì1 (Y -Y Yˆ - Y ³ 0 t +1 t t +1 t ï at ´ 100%, at = í 0 otherwise t =1 îï n

å

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A forecasting approach

where Yt and Yˆt represent the actual value and the forecast value at time t, respectively, and n is the number of observations. The MAPE is utilized to measure the deviation between the actual value and the forecasting value, and the smaller values represent higher accuracy. The performance of the directional forecasting accuracy is evaluated by the DS; the higher the directional forecasting accuracy, the better the forecasting performance (Chang, 2010; Wang et al., 2011b; Sun et al., 2017).

Comparison of forecasting performance The forecasting performance of the EEMD-LSSVR decomposition and integrated approach and the benchmark models are discussed in this section. To evaluate the out-of-sample forecasting accuracy of the proposed EEMD-LSSVR decomposition and integrated approach, four single models – LSSVR, autoregressive moving average (ARMA), autoregressive integrated moving average (ARIMA) and Random Walk (RW) – are accomplished on the daily and monthly RMB/USD for model evaluation and model comparison. MAPE is employed to assess the performance of level forecasting and DS is utilized to assess the directional forecasting accuracy. Table 4.5 provides the statistical evaluation results of level forecasting accuracy and directional forecasting accuracy of EEMD-LSSVR and the benchmark models. Table 4.5 shows the EEMD-LSSVR decomposition and integrated approach performs better in forecasting the daily and monthly central parity of RMB/USD with the three-step-ahead. 1. For the daily forecasting, the EEMD-LSSVR decomposition and integrated approach outperforms the benchmark models in the level forecasting, which obtains the smallest MAPE of 0.471. For directional forecasting, the DS of the EEMD-LSSVR decomposition and integrated approach is 68.75%, which is better than the benchmarks. 2. For the monthly forecasting, the EEMD-LSSVR decomposition and integrated approach outperforms the benchmark models in the level forecasting, which obtains the smallest MAPE of 0.741. For directional forecasting, the DS of the EEMD-LSSVR decomposition and integrated approach is 77.78, which is better than the benchmark models.

Table 4.5 Performance comparison of different models for daily and monthly exchange rates: three-step-ahead forecasting results Evaluation criteria Daily Monthly

MAPE (%) DS (%) MAPE (%) DS (%)

EEMDLSSVR

LSSVR

ARMA

ARIMA

RW

0.471 68.75 0.741 77.78

0.499 56.25 0.858 44.44

1.010 53.13 1.630 55.56

0.561 56.25 1.032 55.56

0.975 50.00 2.347 44.44

A forecasting approach 87 3. From the comparison of the forecasting performance of the EEMD-LSSVR decomposition and integrated approach and LSSVR, it can be confirmed that the idea of decomposition and ensemble is effective for improving forecasting accuracy. The EEMD-LSSVR decomposition and integrated approach can improve level forecasting accuracy and directional forecasting accuracy compared to LSSVR in daily and monthly forecasting.

Conclusions In this chapter, a forecasting approach based on the characteristics of China’s exchange rate is developed. The EEMD-LSSVR–based decomposition and ensemble methodology is employed to forecast the exchange rate for the first time. The EEMD-LSSVR decomposition and integrated approach mainly consists of three stages: Firstly, data decomposition. The EEMD algorithm is used to decompose the exchange rate to several different IMFs and a residual sequence. Secondly, single forecasting. LSSVR is employed to forecast those different IMFs and the residual sequence. Thirdly, ensemble forecasting. Based on the simple addition ensemble method, the results are aggregated into final integrated results. The empirical study shows that (1) for daily and monthly forecasting, the EEMD-LSSVR decomposition and integrated approach outperforms LSSVR, ARIMA, ARMA and RW in level forecasting and directional forecasting; and (2) the EEMD-LSSVR decomposition and integrated approach can improve level forecasting accuracy and directional forecasting accuracy compared to LSSVR in daily and monthly forecasting.

5

A forecasting approach based on the domestic economic situation

Introduction Due to the deepening of the internationalization of the renminbi (RMB), the gradual opening of the capital account and the further reform of the RMB pricing mechanism, the fluctuation of the RMB exchange rate has had a markedly enhanced trend. Since March 15, 2014, the RMB exchange rate has been allowed to move within a wider band; the daily trading band for the RMB against the US dollar (USD) increased from ±1% to ±2%. On August 11, 2015, China further improved the quotation mechanism of the RMB’s central parity rate against the US dollar by taking into consideration the previous day’s closing rate on the interbank forex market to reflect the changes of market supply and demand. The People’s Bank of China described this reform as a “one-time correction” in order to bridge previously accumulated differences between the spot market rate and the central parity rate. On that day, the RMB’s central parity rate against the US dollar depreciated sharply by 1136 basis points. From the “811 exchange reform” to June 30, 2016, the RMB against the US dollar, the euro and the Japanese yen depreciated 8.42%, 9.70% and 30.47%, respectively. How could the fluctuations of the exchange rate impact economic development? This is an important issue in international trade and macroeconomics. The fluctuations of the RMB exchange rate can have a significant impact on the macroeconomic, meanwhile the changes of macroeconomic variables will also have an impact on the RMB exchange rates. According to the exchange rate pass-through theory, when the exchange rate pass-through is complete, the movements of the nominal exchange rate will lead the price of imported goods to change in the same proportion. The definition of exchange rate pass-through is the degree to which exchange rate changes are passed through to price level changes between the exporting and importing country (Goldberg and Knetter, 1997; Campa and Goldberg, 2002; Jiang and Kim, 2013). In addition, the devaluation of currency will cause the government to implement an expansionary monetary policy, which will have great impact on economic activities and stock prices. Meanwhile, the changes of macroeconomic variables will also have a significant impact on the movements of the exchange rates. A lot of research has analyzed the relationship between macroeconomic variables and the movements of exchange

A forecasting approach based on the domestic economic situation

89

rates and the selected macroeconomic variables, including stock prices (Abdalla, 1997; Ajayi et al., 1998; Ibrahim, 2000; Granger et al., 2000; Deng and Yang, 2007; Aydemir and Demirhan, 2017), inflation (Romero, 2017; McCarthy, 2000; Ito and Sato, 2008; Lin and Ye, 2009), imports and exports (Bini, 1991; Chowdhury, 1993; Doğanlar, 2002; Romero, 2017), foreign exchange reserves (Eichengreen and Mathieson, 2000; Kim, 2003; Bhattacharya et al., 2011), and short-term capital flows (Zhao and Zhang, 2013). The devaluation of the domestic currency will increase the price of imported goods, thereby increasing the level of domestic inflation and so on. Fluctuations in the exchange rate will impact the prices of exported goods, money supply (M2), prices of imported goods, consumer price index (CPI), stock prices, import price indices and producer price index (PPI). For different countries, the relationship between the exchange rate and the macroeconomic variables is different. Take stock prices as an example. Granger et al. (2000) analyzed the relationship between exchange rates and stock prices in Hong Kong, Indonesia, Japan, Korea, Malaysia, Philippines, Singapore, Thailand and Taiwan during the Asian flu. The results indicated that (1) in Korea, the exchange rate led the stock prices; (2) the stock prices led the exchange rate to some extent in Hong Kong, Malaysia, Singapore, Thailand and Taiwan; (3) there existed no relation between the stock prices and the exchange rate market in Japan and Indonesia. The existing literature mainly focuses on analyzing the relationship of the exchange rate and one or several macroeconomic variables, or comparing the differences of the relationships of different countries’ exchange rates and one macroeconomic variable. There are quite a few studies on filtering out the main macroeconomic variables that have the highest degrees of relevance with the exchange rate to represent the domestic economic situation and to forecast the exchange rate. In this chapter, a vector error correction model (VECM)-based forecasting approach integrating the Granger causality test, correlation test and grey relational analysis is proposed for exchange rate forecasting, as shown in Figure 5.1. This framework mainly describes a modeling process that starts from data extraction, data selection and data computing. The proposed VECM-based ensemble learning approach includes the following three steps: Step 1 – Data extraction. According to the existing literature, 16 macroeconomic variables were selected, including import, export and foreign exchange reserves, which are often selected to study the relationship between the exchange rate and the macroeconomic variables. Step 2 – Data selection. By integrating the Granger causality test, correlation test and grey relational analysis, we rank the correlation of RMB/USD with China’s 16 major macroeconomic variables, and then filter the three variables that have the highest degrees of relevance with the exchange rate to represent the domestic situation. Step 3 – Data computing. Based on the domestic situation, the VECM is used to forecast the central parity of RMB/USD. And multiple evaluation criteria

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A forecasting approach based on the domestic economic situation

Figure 5.1 A forecasting approach based on the domestic economic situation

are employed to comprehensively evaluate the forecasting performance of the proposed approach and benchmarks.

Data collection According to the existing literature, 16 macroeconomic variables were selected: import (IM), export (EX), import growth (IM_YOY), export growth (EX_ YOY), import price index (IPI), export price index (EPI), foreign exchange reserves (FER), growth of foreign exchange reserves (FER_YOY), consumer price index (CPI), producer price index (PPI), retail price index (RPI), money supply (M2), growth of money supply (M2_YOY), industrial value added (IVA), Shenzhen composite index (SZCOMP) and the Shanghai composite index (SHCOMP). The RMB exchange rate regime has been reformed several times. In July 2008, in order to preserve the exchange rate stability in China and help China’s economy ride through the impact of the US subprime mortgage crisis, China’s central bank pegged the RMB against the US dollar at 6.83 and narrowed the floating range of the RMB exchange rate. On June 19, 2010, China’s central bank announced resuming and further reforming the RMB exchange rate based on measures taken in 2005 to increase the flexibility of the RMB exchange rate. Since the RMB against the US dollar was pegged at 6.83 from the middle of 2008 to June 2010, the monthly data used in this chapter are obtained from the

A forecasting approach based on the domestic economic situation

91

Table 5.1 Statistics of the domestic economic variables and the exchange rate Variable RMB/ USD IM_LN EX_LN IM_YOY EX_YOY IPI EPI FER_LN FER_YOY CPI PPI RPI M2_LN M2_YOY IVA SZ_LN SH_LN

Mean

Standard deviation

Skewness

Kurtosis

JB

P-value

6.79

0.63

0.87

2.46

17.92

0.00

7.02 7.20 11.25 12.44 101.63 101.98 10.06 17.98 2.79 0.75 2.06 13.44 16.66 12.09 6.88 7.84

0.35 0.34 20.86 17.54 10.61 5.05 0.49 16.75 2.17 4.66 2.31 0.51 4.30 4.95 0.50 0.34

–0.48 –0.46 0.24 –0.29 0.00 0.01 –0.87 –0.16 0.54 0.04 0.66 –0.20 1.37 0.16 –0.78 –0.17

1.98 2.16 3.50 2.58 2.27 2.50 2.48 2.23 3.32 1.91 2.98 1.72 4.65 3.34 3.60 3.43

10.78 8.52 2.66 2.78 2.89 1.39 17.87 3.82 6.94 6.51 9.39 9.80 55.61 1.16 15.40 1.61

0.00 0.01 0.27 0.25 0.24 0.50 0.00 0.15 0.03 0.04 0.01 0.01 0.00 0.56 0.00 0.45

Wind Database (www.wind.com.cn/), covering the period from August 2005 to June 2016, with a total of 131 observations of each variable. A logarithmic transformation was applied to IM, EX, FER, M2, SZCOMP and SHCOMP, namely IM_LN, EX_LN, FER_LN, M2_LN, SZ_LN and SH_ LN. The statistics of the selected variables are displayed in Table 5.1. It clearly indicates the difference in the statistical features among the subsets. Skewness analysis is utilized to depict the symmetry of the subset. For skewness, the greater the absolute skewness value, the more obvious the asymmetry. And kurtosis is used to depict the steepness of the subset. For kurtosis, values greater than zero indicate that the distribution of the dataset is steeper than the standard Gaussian distribution.

Correlation analysis Granger causality test Granger (1969) proposed the Granger causality test based on the assumption of linear relationships between variables. A time series X is said to Granger-cause another time series Y if the predication error of the current Y declines by using past values of X in addition to past values of Y. The Granger causality test has been widely used to analyze the correlation of economic and financial variables. The test is sensitive to the lag order, and the Akaike information criterion (AIC)

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A forecasting approach based on the domestic economic situation

and Schwarz information criterion (SIC) are used in this section to determine the optimal lag order. The results of the Granger causality test of the central parity of RMB/USD and the major domestic economic variables are shown in Table 5.2. Table 5.2 indicates that under a 5% significance level, PPI, SZ_LN and SH_LN Grangercause RMB/USD and vice versa. The movements of RMB/USD will cause the fluctuations of IM_LN, EX_LN, EX_YOY, EPI, FER_LN, M2 and IVA, and the changes in RPI will also have an impact on RMB/USD. A lot of literature has shown that with the opening of the capital market, the appreciation of domestic currency would lead the stock prices to rise. If the Table 5.2 Results of the Granger causality test

IM_LN does not Granger-cause RMB/USD RMB/USD does not Granger-cause IM_LN EX_LN does not Granger-cause RMB/USD RMB/USD does not Granger-cause EX_LN IM_YOY does not Granger-cause RMB/USD RMB/USD does not Granger-cause IM_YOY EX_YOY does not Granger-cause RMB/USD RMB/USD does not Granger-cause EX_YOY IPI does not Granger-cause RMB/USD RMB/USD does not Granger-cause IPI EPI does not Granger-cause RMB/USD RMB/USD does not Granger-cause EPI FER_LN does not Granger-cause RMB/USD RMB/USD does not Granger-cause FER_LN FER_YOY does not Granger-cause RMB/USD RMB/USD does not Granger-cause FER_YOY CPI does not Granger-cause RMB/USD RMB/USD does not Granger-cause CPI PPI does not Granger-cause RMB/USD RMB/USD does not Granger-cause PPI RPI does not Granger-cause RMB/USD RMB/USD does not Granger-cause RPI M2 does not Granger-cause RMB/USD RMB/USD does not Granger-cause M2 M2_YOY does not Granger-cause RMB/USD RMB/USD does not Granger-cause M2_YOY IVA does not Granger-cause RMB/USD RMB/USD does not Granger-cause IVA SZ_LN does not Granger-cause RMB/USD RMB/USD does not Granger-cause SZ_LN SH_LN does not Granger-cause RMB/USD RMB/USD does not Granger-cause SH_LN Under 1% significance level. Under 5% significance level. * Under 10% significance level. *** **

F-statistic

Prob.

1.443 3.002 1.443 3.469 1.733 2.380 0.949 2.976 0.796 1.883 1.354 2.294 0.472 2.509 2.215 2.142 1.350 1.782 3.883 4.020 3.122 2.378 1.623 3.169 0.565 0.599 1.907 5.559 7.225 4.088 4.964 3.366

0.173 0.002*** 0.173 0.000*** 0.181 0.097* 0.503 0.002*** 0.555 0.103 0.219 0.022** 0.891 0.012** 0.072 0.080 0.204 0.062* 0.023** 0.020** 0.018** 0.056* 0.118 0.002*** 0.570 0.551 0.153 0.005*** 0.000*** 0.002*** 0.003*** 0.021***

A forecasting approach based on the domestic economic situation

93

future expectation of the domestic currency is that it will appreciate for a long time, the foreign capital will flow into the country and push the stock prices to rise. Otherwise, there are mainly four channels for exchange rate market impacts on the stock market: (1) affect the stock prices through the impact on the liquidity of the stock market; (2) exchange rate fluctuations will affect the adjustment of the government’s economic policy, and through policy-oriented changes, the exchange rate can affect the stock prices; (3) the exchange rate will influence the substitution of investors’ portfolios, which will lead to changes in the supply and demand relationships of different assets, and stock prices will be affected; and (4) export-oriented enterprises have many account receivables and assets of foreign currency accounts. If the domestic currency is devalued, those assets and account receivables will appreciate. On the contrary, export-oriented enterprises also have many foreign currency liabilities. If the domestic currency is devalued, foreign currency liabilities will increase, which will have a negative impact on the stock prices of those enterprises. It has been confirmed by many studies on the Granger causality of RMB/USD and PPI, export growth and stock prices (Granger et al., 2000; Deng and Yang, 2007; Aydemir and Demirhan, 2017).

Correlation test The results of the correlation test are given in Table 5.3.

Grey relational analysis Grey relational analysis is employed to solve problems with complicated interrelationships between multiple factors and variables. It is a measurement method to determine the relationship between sequences using limited amounts of data. The fundamental idea of grey relational analysis is that the closeness of a relationship is judged based on the similarity level of the geometric patterns of sequence curves. Then the variables are ranked by the degree of relevance. The higher the degree of geometric similarity, the greater the degree of correlation (Tan and Deng, 1997, Hsu and Wang, 2009). Table 5.4 shows the results of grey relational analysis. The five variables with the highest degrees of relevance with RMB/USD are SH_LN, FER_LN, SZ_ LN, EX_LN and IM_LN, with the relevant degrees of 0.922, 0.912, 0.827, 0.788 and 0.786, respectively. SZ_LN and SH_LN are both stock market data, and by considering the results of the correlation test, SZ_LN is selected with the higher correlation coefficient with RMB/USD. Meanwhile, EX_LN and IM_LN are both foreign trade data, and the gray relevant degrees of them are similar. However, the correlation coefficient of IM_LN is higher than that of EX_LN. Therefore, IM_LN is selected in the model. Based on these approaches, FER_LN, SZ_LN and IM_LN are selected to represent the major domestic macroeconomic variables and to forecast the central parity of the RMB against the US dollar.

RMB/USD IM_LN EX_LN IM_YOY EX_YOY IPI EPI FER_LN FER_YOY CPI PPI RPI M2_LN M2_YOY IVA SZ_LN SH_LN

1.00 –0.89 –0.88 0.36 0.44 0.24 0.19 –0.99 0.75 0.01 0.43 0.07 –0.92 0.42 0.63 –0.68 –0.25

1.00 0.95 –0.11 –0.19 -0.04 –0.03 0.91 –0.65 0.16 –0.24 0.08 0.86 –0.52 –0.42 0.63 0.22

RMB/ IM_ USD LN

1.00 –0.26 –0.22 -0.13 –0.06 0.90 –0.70 0.12 0.32 0.03 0.88 –0.58 –0.55 0.67 0.27

EX_ LN

1.00 0.73 0.81 0.46 –0.32 0.57 0.50 0.79 0.57 –0.43 0.25 0.80 –0.20 0.01

IM_ YOY

1.00 0.74 0.55 –0.40 0.53 0.49 0.76 0.53 –0.46 –0.01 0.57 –0.31 –0.08

EX_ YOY

1.00 0.76 –0.23 0.58 0.79 0.94 0.85 –0.38 –0.01 0.56 –0.14 0.09

IPI

1.00 –0.20 0.47 0.80 0.79 0.84 –0.33 –0.31 0.32 –0.11 0.10

EPI

1.00 –0.76 0.00 –0.42 -0.07 0.95 –0.42 –0.59 0.73 0.30

FER_ LN

1.00 0.40 0.71 0.48 –0.89 0.44 0.73 –0.56 –0.09

FER_ YOY

1.00 0.66 0.94 –0.20 –0.10 0.32 0.26 0.52

CPI

1.00 0.81 –0.56 0.05 0.61 –0.31 –0.04

PPI

Table 5.3 Results of the correlation test of RMB/USD and domestic economic variables

1.00 –0.24 –0.18 0.36 0.10 0.32

RPI

1.00 –0.52 –0.67 0.73 0.23

M2

1.00 0.45 –0.25 0.04

M2_ YOY

1.00 –0.35 0.02

IVA

1.00 0.82

1.00

SZ_LN SH_LN

94 A forecasting approach based on the domestic economic situation

A forecasting approach based on the domestic economic situation

95

Table 5.4 Results of the grey relational analysis of RMB/USD and domestic economic variables Variable

Correlation degree Variable Correlation degree

IM_LN EX_LN IM_YOY EX_YOY IPI EPI FER_LN FER_YOY

0.786 0.788 0.606 0.582 0.704 0.732 0.912 0.573

CPI PPI RPI M2_LN M2_YOY IVA SZ_LN SH_LN

0.756 0.621 0.693 0.783 0.690 0.753 0.827 0.922

Table 5.5 Statistics of RMB/USD and the main domestic economic variables Variable

Mean Standard deviation Skewness Kurtosis P-value Observations

RMB/USD 6.33 0.19 FER_LN 10.43 0.11 SZ_LN 7.12 0.31 IM_LN 7.29 0.14

0.72 –0.56 0.88 –0.88

2.58 3.15 2.79 3.77

0.03 0.14 0.01 0.00

72 72 72 72

VECM based on the domestic economic situation In this section, a VECM based on the three selected variables representing the domestic economic situation ( FER_LN, SZ_LN and IM_LN) is proposed to forecast the monthly central parity of the RMB against the US dollar.

Data Statistics Since the main domestic economic variables are monthly data, the sample data are monthly data covering the period from July 2010 to June 2016. The data were derived from the Wind Database. Each variable had a total of 72 observations. The statistics are showed in Table 5.5. In this section, the seasonally adjusted data are used to forecast the monthly central parity of the RMB against the US dollar; the statistics of the seasonally adjusted data are shown in Table 5.6.

Unit root test The augmented Dickey-Fuller test is utilized to verify the stationary of the data; the results are displayed in Table 5.7. From Table 5.7, it can be concluded that all of the RMB/USD_SA, SZ_LN_ SA and IM_LN_SA are nonstationary data, which have unit roots. FER_LN_SA

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A forecasting approach based on the domestic economic situation

Table 5.6 Statistics of the seasonally adjusted data Variable

Mean

Standard deviation

Skewness Kurtosis P-value

Observations

RMB/USD_SA FER_LN_SA SZ_LN_SA IM_LN_SA

6.33 10.43 7.12 7.29

0.19 0.11 0.31 0.11

0.72 –0.54 0.86 –0.42

72 72 72 72

2.53 3.09 2.70 2.64

0.03 0.17 0.01 0.29

Table 5.7 Unit root test of RMB/USD and the main domestic economic variables Variable

RMB/USD_SA FER_LN_SA SZ_LN_SA IM_LN_SA

Level

First order

t-Statistic

Prob.

t-Statistic

Prob.

–2.00 –3.10 –0.75 –2.13

0.29 0.03** 0.83 0.23

–5.23 –4.59 –6.61 –10.59

0.00*** 0.00*** 0.00*** 0.00***

Under 1% significance level. Under 5% significance level.

*** **

Table 5.8 Results of the Johansen cointegration test Null hypothesis

Eigenvalue

Trace test

5% critical value

Prob.

None At most 1 At most 2 At most 3

0.332 0.191 0.103 0.029

51.972 24.133 9.531 1.996

47.856 29.797 15.495 3.841

0.020** 0.195 0.319 0.158

**

Under 5% significance level.

can reject the null hypothesis under the 5% significance level, which means the sequence is a stationary sequence. After the first-order difference, all of the RMB/ USD_SA, FER_LN_SA, SZ_LN_SA and IM_LN_SA are stationary data under the 1% significance level.

Johansen cointegration test In this section, the Johansen cointegration test is used to verify whether there exist cointegration relationships between variables. The results are shown in Table 5.8. From Table 5.8, it can be concluded that under the 5% significance level, the null hypothesis can be rejected (there is no cointegration relationship), that is, there is a long-term cointegration relationship between variables. And from Table 5.8 if the null hypothesis is at most 1, the cointegration relationship can’t be rejected.

A forecasting approach based on the domestic economic situation

97

Due to the nonstationary of the data and the cointegration relationship between the data, a VECM based on the domestic economic situation is developed in this section to forecast the monthly central parity of the RMB against the US dollar.

Empirical study The VECM, which contains cointegration constraints, can only be used for modeling nonstationary time series including cointegration relations. In this section, the VECM is used to forecast the central parity of the RMB against the US dollar based on the domestic economic situation. The monthly sample data cover the period of July 2010 to June 2016, including FER_LN_SA, SZ_LN_SA, IM_LN_SA and RMB/USD_SA. For modeling and validation purposes, the sample data are divided into two subsets: an in-sample subset and out-of-sample subset. The in-sample subset is from July 2010 to September 2015. The out-of-sample subset is from October 2015 to June 2016 and is used for model testing.

Evaluation criteria To assess the forecasting accuracy of the proposed VECM-based forecasting approach from different perspectives, such as level forecasting and directional forecasting, two evaluation criteria are employed. For assessing the performance of level forecasting, the mean absolute percentage error (MAPE) is employed. The directional change (DS) is utilized to assess the directional forecasting accuracy. For further detail, please refer to Chapter 4.

Comparison of forecasting performance The forecasting performance of a VECM based on the domestic economic situation and the benchmark models are discussed in this section. To compare the forecasting performance of the VECM and the benchmark models (ARMA, ARIMA and RW), MAPE is employed to assess the performance of level forecasting, and DS is utilized to assess the directional forecasting accuracy. The results of the level forecasting accuracy and the directional forecasting accuracy of the VECM and the benchmark models are displayed in Table 5.9. Table 5.9 shows that the VECM based on the domestic economic situation performs better in monthly forecasting for the central parity of RMB/USD. For Table 5.9 Performance comparison of different models for daily and monthly exchange rates: three-step-ahead forecasting results

Monthly

Evaluation criteria

VECM

ARMA

ARIMA

RW

MAPE (%) DS (%)

0.810 66.67

1.630 55.56

1.032 55.56

2.347 44.44

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A forecasting approach based on the domestic economic situation

the monthly forecasting, the VECM based on the domestic economic situation outperforms the benchmark models in the level forecasting, which obtains the smallest MAPE of 0.810. For directional forecasting, DS of the VECM based on the domestic economic situation is 66.67%, which is better than the benchmarks.

Conclusions In this chapter, a VECM-based ensemble learning approach, integrating the Granger causality test, grey relational analysis and VECM, is proposed for exchange rate forecasting. The framework of the proposed approach includes three steps. First, the data extraction. According to the existing literature, a set of 16 macroeconomic variables is selected, including import, export and foreign exchange reserves. Second is data selection. The selected 16 macroeconomic variables are ranked, and the three of them with the highest degrees of relevance with the exchange rate are filtered out to represent the domestic situation by using the Granger causality test and grey relational analysis. The third step is data computing. Based on the domestic situation, the VECM is utilized for forecasting the central parity of RMB/USD based on the domestic economic situation. The main conclusions of this chapter are as follows: Firstly, the Granger causality test and correlation analysis are employed to analyze the correlation of the RMB against the US dollar and China’s 16 major macroeconomic variables. Then the grey relational analysis is utilized to further filter out the three variables that have the highest degrees of relevance with the exchange rate to represent the domestic economic situation. Secondly, based on the results of the unit root test and the Johansen cointegration test, the VECM based on the domestic economic situation is proposed to forecast the central parity of RMB/USD. The empirical study shows that compared with benchmark models, a VECM based on the domestic economic situation can significantly improve the level forecasting accuracy and directional forecasting accuracy in monthly forecasting.

6

A forecasting approach based on the international economic situation

Introduction With the integration of the international economy and the diversification of the international portfolio, along with the gradual relaxation of China’s capital controls and the reform of the renminbi (RMB) exchange rate, the dependency of international financial markets is increasing. Therefore, accurately analyzing the relationship between the international economic situation and exchange rates is of great significance for policy makers and investors. In this chapter, the major foreign currencies are selected, including the currencies of the Special Drawing Right (SDR) currency basket and the Hong Kong dollar, to reflect the international economic situation. Previous studies have shown that the artificial neural network (ANN) technique and the support vector regression (SVR) technique are the most commonly used models in both individual model forecasting and multiscale decomposition ensemble approach forecasting, indicating that the ANN technique and SVR technique are indeed appropriate for forecasting exchange rates. If we combine the advantages of these two techniques, we can get better predictive performance. The support vector neural network (SVNN) technique is an artificial neural network with similar properties of the SVR technique. Therefore, it supports better alternatives for forecasting exchange rates and a new vine copula–SVNN hybrid forecasting approach based on the international economic situation is proposed. In this chapter, a forecasting approach based on the international economic situation is proposed by integrating the vine copula and SVNN for the first time. In this chapter, the major foreign currencies are selected, including the currencies of the SDR currency basket. By considering the particularity of China’s exchange market, the Hong Kong dollar is also taken into consideration. First, AR-GJR-GARCH is utilized to filter the log yield. Secondly, the vine copula is used to study the dependencies between the RMB and the major foreign exchange assets, including the RMB against the US dollar, the RMB against the euro, the RMB against the 100 Japanese yen, the RMB against the Hong Kong dollar and the RMB against the British pound sterling, under the exchange rate reforms. Thirdly, three variables are selected to represent

100

Forecasting approach

the international economic situation, for they have higher dependencies with RMB/USD. Fourthly, a vine copula–SVNN hybrid forecasting approach based on the international economic situation is proposed to forecast the central parity of the RMB against the US dollar.

Related methodologies AR-GJR-GARCH The time sequences of the financial market have asymmetric characteristics, and the t distribution can be used to describe this characteristic. The volatility of the time series of the financial data can be fitted by the generalized autoregressive conditional heteroscedasticity (GARCH) model. Based on this analysis, this chapter utilizes the AR(p)-GJR-GARCH (1,1)-t model, which adopts the Canonical Maximum Likelihood (CML) estimation method and obtains the optimal parameter values according to the Akaike information criteria (AIC) and Bayesian information criterion (BIC) information criteria. The formulas of the AR(p)-GJR-GARCH (1,1)-t model are as follows:

ri ,t = ci + ai,1 × ri ,t -1 + e i ,t , i = 1, 2, ˜,n, 2 hi ,t = wi + Æ i × e i2,t -1 + di I éëe i ,t -1 < 0ùû e i,t -1 + qi hi ,t -1,

y i ,t =

e i ,t ~ t (hi ) hi ,t

(

)

where yi,t obeys independent identical distribution (IID), and E y i ,t I t -1 = 0,

var ( yi ,t I t -1 ) = 1. All of parameters ωi, Øi and θi are nonnegative, and Øi + δi >

0, Øi + 0.5δi + θi < 1. I[εi,t−1 < 0] is the indicative function. Parameter δi is used to measure the leverage effect: δi > 0 indicates a negative leverage effect, and δi < 0 indicates a positive leverage effect. Parameter ηi denotes the degree of freedom.

Vine copula The dependencies of the RMB exchange rate against the US dollar (USD) and the RMB exchange rate against the other four main foreign exchange assets are analyzed in this section. In the D-vine copula structure, each node can link two edges at most (Figure 6.1). In the C-vine copula, a particular variable is chosen as the key one in governing the relations (or connections) with all the remaining ones (Figure 6.2). Therefore, in this chapter, the C-vine copula is utilized to model the dependencies among the RMB exchange rates. In this chapter, the C-vine copula is utilized, which can be formulated as follows:

Forecasting approach 101

Figure 6.1 Structure of D-vine copula

Figure 6.2 Structure of C-vine copula

102

Forecasting approach

f ( x 1, x 2 , x 3 , x 4 , x 5 ) = f 1 ( x1 ) × f 2 ( x 2 ) × f 3 ( x 3 ) × f 4 ( x 4 ) × f 5 ( x 5 ) × c12 {F1 ( x1 ) , F2 ( x 2 )} × c13 {F1 ( x1 ) , F3 ( x 3 )} × c14 {F1 ( x1 ) , F4 ( x 4 )} ×c15 {F1 ( x1 ) , F5 ( x 5 )} × c15 {F1 ( x1 ) , F5 ( x 5 )} ×c 23|1 {F ( x 2 | x1 ) , F ( x 3 | x1 )} × c 24|1 {F ( x 2 | x1 ) , F ( x 4 | x1 )} ×c 25|1 {F ( x 2 | x1 ) , F ( x 5 | x1 )} × c34|12 {F ( x 3 | x1, x 2 ) , F ( x 4 | x1, x 2 )} ×c35|12 {F ( x 3 | x1, x 2 ) , F ( x 5 | x1, x 2 )} × c 45|123 {F ( x 4 | x1, x 2 , x 3 ) , F ( x 5 | x1, x 2 , x 3 )} Support vector neural network Support vector neural network (SVNN) is an extension of SVR. It is selected as the individual forecasting and ensemble learning tool in this study. For illustration, this section first introduces the SVR technique, and then presents the SVNN technique.

Support vector regression Support vector regression (SVR) is an extension of support vector machine (SVM). SVR is a nonlinear regression method by means of the principle of structural risk minimization and it can well capture the nonlinear patterns hidden in the raw data. The main work of SVR is to map input data x into the high-dimensional feature space F using a nonlinear function ϕ, and then to perform linear regression in the feature space F. If we introduce two slack variables ξi and xi* that correspond to the distance of the actual values from the corresponding boundary values of the ε– insensitive loss function, then SVR can be transformed to the following argument: n ì 1 xi + xi* + w ï min C 2 ï i =1 ï í yi - yi £ e + xi ï yi - yi £ e + xi* ïs .t . ïî 0 >0 xi ³ 0, xi* ³ 0,C

å(

)

2

where ε is a predefined parameter, C is a regularized constant, and yˆi = wT f ( xi ) + b . n

The term

å (x + x ) is the error of the in-sample data set. This optimization i

* i

i =1

problem can be transformed into a dual problem whose solution is based on the

Forecasting approach 103 Lagrangian multipliers (αi and aˆi ) and mapping by a kernel function K (xi,x). Hence, the preceding equation can be transformed as follows: n

yˆi =

å (aˆ - a ) K ( x , x ) + b i

i

i

i =1

Factor b is estimated by the Karush-Kuhn-Tucker (KKT) conditions (for a detailed mathematical derivation, please refer to Vapnik 1995). In this study, the radial basis kernel function is as follows:

(

K ( xi , x ) = exp -g xi - x

2

), g > 0

Support vector neural network The support vector neural network (SVNN), introduced by Ludwig et al. (2014), is a special kind of single hidden layer feedforward neural network (SLFN) and employs eigenvalue decay as the regularization term. The main work of the SVNN is to introduce the eigenvalue decay algorithm for maximum margin training that is based on regularization and evolutionary computing. The formulation of SLFN is expressed as follows:

y h = j (W1 × x + b1) yˆ = W2T × y h + b2 where yh denotes the outputs of the hidden layer, x is the input vector, W1 represents the weights matrix from the input layer to the hidden layer, W2 represents the weights matrix from the hidden layer to the output layer, b1 denotes the bias of the hidden layer, b2 denotes the bias vector of the output layer, and φ(∙) represents the sigmoid function. The objective function of SLFN is evaluated by the mean squared error (MSE) of the in-sample data set:

1 MSE = n

n

å(y - yˆ ) i

i

2

i =1

where n is the number of in-sample data sets, and yi and ŷi represent the target output and the predicted output, respectively. In the SVNN method, the main purpose of eigenvalue decay is to establish a relationship between the eigenvalue minimization and the classification margin. The objective function of eigenvalue decay is expressed by

MSE =

1 n

n

å(y - yˆ ) + k (l i

i =1

i

2

min

+ lmax )

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Forecasting approach

where κ is the regularization hyperparameter, λmin is the minimum eigenvalue of

W1W1T , and λmin is the maximum eigenvalue of W1W1T . The SVNN method can be considered by solving the similar optimization problem as follows:

ì ïmin ï ï í ï ï s.t. ïî

n

C

å (x + x ) + ( l i

* i

min

+lmax )

i =1

yˆi - yi £ e + xi yi - yˆi £ e + xi* xi ³ 0, xi* ³ 0, C > 0.

where yˆi = W2T j (W1 × xi + b1) + b2 , yi is the target output, ε is a predetermined parameter, C is a regularization hyperparameter, and ξi and xi* are two nonnegative slack variables. For a detail mathematical derivation of the SVNN method, please refer to Ludwig et al. (2014).

Overall process of the vine copula–SVNN hybrid forecasting approach In this study, the h-step-ahead forecasting horizons are used to assess the superiority of the vine copula–SVNN hybrid forecasting approach. Given a time series yt,(t = 1, 2, ⋯, n), the h-step-ahead forecasting for ŷt+h is as follows:

(

yˆt +h = f y t , y t -1,…, y t -(l -1)

)

where ŷt+h is the h-step-ahead forecasted value at time t, yt is the actual value at time t, and l denotes the lag orders selected by autocorrelation and partial correlation analysis. The proposed vine copula–SVNN hybrid forecasting approach consists of four main parts: 1. The AR-GJR-GARCH is utilized to filter the log yield. 2. The vine copula is used to study the dependencies between the RMB and the major foreign exchange assets, including the RMB against the US dollar, the RMB against the euro, the RMB against the 100 Japanese yen, the RMB against the Hong Kong dollar and the RMB against the British pound sterling, under the exchange rate reforms. 3. Three variables are selected to represent the international economic situation, since they have higher degrees of dependence with RMB/USD. 4. The SVNN is used to forecast the central parity of RMB/USD based on the international economic situation.

Forecasting approach 105

Vine copula based on the dependencies of the RMB and the major foreign exchange assets Data analysis The reforms of the exchange rate mechanism have significant impacts on exchange rate fluctuations. Since 2005, the RMB exchange rates have experienced five major exchange rate reforms: 1. On July 21, 2005, in order to enhance the managed floating exchange rate and increase the importance of market supply and demand, China improved the managed floating exchange rate regime by moving into a managed floating exchange rate regime based on market supply and demand with reference to a basket of currencies. 2. On May 21, 2007, the exchange rate was allowed to move within a wider band, from a daily band of 0.3% against the US dollar to 0.5%. 3. On July 2008, in order to preserve the exchange rate stability in China and help China’s economy ride through the impact of the US subprime mortgage crisis, China’s central bank pegged the RMB against the US dollar at 6.83 and narrowed the floating range of the RMB exchange rate. 4. On June 19, 2010, China’s central bank announced resuming and furthering the reform of the RMB exchange rate regime based on measures taken in 2005 to increase the flexibility of the RMB exchange rate, and continued emphasis would be placed to reflect market supply and demand with reference to a basket of currencies. 5. On August 11, 2015, China further improved the quotation mechanism of the RMB’s central parity rate against the US dollar by taking into consideration the previous day’s closing rate on the interbank forex market to reflect the changes of market supply and demand. (Also known as the “811 exchange rate reform”.) The sample database includes five variables: the RMB exchange rate against the US dollar, the RMB exchange rate against the euro, the RMB exchange rate against the 100 yen, the RMB exchange rate against the British pound sterling and the RMB exchange rate against the Hong Kong dollar. The sample period covers from July 21, 2005, to June 30, 2016, with a total of 2663 observations of each variable, downloaded from the Wind Database (www .wind.com.cn/). Combined with the process of the reforms of the RMB exchange rate mechanism in China, the formation mechanism of the RMB exchange rate against the US dollar can be divided into five periods: (1) from July 22, 2005, to May 18, 2007, with a total of 422 observations; (2) from May 21, 2007, to July 11, 2008, with a total of 284 observations; (3) from July 14, 2008, to June 21, 2010, with a total of 472 observations; (4) from June 22, 2010, to August 10, 2015, with a total of 1249 observations; and (5) from August 11, 2015, to June 30, 2016, with a total of 216 observations.

106

Forecasting approach

The logarithmic yield is obtained for the selected variables in this section, where rt = ln(Pt/Pt−1) × 100. Wu et al. (2016) estimated the analysis of the structural characteristics of the RMB exchange rate market and found that when the original data were adjusted by the logarithmic yield, the results were consistent with the real values. Figure 6.3 describes the time series of five RMB exchange rates and the returns, including the RMB against the US dollar, the RMB against the euro, the RMB against the 100 Japanese yen, the RMB against the British pound sterling and the RMB against the Hong Kong dollar. The statistics of time series of the five major RMB exchange rates and the statistics of the returns of five RMB exchange rates are displayed in Table 6.1 and Table 6.2. Table 6.2 shows that in the total sample periods, all of the means of the RMB against the US dollar, the RMB against the euro, the RMB against the 100 Japanese yen, the RMB against the Hong Kong dollar and the RMB against the British pound sterling are less than 0, in other words, in the total sample periods, the trend of the RMB exchange rate is appreciate. However, in each period, the situation of the RMB exchange rate is different. Take the exchange rate of the RMB against the US dollar as an example. In the first and the second period, with the development of China’s economy, the RMB against the US dollar appreciated. In the third period, due to the policy of pegging the RMB against the US dollar at 6.83, the RMB against the US dollar was stable. In the fourth period, the RMB against the US dollar appreciated. After the 811 exchange rate reform, the trend of the RMB against the US dollar depreciated. From the perspective of standard deviation, take the RMB exchange rate against the US dollar as an example. Compared with the first period to the fourth period, the standard deviation of the RMB exchange rate against the US dollar in the fifth period had significantly increased, which means that the volatility of the RMB exchange rate against the US dollar was increasing. Take the RMB exchange rate against the 100 Japanese yen as another example. The standard deviation of the third period is the largest; in other words, the volatility of the RMB exchange rate against the 100 Japanese yen is largest during July 14, 2008, to June 21, 2010. The reason is that with the effect of the Asia financial crisis, the Japanese yen depreciated, and in order to preserve financial stability in Asia and prevent further contagion of the crisis, China kept the RMB stable around 8.28 yuan to 1 dollar and narrowed the floating range of the RMB exchange rate. Compared with the first period, the second period and the fourth period, the volatility of the RMB exchange rate against the 100 Japanese yen increased in the fifth period. From the results of Jarque – Bera test and the P-value, it can be concluded that except for the RMB against the US dollar in the second period, the RMB against the euro in the first period and the RMB against the Hong Kong dollar in the second period, the significance levels of the RMB exchange rate at other time series are under the 1% significance level, which can reject the original hypothesis that “the sample obey the normal distribution”. This result is consistent with that of Wu et al. (2016).

Figure 6.3 Time series of five RMB exchange rates and the returns

Forecasting approach 107

108

Forecasting approach

Table 6.1 Statistics of five RMB exchange rates Exchange rate Period

Mean

Standard Skewness Kurtosis P-value Observations deviation

RMB/USD

6.793 7.957 7.307 6.831 6.306 6.466 8.916 9.997 10.647 9.443 8.241 7.181 6.806 6.839 6.567 7.208 6.906 5.594 0.874 1.023 0.937 0.880 0.812 0.833 11.402 14.701 14.629 10.896 10.014 9.535

0.634 0.129 0.264 0.007 0.192 0.084 1.149 0.273 0.260 0.589 0.679 0.177 0.916 0.256 0.232 0.401 1.154 0.354 0.081 0.019 0.034 0.002 0.024 0.010 2.116 0.477 0.696 0.931 0.413 0.248

Total First Second Third Fourth Fifth RMB/EUR Total First Second Third Fourth Fifth RMB/100JPY Total First Second Third Fourth Fifth RMB/HKD Total First Second Third Fourth Fifth RMB/GBP Total First Second Third Fourth Fifth

0.855 –0.667 –0.289 1.790 1.047 –0.150 –0.096 –0.261 –0.089 0.072 –0.614 -0.581 –0.191 0.257 0.279 –0.931 –0.260 0.476 0.877 –0.712 –0.341 –1.170 1.097 –0.140 0.861 –0.214 –0.263 1.075 –0.163 –0.237

2.438 2.051 1.586 9.071 3.120 1.927 2.075 2.045 1.973 2.425 3.321 2.726 2.134 2.496 2.822 3.099 1.497 2.211 2.500 2.147 1.589 3.766 3.281 2.148 2.051 1.691 1.447 4.096 2.162 2.672

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.03 0.00 0.00 0.00 0.01 0.13 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.03 0.00 0.00 0.00 0.00 0.00 0.23

2663 442 284 472 1249 216 2663 442 284 472 1249 216 2663 442 284 472 1249 216 2663 442 284 472 1249 216 2663 442 284 472 1249 216

Most of the research studies showed that the assumption that the financial time sequences obey the normal distribution is inconsistent. The T-distribution can fit the asymmetric characteristics of the time series in financial markets better. Therefore, AR-GJR-GRACH is utilized to capture the volatile clustering and asymmetric structure of the returns of the RMB exchange rates. Then the vine copula is introduced to study the nonlinear dependencies of the RMB exchange rates during the five periods.

Empirical study The exchange rates are one of the important links of the economic and trade between China and foreign countries, which can reflect the economic and

Forecasting approach 109 Table 6.2 Statistics of the return of five exchange rates Period Mean RMB/USD_r

Total First Second Third Fourth Fifth RMB/EUR_r Total First Second Third Fourth Fifth RMB/100JPY_r Total First Second Third Fourth Fifth RMB/HKD_r Total First Second Third Fourth Fifth RMB/GBP_r Total First Second Third Fourth Fifth

–0.008 –0.017 –0.041 0.000 –0.009 0.037 –0.011 0.008 0.015 –0.051 –0.019 0.043 –0.005 –0.033 0.003 0.035 –0.034 0.123 –0.008 –0.018 –0.040 0.000 –0.009 0.037 –0.018 0.012 –0.040 –0.061 –0.005 –0.029

Standard Skewness Kurtosis P-value Observations deviation 0.115 0.113 0.122 0.044 0.081 0.265 0.632 0.479 0.441 0.920 0.585 0.608 0.655 0.519 0.698 0.893 0.567 0.688 0.116 0.099 0.128 0.049 0.091 0.263 0.611 0.491 0.458 0.959 0.461 0.776

0.966 –12.737 –0.157 –2.053 –0.336 2.704 –0.300 0.021 –0.234 –0.658 0.127 0.948 –0.072 0.534 0.529 –0.137 –1.021 1.404 1.874 –8.047 –0.275 0.478 –0.436 2.652 –0.819 0.698 –0.375 –0.352 0.075 –3.423

85.212 228.837 3.033 27.465 5.315 18.419 10.328 3.436 3.475 9.799 4.831 7.295 8.238 5.277 6.398 5.111 11.160 7.925 60.093 123.297 2.889 13.217 37.663 18.100 14.702 6.440 3.233 5.310 4.096 36.953

0.00 0.00 0.55 0.00 0.00 0.00 0.00 0.17 0.07 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.16 0.00 0.00 0.00 0.00 0.00 0.03 0.00 0.00 0.00

2663 442 284 472 1249 216 2663 442 284 472 1249 216 2663 442 284 472 1249 216 2663 442 284 472 1249 216 2663 442 284 472 1249 216

financial situation of one country to some extent. It is of great practical significance to study the dependencies among the major RMB exchange rates. The vine copula is utilized to further filter out the major RMB exchange rates that have the highest dependencies with the RMB against the US dollar. In this section, the major RMB exchange rates are used to represent the international economic situation, and the vine copula is employed to study the dependencies among the major RMB exchange rates. From the existing literature, the C-vine copula can be used to estimate the dependencies of RMB exchanges (Wu et al., 2016). In this section, we further analyze the impact of the five exchange rate mechanism reforms on the dependencies among the five RMB exchange rates. The results of Student t-copula of the C-vine of the first period to the fifth period are displayed in Table 6.3. The numbers 1, 2, 3, 4 and 5 are used to

110

Forecasting approach

represent the RMB against the US dollar, the RMB against the euro, the RMB against the 100 Japanese yen, the RMB against the Hong Kong dollar and the RMB against the British pound sterling, respectively. Under the C-vine copula structure, the lower the degree of the freedom (d.o.f.), the higher of the contagion effect between two markets. From Table 6.3, it can be concluded that (1) in all of the five periods, the dependency of the RMB against the US dollar and the RMB against the Hong Kong dollar is the highest; (2) in the first period and the fourth period, the dependence of the RMB against the US dollar and the RMB against the euro is higher than that of the RMB against the 100 Japanese yen and the RMB against the British pound sterling, while in the second period, the third period and the fifth period, the dependence of the RMB against the US dollar and the RMB against the 100 Japanese yen is higher than that of the RMB against the euro and the RMB against the British pound sterling; (3) in all of the five periods, the dependence of the RMB against the US dollar and the RMB against the British pound sterling is the lowest; and (4) the 811 exchange rate reform is further improved the quotation mechanism of the RMB’s central parity rate against the US dollar and have some impact on the dependencies of the RMB exchange rates. Firstly, after the 811 exchange rate reform, the dependence of the RMB against the US dollar and the RMB against the Hong Kong dollar is increasing. Secondly, after the “811 exchange rate reform” the dependence of the RMB against the US dollar and the RMB against the 100 Japanese yen increased, while the dependence of the RMB against the US dollar and the RMB against the euro decreased. Under the condition of the RMB against the US dollar, in those five periods, the dependence of the RMB against the euro and the RMB against the 100 Japanese yen is the highest. The results of Clayton copula model under the C-vine structure are shown in Table 6.4, which implies in those five periods, the dependence of the RMB against the US dollar and the RMB against the Hong Kong dollar is the highest. Furthermore, the contagion effect of the structure risk of the RMB exchange rates is analyzed through the tail dependence, and the results are displayed in Table 6.3 Results of Student t-copula of C-vine copula d.o.f.

First period

Second period Third period

Fourth period Fifth period

d1,2 d1,3 d1,4 d1,5 d2,3|1 d2,4|1 d2,5|1 d3,4|1,2 d3,5|1,2 d4,5|1,2,3

6.5340 9.6307 2.0713 10.3132 3.5318 16.8761 5.4859 3243.0680 59.2141 13.8824

9.9482 7.0991 5.7034 10.1924 5.3310 45.3570 64.7189 23.1606 12.9391 19.6194

5.3334 9.1204 3.6041 10.3527 5.8796 10.5299 9.1982 18.5212 9.8289 38.0306

8.6963 5.8792 2.0100 46.4972 6.8534 19.5843 15.8324 3266.8950 8.5246 3775.8110

4.4499 3.6985 2.0110 7.1492 4.5002 1481.1760 8.0311 10.0566 11.7765 764.9097

Forecasting approach 111 Table 6.4 Results of Clayton copula of C-vine copula Pair

First period

Second period

Third period

Fourth period

Fifth period

d1,2 d1,3 d1,4 d1,5 d2,3|1 d2,4|1 d2,5|1 d3,4|1,2 d3,5|1,2 d4,5|1,2,3

0.00010 0.00010 0.57542 0.00507 0.29015 0.02209 0.26544 0.02672 0.00010 0.01472

0.00010 0.00010 0.70410 0.00010 0.09684 0.00013 0.27418 0.00011 0.00010 0.03221

0.00010 0.00010 0.39983 0.00010 0.00011 0.04469 0.33416 0.00010 0.00010 0.00010

0.00010 0.00010 0.67063 0.00011 0.05236 0.00019 0.28117 0.00010 0.02756 0.01300

0.00010 0.01470 0.79667 0.00010 0.18021 0.00010 0.18605 0.00010 0.00010 0.03717

Table 6.5 Results of SJC copula of C-vine copula Pair First period Second period Third period Fourth period Fifth period

τU τL τU τL τU τL τU τL τU τL

12

13

14

15

0.0001 0.0001 0.000138 0.000177 0.0001 0.0001 0.000152 0.000175 0.000108 0.000106

0.0001 0.0001 0.000265 0.000751 0.0001 0.0001 0.000588 0.000695 0.090373 0.000357

0.746543 0.717544 0.843049 0.841733 0.600424 0.482185 0.773592 0.798505 0.847582 0.849788

0.000108 0.007857 0.000658 0.000535 0.0001 0.0001 0.00036 0.000389 0.014624 0.000162

Notes: τU represents the upper tail, and τL represents the lower tail.

Table 6.5. From the comparison of the coefficients of upper and lower tails, it can be concluded that (1) in the first period and the fourth period, the lower tail dependence of RMB/USD and RMB/EUR is higher than the upper tail dependence, which implies the negative effect is higher than the positive effect; (2) in the fifth periods, the upper tail dependence of RMB/USD and RMB/EUR is higher than the lower tail dependence. The dependencies of the RMB against the US dollar and the other four RMB exchange rates are analyzed by the C-vine copula. The results indicate that the dependencies of the RMB against the US dollar is higher relative to the RMB against the Hong Kong dollar, the RMB against the euro and the RMB against the 100 Japanese yen. In the next section, the aforementioned three variables will be used to represent the international economic situation and SVNN model will be developed for forecasting the RMB exchange rate against the US dollar.

112

Forecasting approach

Vine copula–SVNN hybrid forecasting approach Data In this section, an SVNN model based on the selected variables will be proposed to forecast the daily and monthly RMB/USD. The sample data sets include four variables, named RMB/USD_D, RMB/EUR_D, RMB/HKD_D and RMB/100JPY_D. For the daily forecast, the period of the sample data sets is from August 11, 2015, to June 30, 2016, with a total of 216 observations of each variable. For the monthly forecast, the period of the sample data sets is from July 2010 to June 2016, with a total of 72 observations of each variable. All of the sample data sets are obtained from the Wind Database, and the statistics are displayed in Table 6.6. For modeling and validation purposes, the sample data are divided into two subsets – an in-sample subset and an out-of-sample subset – which are shown in Table 6.7. The in-sample subset is used for model training, and the out-of-sample subset is used for model testing.

Empirical study The SVNN is utilized to forecast the central parity of the RMB against the US dollar based on the international economic situation, which is represented by the selected variables, including RMB/EUR, RMB/HKD, RMB/100JPY and RMB/USD. Table 6.6 Statistics of four RMB exchange rates Variable Daily

Mean Standard Skewness Kurtosis P-value Observations deviation

RMB/USD_D RMB/EUR_D RMB/HKD_D RMB/100JPY_D Monthly RMB/USD_M RMB/EUR_M RMB/HKD_M RMB/100JPY_M

6.47 7.18 0.83 5.59 6.33 8.09 0.82 6.71

0.08 0.18 0.01 0.35 0.19 0.73 0.02 1.17

–0.15 –0.58 –0.14 0.48 0.72 –0.25 0.74 0.05

1.93 2.73 2.15 2.21 2.57 2.28 2.67 1.39

0.00 0.00 0.03 0.00 0.04 0.32 0.03 0.02

216 216 216 216 72 72 72 72

Table 6.7 Sample period of training subset and testing subset In-sample subset Central parity of RMB/ 2015.08.11–2016.05.13 USD (daily) Central parity of RMB/ 2010.07–2015.09 USD (monthly)

Out-of-sample subset 2016.05.16–2016.06.30 2015.10–2016.06

Forecasting approach 113

Evaluation criteria To assess the forecasting accuracy of the proposed vine copula–SVNN hybrid forecasting approach from different perspectives, such as level forecasting and directional forecasting, two evaluation criteria are employed. For assessing the performance of level forecasting, the mean absolute percentage error (MAPE) is employed. The directional change (DS) is utilized to assess the directional forecasting accuracy. For further details, please refer to Chapter 4.

Comparison of forecasting performance The forecasting performance of the vine copula–SVNN hybrid forecasting approach and the benchmark models are discussed in this section. To compare the forecasting performance of the vine copula–SVNN hybrid forecasting approach and the benchmark models (ARMA, ARIMA and RW), MAPE is employed to assess the performance of level forecasting and DS is utilized to assess the directional forecasting accuracy. The results of the level forecasting accuracy and the directional forecasting accuracy of the vine copula– SVNN hybrid forecasting approach and the benchmark models are displayed in Table 6.8. Table 6.8 shows that the vine copula–SVNN hybrid forecasting approach performs better in forecasting the daily and monthly central parity of the RMB against the US dollar with the three-step-ahead. 1. For the daily forecasting, vine copula–SVNN hybrid forecasting approach outperforms the benchmark models in the level forecasting, which obtains the smallest MAPE of 0.488. Meanwhile, in comparing with the other benchmark models, the directional forecasting accuracy of vine copula– SVNN hybrid forecasting approach is 65.63%, which outperforms the benchmarks. 2. For the monthly forecasting, the vine copula–SVNN hybrid forecasting approach outperforms the benchmark models in the level forecasting, which obtains the smallest MAPE of 0.694. For directional forecasting, the DS of vine copula–SVNN hybrid forecasting approach is 66.67%, which implies the proposed approach performs better than the benchmark models. Table 6.8 Performance comparison of different models for daily and monthly exchange rates: three-step-ahead forecasting results

Daily Monthly

Evaluation criteria

SVNN

ARMA

ARIMA

RW

MAPE (%) DS (%) MAPE (%) DS (%)

0.488 65.63 0.694 66.67

1.010 53.13 1.630 55.56

0.561 56.25 1.032 55.56

0.975 50.00 2.347 44.44

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3. The vine copula is used to analyze the dependencies of the RMB exchange rates. Based on the degree of dependencies, the three variables that have the highest dependencies of RMB/USD are selected. The vine copula–SVNN hybrid forecasting approach is developed for forecasting the central parity of RMB/USD. The daily and monthly forecasting results show that the proposed model outperforms the benchmark models in both level forecasting and directional forecasting.

Conclusions In this chapter, a forecasting approach based on the international economic situation is proposed by integrating the vine copula and SVNN for the first time. Major foreign currencies were selected, including the currencies of SDR currency basket. First, the AR-GJR-GARCH was utilized to filter the log yield. Secondly, the vine copula was used to study the dependencies between the RMB and the major foreign exchange assets, including the RMB against the US dollar, the RMB against the euro, the RMB against the 100 Japanese yen, the RMB against the Hong Kong dollar and the RMB against the British pound sterling, under five exchange rate reforms. Thirdly, three variables were selected to represent the international economic situation, for they had higher dependencies with RMB/ USD. Fourthly, a vine copula–SVNN hybrid forecasting approach based on the international economic situation was proposed to forecast the central parity of the RMB against the USD. The main conclusions of this chapter are as follows: First, the results of vine copula imply that (1) in the five periods, the dependence of the RMB against the US dollar and the RMB against the Hong Kong dollar is highest; and (2) the 811 exchange rate reform further improved the quotation mechanism of the RMB’s central parity rate against the US dollar, and had some impact on the dependencies of the RMB exchange rates. For example, after the 811 exchange rate reform the dependence of the RMB against the US dollar and the RMB against the Hong Kong dollar increased. After the 811 exchange rate reform, the dependence of the RMB against the US dollar and the RMB against the 100 Japanese yen increased, while the dependence of the RMB against the US dollar and the RMB against the euro decreased. Also, the RMB against the euro, the RMB against the 100 Japanese yen and the RMB against the Hong Kong dollar have higher degrees of dependence with the RMB against the US dollar. Secondly, the vine copula–SVNN hybrid forecasting approach was proposed to forecast the central parity of the RMB against the US dollar. The empirical study showed that the proposed model outperformed the benchmark models in both the level forecasting and the directional forecasting.

7

A forecasting approach based on the public’s expectations

Introduction Since web search data can reflect the public’s attention and expectations, and reflect the behavior of public trends, it is considered as an indicator that can be used to predict some time series data. More researchers began to use web search data to forecast, for example, stock prices, epidemic disease and inflation (Das and Chen, 2001; Gloor et al., 2009; Bordino et al., 2012; Nardo et al., 2016; Li et al., 2015). Li et al. (2015) used the weekly Google Trends index for inflation forecasting and the study found that the search data were strongly correlated with the consumer price index (CPI), and the mixed-data sampling (MIDAS) model including the search data outperformed the benchmark models, with the average reduction of the root mean square error (RMSE) by 32.9%. However, web search data are barely used for exchange rate forecasting. When adding the Baidu Index or Google Trends data into forecasting models, the selection of keywords and the composite of indices needs to be carefully dealt with. The keywords can be selected according to the correlation coefficient, the tendency chart or the crowd-squared method (Brynjolfsson, Geva, and Reichman, 2016). Additionally, the composite of indices can be conducted by the Hurst exponent and time difference correlation (HE-TDC) method (Peng, Liu, Wang, and Gu, 2017) or principal component analysis (PCA). Obviously, multicollinearity and overfitting problems need to be paid attention to and avoided to the greatest extent possible. In this chapter, a forecasting approach based on the public’s expectations is proposed. With wide use of the Internet, web search data can reflect the public’s attention and expectations. Firstly, data extraction. By using different keywords, the Google search volume index (GSVI) and Baidu search volume index (BSVI) are extracted from Google Trends and the Baidu Index, respectively. Those two indices are used to represent the public’s expectations. Secondly, data selection. The Granger causality test and gray relational analysis are utilized to analyze the dynamic relationship between the renminbi (RMB) exchange rate and web search data, including GSVI and BSVI. Thirdly, data computing. A kernel extreme learning machine (KELM) forecasting approach based on web search data to present the public’s expectations is proposed, by integrating the

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GSVI, BSVI and KELM to forecast the daily and monthly central parity of the RMB against the US dollar. And multiple evaluation criteria are employed to comprehensively evaluate the forecasting performance of the proposed approach and benchmarks.

Web search data The GSVI is in the form of a time series, and daily, weekly and monthly frequency have been available for free download from the Google Trends website since January 2004. The BSVI is downloaded from the Baidu Index website. The data are generated based on the volume of search queries of keywords that the public submits through the Internet. The keywords could reflect Internet users’ interests and attention on economic issues. In this chapter, the GSVI and BSVI are chosen to forecast the exchange rate. The reasons are as follows: (1) The statistics show that among a large quantity of search engines, Google ranked first with a market share of 65.44%, following by Bing (15.82%) and Baidu (8.30%). Because Google shut down its Chinese search engine, the Baidu Index is also utilized to represent the public’s expectation. (2) Both the GSVI and BSVI can be downloaded from the internet for free, and the data cover a wide scope and provide a huge amount of information.

Figure 7.1 A forecasting approach based on the public’s expectations

A forecasting approach based on the public’s expectations

117

Keywords The selection of keywords is very important for it affects the quality of the web search data. In this chapter, the selected keywords of Google search volume index and Baidu search volume index are shown in Table 7.1. In the Baidu Index, the keyword “cnh” is available from July 8, 2015, and the other keywords are available from January 1, 2011. Therefore, in the monthly forecasting, the keywords of the Baidu Index are “the RMB against the US dollar” and “the US dollar against the RMB”.

Statistics In this chapter, the sample data sets include three variables: the GSVI, the BSVI and the RMB against the US dollar (RMB/USD). The GSVI and BSVI are the web search data that are used to represent the public’s expectations. And a logarithmic transformation has been applied to BSVI, named BSVI_LN. The GSVI is available from 2004, while the BSVI, which was integrated by the selected keywords of the Baidu Index, is available from January 2011. Therefore, for daily forecasting, the period of the sample data sets, including RMB/USD_D, GSVI_D and BSVI_LN_D, is from August 11, 2015, to June 30, 2016 with a total of 216 observations of each variable. For monthly forecasting, the period of the sample data sets, including RMB/USD_M, GSVI_M and BSVI_LN_M, is from January 2011 to June 2016 with a total of 66 observations of each variable. The statistics are displayed in Table 7.2.

Table 7.1 Keywords for web search data Search engine Keywords Google Baidu

China exchange rate, cny, rmb, cnh cnh, the RMB against the US dollar, the US dollar against the RMB*

* In Baidu index we searched the keywords in simplified Chinese that are CNH, the RMB against the US dollar, the US dollar against the RMB.

Table 7.2 Statistics of RMB/USD and the web search data Variable Daily

RMB/USD_D GSVI_D BSVI_LN_D Monthly RMB/USD_M GSVI_M BSVI_LN_M

Mean

Standard Skewness Kurtosis P-value deviation

6.466 0.084 63.065 13.731 7.609 0.358 6.292 0.150 50.318 8.780 7.116 0.445

–0.150 0.625 1.450 0.507 1.185 –0.166

1.927 3.653 6.061 2.088 4.413 3.123

0.004 0.000 0.000 0.077 0.000 0.842

Observations 216 216 216 66 66 66

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A forecasting approach based on the public’s expectations

Correlation analysis In this section, the Granger causality analysis and the gray relational analysis are employed to analyze the dynamic relationship of the web search data and the RMB exchange rate.

Granger causality analysis Granger (1969) proposed the Granger causality test, based on the assumption of linear relationships between variables. The test is sensitive to the lag order, and the Akaike information criterion (AIC) and Schwarz information criterion (SIC) are used in this section to determine the optimal lag order. The results of the Granger causality test of the daily central parity of RMB/ USD and the daily web search data are shown in Table 7.3. Table 7.3 implies that under the 10% significance level, GSVI_D Granger-cause RMB/USD_D, and under the 1% significance level, BSVI_LN_D Granger-cause RMB/USD_D, and vice versa. The results of the Granger causality test of the monthly central parity of RMB/ USD and the monthly web search data are displayed in Table 7.4. Table 7.4 implies that under the 1% significance level, GSVI_M and BSVI_LN_M Grangercause RMB/USD_D.

Gray relational analysis The results of the gray relational analysis of the daily and monthly central parity of the RMB against the US dollar and the web search data are displayed in Table 7.5. Table 7.3 Results of the Granger causality test of daily data

GSVI_D does not Granger-cause RMB/USD_D RMB/USD_D does not Granger-cause GSVI_D BSVI_LN_D does not Granger-cause RMB/USD_D RMB/USD_D does not Granger-cause BSVI_LN_D

F-statistic

Prob.

2.072 0.992 5.6457 4.8019

0.058* 0.432 0.0010*** 0.0030***

Notes: *** Under 1% significance level. * Under 10% significance level.

Table 7.4 Results of the Granger causality test of monthly data

GSVI_M does not Granger-cause RMB/USD_M RMB/USD_M does not Granger-cause GSVI_M BSVI_LN_M does not Granger-cause RMB/USD_M RMB/USD_M does not Granger-cause BSVI_LN_M Notes: *** Under 1% significance level.

F-statistic

Prob.

10.3084 0.8174 11.7738 0.9285

0.0021*** 0.3694 0.0011*** 0.3390

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119

Table 7.5 Results of the gray relational analysis of RMB/ USD and web search data Variable GSVI BSVI_LN

Daily

Monthly

Correlation degree

Correlation degree

0.6075 0.6945

0.7380 0.6617

Table 7.5 implies that for daily data, RMB/USD_D and GSVI_D, and RMB/ USD_D and BSVI_LN_D are highly correlated, with the correlation degrees of 0.6075 and 0.6945, respectively. And the correlation degree of RMB/USD_D and BSVI_LN_D is higher than that of RMB/USD_D and GSVI_D. Therefore, the daily BSVI_LN_D and GSVI_D can be used to forecast the central parity of the RMB against the US dollar. For monthly data, RMB/USD_M and GSVI_M, and RMB/USD_M and BSVI_LN_M are also highly correlated, with the correlation degrees of 0.7380 and 0.6617, respectively. And the correlation degree of RMB/USD_M and GSVI_M is higher than that of RMB/USD_D and BSVI_ LN_M. Therefore, the monthly BSVI_LN_M and GSVI_M can be used to forecast the central parity of the RMB against the US dollar.

Forecasting approach based on kernel extreme learning machine (KELM) In this section, a KELM forecasting approach based on web search data to present the public’s expectations is proposed, by integrating GSVI, BSVI and KELM to forecast the daily and monthly central parity of the RMB against the US dollar.

Data Daily and monthly central parity of RMB/USD are obtained from the Wind Database (www.wind.com.cn/). The daily data covers the period of August 11, 2015, to June 30, 2016, with a total of 216 observations, excluding weekends and holidays. The monthly data covers the period of July 2010 to June 2016, with 72 observations. For modeling and validation purposes, the sample data are divided into two subsets – an in-sample subset and out-of-sample subset – which are shown in Table 7.6. The in-sample subset is used for model training, and the out-of-sample subset is used for model testing.

The model Huang et al. (2012) extended the extreme learning machine (ELM) and proposed the KELM. ELM is a single-layer feedforward neural network (SLFN)

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Table 7.6 Sample period of training subset and testing subset

Central parity of RMB/ USD (daily) Central parity of RMB/ USD (monthly)

In-sample subset

Out-of-sample subset

2015.08.11–2016.05.13

2016.05.16–2016.06.30

2010.07–2015.09

2015.10–2016.06

architecture. The main drawbacks of ELM are that it has random initialization and its prediction precision is very sensitive to the noise and number of hidden layer nodes, which will lead to a poor robustness. Therefore, KELM is proposed to overcome the disadvantages of basic ELM with faster convergence speed, multi-output, better stability and generalization ability. KELM is widely used in global solar radiation prediction, illumination correction and wind forecasting (Zhou et al., 2016). KELM has not been used in exchange rate forecasting. For a given N sample (xi,yi) with L hidden neurons, xi∈RN as the input vector, yi∈RN as the corresponding output vector and h(x) as the activation function, the output function of ELM can be defined as

f (x ) =

L

å b h (x ) = h (x ) b i i

i =1

where H = {hij} is the hidden layer output matrix of the neural network, and β = [β1, β2, …, βL] is the output weight connecting hidden nodes to output nodes. The output weights can be calculated by the least squares method:

b = H +T where H+ is the Moore-Penrose generalized inverse of matrix H (Huang et al. 2006). According to the Karush-Kuhn-Tucker (KKT) theorem, it can be written as -1

æI ö b = H ç + HH T ÷ T èC ø The output function can be formulated as follows: -1

æI ö f ( x ) = h ( x ) H ç + HH T ÷ T C è ø Huang et al. (2006) introduced the kernel function in ELM, and by applying Mercer’s conditions on ELM, a kernel matrix for ELM can be formulated as follows:

WELM = HH T : WELM i , j = h ( xi ) × h ( x j ) = K ( xi , x j )

A forecasting approach based on the public’s expectations

121

where i,j = 1, 2, ⋯, N; K(xi,xj) is a kernel function. The output function of KELM can be formulated as follows: T

é K ( x , x1 ) ù -1 ê ú æI ö æI T ö f ( x ) = h ( x ) H ç + HH ÷ T = ê T ˜ + W ELM M ç ÷ ú C èC ø ø êK ( x , xN ) ú è ë û -1

From the preceding equations, it can be derived that by introducing the kernel function into the ELM to get the least squares optimal solution leads to a better generalization performance and more stable than basic ELM.

Empirical study In this section, a KELM forecasting approach based on the public’s expectations is developed to forecast the daily and monthly central parity of the RMB against the US dollar.

Evaluation criteria To assess the forecasting accuracy of the proposed KELM forecasting approach based on the public’s expectations from different perspectives, such as level forecasting and directional forecasting, two evaluation criteria are employed. For assessing the performance of level forecasting, the mean absolute percentage error (MAPE) is employed. The directional change (DS) is utilized to assess the directional forecasting accuracy. For further detail, please refer to Chapter 4.

Comparison of forecasting performance The forecasting performance of the KELM forecasting approach based on the public’s expectations and the benchmark models are discussed in this section. To compare the forecasting performance of the KELM forecasting approach based on the public’s expectations and the benchmark models (ARMA, ARIMA and RW), MAPE is employed to assess the performance of level forecasting and DS is utilized to assess the directional forecasting accuracy. Table 7.7 shows that the KELM forecasting approach based on the public’s expectations performs better in forecasting the daily and monthly central parity of RMB/USD with three-step-ahead. 1. For the daily forecasting, the KELM forecasting approach based on the public’s expectations outperforms the benchmark models in the level forecasting, which obtained the smallest MAPE of 0.512. For directional forecasting, the DS of the KELM forecasting approach based on the public’s expectations is 62.50%, which is smaller than the benchmark models. 2. For the monthly forecasting, the KELM forecasting approach based on the public’s expectations outperforms the benchmark models in the level

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Table 7.7 Performance comparison of different models for daily and monthly exchange rates: three-step-ahead forecasting results

Daily Monthly

Evaluation criteria

KELM

ARMA

ARIMA

RW

MAPE (%) DS (%) MAPE (%) DS (%)

0.512 62.50 0.623 77.78

1.010 53.13 1.630 55.56

0.561 56.25 1.032 55.56

0.975 50.00 2.347 44.44

forecasting, obtaining the smallest MAPE of 0.623. For directional forecasting, the DS of the KELM forecasting approach based on the public’s expectations is 77.78%, which implies that the proposed model performs better than the benchmark models. 3. The Granger causality test and the gray relational analysis are utilized to analyze the dynamic relationship between the web search data and the RMB exchange rate. And a KELM forecasting approach based on the public’s expectations is proposed. The daily and monthly forecasting results show that the proposed approach outperforms the benchmark models in both level forecasting and directional forecasting.

Conclusions In this chapter, a forecasting approach based on the public’s expectations is proposed, which mainly consists of four parts. First, data extraction. By using different keywords, the Google search volume index (GSVI) and Baidu search volume index (BSVI) are extracted from Google Trends and the Baidu Index, respectively. Those two indices are used to represent the public’s expectation. Secondly, data selection. The Granger causality test and the gray relational analysis are utilized to analyze the dynamic relationship between the RMB exchange rate and the web search data, including GSVI and BSVI. Thirdly, data computing. A kernel extreme learning machine (KELM) forecasting approach based on the web search data to present the public’s expectations is proposed, by integrating GSVI, BSVI and KELM to forecast the daily and monthly central parity of the RMB against the US dollar. And multiple evaluation criteria are employed to comprehensively evaluate the forecasting performance of the proposed approach and benchmarks. The main conclusions of this chapter are as follows: Firstly, the results of the Granger causality test and the gray relational analysis show that the daily and monthly web search data and the central parity of the RMB/USD are highly correlated. And web search data can be used to forecast the exchange rate. Secondly, a KELM forecasting approach based on the public’s expectations is proposed to forecast the central parity of RMB/USD. The empirical study shows that the proposed model outperforms the benchmark models in both level forecasting and directional forecasting.

8

A comprehensive integrated forecasting approach based on long short-term memory (LSTM)

Introduction The forecasting accuracy of nonlinear artificial intelligence methods is usually better than the common econometric and statistical models, but they also suffer from many problems, such as parameter optimization and overfitting. Hence, many hybrid forecasting approaches and ensemble forecasting approaches have been proposed to get better forecasting performance. Wang et al. (2004) proposed the TEI@I methodology, which is based on the idea of “decomposition and ensemble” and can significantly improve forecasting accuracy. The effectiveness of the idea of decomposition and ensemble has been confirmed (Wang et al., 2011; Lin et al., 2012; Tang et al., 2012; Xie et al., 2014). Exchange rate data are very complex, and their volatility is not only affected by the domestic economic situation, but is also influenced by the international economic situation and the public’s expectations. Forecasting models based on a unilateral aspect or a single forecasting model are not conducive to improve forecasting accuracy. So far, the decomposition ensemble learning approach has been widely used to forecast time series in many fields, including financial time series forecasting (Wang et al., 2011), crude oil price forecasting (Yu et al., 2015) and nuclear energy consumption forecasting (Tang et al., 2012). According to the existing literature, artificial neural networks (ANNs) are the most commonly used methods both in single model forecasting and hybrid model forecasting, which demonstrates that ANNs are really suitable for time series forecasting. If the advantages of different ANNs methods are combined, a better forecasting performance can be obtained. A long short-term memory (LSTM) neural network is a kind of deep neural network, and it possesses similar properties of a recurrent neural network (RNN). Therefore, LSTM is a better choice for financial time series forecasting. In addition, the aforementioned ensemble learning approach usually chooses AdaBoost to integrate different LSTM forecasters. In this chapter, a comprehensive integrated approach based on LSTM is proposed to forecast the exchange rate. LSTM is used to integrate the forecasting results of four aspects – exchange rate data decomposition and integration, the domestic economic situation, the international economic situation and the public’s expectations – to get the final forecasting results.

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The model An LSTM network is a special kind of RNN. It is capable of learning long-term dependencies, which makes it suitable for time series forecasting. LSTM is the same as traditional neural networks, including input layer, hidden layer and output layer. Although its hidden layer is really different and more complicated, which contains four main parts: forget gate layer, input gate layer, cell state layer and output gate layer. The main steps of the hidden layer can be explained as follows: 1. Forget gate. The forget rate can be computed as follows:

f t = s (w f [ht -1, x t ] + b f ) where ft is the forget rate, σ(∙) is the sigmoid activation function, ht−1 is the output of the last hidden layer, xt is the input of this hidden layer, and wf and bf are the weights and bias, respectively, of the forget gate. 2. Input gate. The input rate can be computed as follows:

it = s (wi [ht -1, x t ] + bi ) where it is the forget rate, and wi and bi are the weights and bias, respectively, of input gate. 3. Cell state layer. The cell state value can be computed as follows:

C˜ t = tanh(wC [ht -1, x t ] + bC ) Ct = f tCt -1 + itC˜ t where C˜ t is candidate cell state value; tanh(∙) is the tanh activation function; wC and bC are the weights and bias, respectively, of the cell state layer; Ct-1 is the cell state value of the previous hidden layer; and Ct is the cell state value of this hidden layer. 4. Output gate. The output rate and output of this hidden layer can be computed as follows:

ot = s (wo [ht -1, x t ] + bo ) ht = ot tanh(Ct ) where ot is the forget rate; wo and bo are the weights and bias, respectively, of the output gate; and ht is the output of this hidden layer. Interested readers may refer to Hochreiter and Schmidhuber (1997) for more information.

A comprehensive integrated forecasting approach 125

Evaluation criteria In order to evaluate the forecasting performance of the comprehensive integrated approach, an integrated approach is introduced as the benchmark model named the simple addition ensemble method (ADD). The ADD gives the same weights to each forecasting model and adds the predicted results together to get the new forecasting results. In this section, two commonly used evaluation criteria are employed to comprehensively evaluate the forecasting performance of the proposed approach. For assessing the performance of level forecasting, the mean absolute percentage error (MAPE) is employed. The directional change (DS) is utilized to assess the directional forecasting accuracy. For further detail, please refer to Chapter 4.

Daily forecasting Since the frequency of the data sets of the domestic economic situation are monthly data, for the daily forecasting integration, LSTM is used to integrate the forecasting results of three aspects – exchange rate data decomposition and integration, the international economic situation and the public’s expectations – to get the final forecasting results. Furthermore, MAPE is employed to assess the performance of level forecasting and DS is utilized to assess the directional forecasting accuracy of the new comprehensive integrated approach and the benchmark approaches, including the integrated approach using ADD, the forecasting approach based on the characteristics of China’s exchange rate (EEMD-LSSVR), the vine copula and support vector neural network hybrid forecasting approach based on the international forecasting situation (SVNN), and the kernel extreme learning machine based on the public’s expectations (KELM). The results of the forecasting performance comparisons among the new comprehensive integrated approach and the benchmark models are shown in Table 8.1. From Table 8.1, it can be concluded that (1) from the perspective of the level forecasting, the new comprehensive integrated approach using LSTM outperforms the benchmark approaches in the daily level forecasting, which obtains the smallest MAPE of 0.285; (2) from the perspective of the directional forecasting, the DS of the new comprehensive integrated approach using LSTM is 71.88%, which also outperforms the benchmark approaches; (3) both the integrated model LSTM and ADD based on the four aspects perform much better than Table 8.1 Performance comparison of different models for daily exchange rates: onestep-ahead forecasting results

MAPE DS

LSTM

ADD

EEMD-LSSVR

SVNN

KELM

0.285 71.88

0.318 62.50

0.471 68.75

0.488 65.63

0.512 62.50

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the models based on only one aspect in daily level forecasting; and (4) the new comprehensive integrated approach is an effective approach for exchange rate forecasting, since it can improve the accuracy of level forecasting and directional forecasting. And the proposed integrated approach using LSTM performs better than the other two integrated approaches in both level forecasting and directional forecasting.

Monthly forecasting In this section, the monthly forecasting results based on four aspects – exchange rate data decomposition and integration, the domestic economic situation, the international economic situation and the public’s expectations – will be integrated by LSTM to get the final forecasting results. Furthermore, MAPE is employed to assess the performance of level forecasting and DS is utilized to assess the directional forecasting accuracy of the new comprehensive integrated approach and the benchmark approaches, that is, the integrated approach using ADD, the forecasting approach based on the characteristics of China’s exchange rate (EEMD-LSSVR), the vector error correction model based on the domestic economic situation (VECM1), the vine copula–SVNN hybrid forecasting approach based on the international forecasting situation (SVNN) and the KELM based on the public’s expectations (KELM). The results of the monthly forecasting performance comparisons among the new comprehensive integrated approach and the benchmark models are shown in Table 8.2. From Table 8.2, it can be concluded that (1) from the perspective of level forecasting, the new comprehensive integrated approach using LSTM outperforms the benchmark approaches, which obtained the smallest MAPE of 0.255; (2) from the perspective of directional forecasting, the DS of the new comprehensive integrated approach using LSTM is 88.89%, which also outperforms the benchmark approaches; (3) both the integrated model LSTM and ADD based on the four aspects perform much better than the models based on only one aspect; and (4) the new comprehensive integrated approach is an effective approach for exchange rate forecasting, since it can improve the accuracy of level forecasting and directional forecasting. The proposed integrated approach using LSTM performs better than the other two integrated approaches in both level forecasting and directional forecasting.

Table 8.2 Performance comparison of different models for monthly exchange rates: one-step-ahead forecasting results

MAPE DS

LSTM

ADD

EEMD-LSSVR

VECM

SVNN

KELM

0.255 88.89

0.287 77.78

0.741 77.78

0.810 66.67

0.694 66.67

0.623 77.78

A comprehensive integrated forecasting approach 127

Conclusions A comprehensive integrated approach for exchange rate forecasting using LSTM to integrate the forecasting results of four aspects – exchange rate data decomposition and integration, the domestic economic situation, the international economic situation and the public’s expectations – is proposed in this chapter. The main conclusions of this chapter are as follows: Firstly, the new comprehensive integrated approach is an effective approach for exchange rate forecasting, since it can improve the accuracy of level forecasting and directional forecasting. In this chapter, there are two kinds of integrated approaches utilized, namely LSTM and ADD. The daily and monthly forecasting performance of the two integrated approaches outperform the forecasting approach based on a single aspect in level forecasting. Secondly, the new comprehensive integrated approach using LSTM outperforms the ADD integrated approach in both level forecasting and directional forecasting. Thirdly, the performance of the new comprehensive integrated approach is stable in daily forecasting and monthly forecasting. The proposed comprehensive integrated approach can significantly improve the forecasting accuracy and outperforms the benchmark approaches both in level forecasting and directional forecasting.

9

Conclusions and future research

Conclusions A new methodology for exchange rate forecasting is proposed in this book. Firstly, from the perspective of China’s exchange rate data analysis, this book systematically studies the lead–lag relationship between the offshore renminbi (RMB) and the onshore RMB under the influence of extreme events. From the perspective of the domestic economic situation, it analyzes the relationship between major domestic economic variables and the exchange rate; specially, we quantitatively measure the impact of renminbi depreciation on China’s imports and exports. From the perspective of the international economic situation, the book analyzes the relationship between the RMB and the major foreign exchange assets following exchange rate reforms. We also systemically study the risk spillover networks and examine the dynamic relationship of exchange rates among the Special Drawing Right (SDR) currencies. From the perspective of the public’s expectations, the book also analyzes the correlation between web search data, which is related to the public’s expectations, and the exchange rate. Secondly, with the new comprehensive integrated approach, the exchange rate is finally weight integrated from four perspectives: exchange rate data decomposition and integration, the domestic economic situation, the international economic situation, and the public’s expectations. The main innovations and features of this book are as follows: 1. Theoretical research. This book analyzes the reasons for exchange rate fluctuations and develops a new methodology for exchange rate forecasting from four perspectives: exchange rate data decomposition and integration, the domestic economic situation, the international economic situation, and the public’s expectations. 2. Basic data. In this book, the research data include not only exchange rate data and macroeconomic variable data, but also daily and monthly web search data, such as the Baidu search volume index and Google search volume index, to forecast the exchange rate. The research results show that there is a dynamic relationship between web search data and the exchange rate. Modeling the exchange rate based on web search data can improve forecasting accuracy.

Conclusions and future research 129 3. Empirical research. This book analyzes the dynamic relationship between the exchange rate and four aspects, namely exchange rate data decomposition and integration, the domestic economic situation, the international economic situation, and the public’s expectations, and forecasts the exchange rate based on these four aspects. In sum, the main innovations and features of the empirical research are as follows: Firstly, a hybrid approach named the EMD-Bry-Boschan method is proposed to study the lead–lag relationship between the offshore RMB (CNH) and the onshore RMB (CNY) under the influence of extreme events. Furthermore, this book analyzes the lead–lag relationship between the CNH spot exchange rate and CNY spot exchange rate when the extreme events are caused by market factors and/or policy factors. Secondly, for evaluating the influence of the RMB joining the SDR basket on RMB’s internationalization, we proposed a new hybrid approach by integrating the directed acyclic graph (DAG) and structural vector autoregression (SVAR) to further analyze and assess the risk spillover and the resulting dynamic change between the SDR currencies before and after the RMB joined the SDR basket. Thirdly, after the “811 exchange rate reform”, the renminbi continued to depreciate against the US dollar, with a cumulative depreciation of 8.42% from August 2015 to June 2016. An extended event analysis method is utilized to quantitatively measure the impact of renminbi depreciation on China’s imports and exports. Fourthly, a forecasting approach based on the exchange rate data analysis is proposed. It is the first time that the decomposition and integration approach named EEMD-LSSVR is utilized to forecast the exchange rate. The ensemble empirical mode decomposition (EEMD) algorithm is used to decompose the exchange rate to several different intrinsic mode functions (IMFs) and a residual sequence, and least squares support vector regression (LSSVR) is employed to forecast those different IMFs and the residual sequence. Fifthly, a forecasting approach based on the domestic economic situation is proposed. According to the Granger causality test, correlation test and grey relational analysis, the book studies the correlation between major domestic economic variables and the exchange rate, and develops a vector error correction model (VECM) to forecast the exchange rate with three variables that are selected by the three correlation analysis methods. Sixthly, a new forecasting approach based on the international economic situation is proposed by integrating a vine copula and support vector neural network (SVNN). The vine copula is used to study the dependencies between the RMB and the major foreign exchange assets, particularly during China’s five exchange rate reforms. Three variables that have higher degrees of dependence with RMB/USD are selected to

130

Conclusions and future research represent the international economic situation to forecast RMB/USD with SVNN. Seventhly, a forecasting approach based on the public’s expectations is proposed by integrating the Granger causality test, grey relational analysis and kernel extreme learning machine (KELM). Daily and monthly web search data, such as the Baidu search volume index and Google search volume index, which are related to the public’s expectations, can be used to forecast the exchange rate. This book analyzes the dynamic relationship between web search data and the exchange rate using the Granger causality test and the grey relational analysis, and develops a KELM forecasting approach based on the public’s expectations. Eighthly, a comprehensive integrated approach is proposed for exchange rate forecasting by using long short-term memory (LSTM) to integrate the forecasting results of four aspects: the exchange rate data decomposition and integration, the domestic economic situation, the international economic situation, and the public’s expectations. The empirical results show that the LSTM-integrated forecasting approach outperforms the benchmarks in level forecasting and directional forecasting.

Future research Based on the proposed new comprehensive integrated approach for exchange rate forecasting, further research can focus on the following directions or topics: 1. Determining the proper weights of forecasting models. We can try the timevary integrated forecasting models and use some other new and better artificial intelligence models to promote the progress of forecasting research. 2. Analysis of the exchange rate forecasting. We should pay more attention to how to combine the traditional exchange rate theory with the exchange rate forecasting models. Based on the economic analysis, we can improve the accuracy of directional forecasting and trend forecasting of the exchange rates. 3. Forecasting of mixed-frequency data. We should develop some approaches to integrate the forecasting results of daily data and the forecasting results of monthly data based on different aspects. 4. Extending the website data search. Using text mining or data mining to get web data from Twitter, Weibo and other websites, to reflect the public’s expectations to forecast the exchange rates.

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Index

811 exchange rate reform 13, 15, 41, 45–46, 50, 69–72, 74–76, 81, 105–106, 110, 114, 129 Akaike information criterion (AIC) 91, 118 AR-GJR-GARCH 16, 99–100, 104, 114 Baidu Index 17, 115–117 Baidu search volume index (BSVI) 17, 115, 122 Bry-Boschan algorithm 44, 47–48, 50–54 cell state layer 124 China’s total imports and exports 1, 66; domestic economic fundamentals 3; China’s general trade 70; China’s processing trade 70–71, 73; China’s reforms of the RMB exchange rate regime 8; high-tech products 72–73; mechanical and electrical products 72–73 Comprehensive Integrated Forecasting Approach 123 copula 14, 16, 23–25, 99–101, 104–105, 108–114, 125–126, 129; correlation test 13, 16, 43, 46, 89, 93–94, 129; Granger causality test 13–15, 17, 23–26, 39, 42–43, 46–47, 57, 89, 91–92, 98, 115, 118, 122, 129–130; grey relational analysis 13–14, 16, 17, 26, 39, 89, 93, 95, 98, 129–130; spillover index 26–28; vine copula 14, 16, 23, 99–101, 104–105, 108–111, 113–114, 125–126, 129

daily forecasting 86, 113, 117, 121, 125, 127, 129 data computing 16–17, 89, 98, 115, 122 data extraction 15, 17, 89, 98, 115, 122 data selection 15, 17, 89, 98, 115, 122 decomposition algorithm: complementary ensemble empirical mode decomposition (CEEMD) 15, 29, 34, 39; empirical mode decomposition method (EMD) 15, 18, 29, 39; ensemble empirical mode decomposition (EEMD) 13, 15, 18, 29, 30, 39, 77; variational mode decomposition (VMD) 15, 18, 29–30, 39; wavelet packet decomposition (WPD) 15, 18, 29, 33, 39 degree of the freedom 110 directed acyclic graph (DAG) 13, 15, 41, 56–57 directional forecasting 14, 17, 85–87, 97–98, 113–114, 121–122, 125, 127, 130 dynamic network structure 62, 85 European debt crisis 46, 48–49 evaluation criteria 16–17, 85–86, 89, 97, 113, 116, 121–122, 125 exchange rate pass-through theory 14, 18–19, 21–22, 88 Extreme Learning Machine (ELM) 36, 119 forecasting approaches: ensemble learning approaches 38; hybrid forecasting approaches 37; single forecasting models 35; TEI@I 38, 77–78 forecasting performance 16–17, 22, 29–30, 37–40, 86–87, 97, 113, 121–122, 125–126 forget gate 124

146

Index

global manufacturing PMI 5 Google search volume index (GSVI) 115, 117, 122, 128, 130 Google Trends 22, 115–116, 122 hidden layer 103, 120, 124 Independent identical distribution (IID) 100 input gate 124 input layer 103, 124 interest rate parity theory 18–19 International Monetary Fund (IMF) 1, 11, 54 Johansen cointegration test 96, 98 kernel extreme learning machine (KELM) 36, 115, 119, 122 least squares support vector machine (LSSVM) 36, 79 least squares support vector regression (LSSVR) 29, 36, 77–80, 83, 85–87 level forecasting 85–87, 97–98, 113– 114, 121–122, 125–127, 130 liquidity squeeze 46–47 long short-term memory (LSTM) 8, 123, 130 long-term network structure 60–61 mean absolute percentage error (MAPE) 85–86, 97–98, 113, 121–122, 125–126

monthly forecasting 86–87, 97–98, 113–114, 117, 121–122, 126–127 output gate 124 output layer 103, 124 public’s expectations 6, 115 purchasing power parity theory 18 recurrent neural network (RNN) 123 Schwarz information criterion (SC) 92, 118 short-term network structure 56, 59, 63, 75 simple addition ensemble method (ADD) 78, 80, 83, 85, 87, 125 Special Drawing Right (SDR) 1, 41, 54, 99, 128 structural vector autoregression (SVAR) 20, 41, 56–57, 129 support vector machine (SVM) 36, 102 support vector neural network (SVNN) 14, 16, 99–100, 102–104, 111–114, 125–126, 129–130 vector error correction model (VECM) 14–16, 35, 39, 69, 74, 89, 95, 97–98, 126, 129 web search data 12–14, 17, 22, 115–119, 122, 128, 130 Worldwide Interbank Financial Telecommunication (SWIFT) 1, 11