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Measuring and forecasting the volatility of USD/CNY exchange rate with multi-fractal theory

Authors: Limei Sun, Lina Zhu, Alec Stephenson, Jinyu Wang

Published in: Soft Computing | Issue 16/2018

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Abstract

Exchange rate fluctuations continue to intensify because of global economic integration. Research on the characteristics of exchange rate volatility is particularly urgent and important. In this paper, the fractal theory is introduced. The function box counting method and the qth-order moment structure partition function method are applied to test the multi-fractal features of USD/CNY exchange rate. On this basis, the multi-fractal spectrum analysis is carried out. It is found that USD/CNY exchange rate has multi-fractal characteristics and there is a strong connection between the standard deviation of the scale index and volatility of USD/CNY exchange rate. By adjusting the standard deviation of scaling exponents, we construct the multi-fractal volatility index and build a dynamic model for testing and forecasting the volatility of USD/CNY exchange rate based on fractal theory. The model \(\ln \bar{{S}}_\alpha -\hbox {ARMA} (1,1) \) for measuring and forecasting volatility proposed in our paper is demonstrated to be a good fit to the exchange rate data, which provides sound methodological reference for exchange rate volatility measurement.

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Apte P (2012) The interrelationship between the stock markets and the foreign exchange market. J Int Money Finance 23(4):553–571CrossRef

Awartani B, Aktam M, Cherif G (2016) The connectedness between crude oil and financial markets: evidence from implied volatility indices. J Commod Mark 4(1):56–69CrossRef

Ayodeji IO (2016) A three-state Markov-modulated switching model for exchange rates. In: Abstract of economic finance & management outlook 2016, no 2, pp 1–9

Babalos V, Balcilar M, Gupta R (2015) Herding behavior in real estate markets: novel evidence from a Markov-switching model. J Behav Exp Finance 8:40–43CrossRef

Barkoulas JT, Barilla AG, Wells W (2016) Long-memory exchange rate dynamics in the Euro era. Chaos Solitons Fractals 86:92–100CrossRefMATH

Batten JA, Kinateder H, Wagner N (2014) Multifractality and value-at-risk forecasting of exchange rates. Phys A Stat Mech Appl 401(5):71–81CrossRef

Bertram P, Ma J, Sibbertsen P (2015) Real exchange rates and economic fundamentals: an investigation based on a Markov-STAR model. Hann Econ Pap 1:187–217

Brooks C (2008) The introductory econometrics for finance. Cambridge University Press, CambridgeCrossRefMATH

Cao G (2013) The study of the impact of time shocks in China’s currency and equity markets. Manag Sci 01:89–100

Caporale GM, Gil-Alana LA (2013) Long memory and fractional integration in high frequency data on the US dollar/British pound spot exchange rate. Int Rev Financ Anal 29(5):1–9CrossRef

Caporale GM, Ali FM, Spagnolo F, Spagnolo N (2017) International portfolio flows and exchange rate volatility in emerging Asian markets. J Int Money Finance 76:1–15CrossRef

Caraiani P (2012) Evidence of multifractality from emerging European stock markets. PLoS ONE 7:e40693CrossRef

Caraiani P, Haven E (2015) Evidence of multifractality from CEE exchange rates against Euro. Phys A Stat Mech Appl 419:395–407CrossRef

Fang Y (2010) Nonlinear noise estimation in international stock markets: coarse-grained entropy method. Int J Econ Finance 2(1):97–104MathSciNetCrossRef

Guo Y, Huang J, Cheng H (2012) Multifractal features of metal futures market based on multifractal detrended cross-correlation analysis. Kybernetes 41(10):1509–1529CrossRef

Hainaut D, Boucher J (2014) Frequency and severity modelling using multifractal processes: an application to tornado occurrence in the USA and CAT bonds. Environ Model Assess 19(3):323–334CrossRef

Haldrup N, Valdés JEV (2017) Long memory, fractal integration, and cross-sectional aggregation. J Econom 199:1–11CrossRefMATH

Huo Z, Zhang Y, Lu X, Li Y (2016) The research of the characteristics of China’s natural rubber futures market based on the MF-DFA method. Can Soc Sci 12(8):30–37

Kang SH, Mclver R, Park SY et al (2014) Long memory features evolve in the time-varying process in Asia-Pacific foreign exchange markets. Procedia Econ Finance 14(14):286–294CrossRef

Khayat GA (2018) The impact of setting negative policy rates on banking flows and exchange rates. Econ Model 68:1–10CrossRef

Kiliç R (2011) Conditional volatility and distribution of exchange rates: GARCH and FIGARCH models with NIG distribution. Stud Nonlinear Dyn Econom 11(3):368–378

Kunnas J (2012) Garch models for foreign exchange rates. J Enviorn Econ Manag 67(2):171–188

Lee H, Song JW, Chang W (2016) Multifractal value at risk model. Phys A Stat Mech Appl 451(1):113–122MathSciNetCrossRef

Li Z, Lu X (2011) Multifractal analysis of China’s agricultural commodity futures markets. Energy Procedia 9:1920–1926CrossRef

Liang Q, Jin D (2011) The comprasion of fractual characteristic of Shenzhen & Shanghai stock market in China. J Jilin Bus Technol Coll 27(2):50–53

Ling PW (2013) The stock price forecasting comparative research of the use of fractal theory at Taiwan traditional industry and technology industry. Appl Mech Mater 2205(274):53–59CrossRef

Luo H, Wang S (2016) Predicting the financial volatility by GARCH model and IV model. Period Zhejiang Sci-Tech Univ 02:322–326

Lux T (2008) The Markov-switching multifractal model of asset returns: GMM estimation and linear forecasting of volatility. J Bus Econ Stat 26(2):194–210MathSciNetCrossRef

Marreh S, Olubusoye OE, Kihoro JM (2014) Modeling volatility in the Gambian exchange rates: an ARMA-GARCH approach. Int J Econ Finance 6(10):118–128CrossRef

Morales R, Di Matteo T, Aste T (2013) Non-stationary multifractality in stock returns. Phys A Stat Mech Appl 392(24):6470–6483CrossRef

Murphy F, Kearney F, Cummins M (2015) An analysis of implied volatility jump dynamics: novel functional data representation in crude oil markets. N Am J Econ Finance 33:199–216

Núñez HFS, Venegas-Martínez F (2015) Exchange rate long memory: international evidence. Contaduría Y Administración 60:615–630CrossRef

Oh GJ (2014) Multifractal analysis of implied volatility in index options. J Korean Phys Soc 64(11):1751–1757CrossRef

Pilbeam K, Langeland KN (2015) Forecasting exchange rate volatility: GARCH models versus implied volatility forecasts. Int Econ Econ Policy 12(1):127–142CrossRef

Rapach DE, Strauss JK (2012) Forecasting US state-level employment growth: an amalgamation approach. Int J Forecast 28(2):315–327CrossRef

Rhee DW, Byun SJ, Kim S (2012) Empirical comparison of alternative implied volatility measures of the forecasting performance of future volatility. Asia-Pacific J Financ Stud 41(1):103–124CrossRef

Sui J, Liu J, Yan C (2013) Is there a long-term memory of RMB exchange rate and volatility in the current exchange rate mechanism? Stud Int Finance 11:56–69

Sznajderska A (2013) Foreign exchange rates in central european economies: nonlinearities in adjustment to interest rate differentials. Metody Ilościowe W Badaniach Ekonomicznych 11:78–93

Tayyab M, Tarar A, Riaz M (2012) Application of smooth transition autoregressive (STAR) models for exchange rate. Math Theory Model 2(9):1–10

Vandewalle N, Ausloos M (1998) Multi-affine analysis of typical currency exchange rates. Eur Phys J 4:257–261CrossRef

Vassilicons JC, Demos A, Tata F (1993) No evidence of chaos but some evidence of multifractals in the foreign exchange and stock market. In: Crilly AJ, Earnshaw RA, Jones H (eds) Applications of fractals and chaos. Springer, Berlin

Vejmëlek J (2016) Some stylised facts about the exchange rate behaviour of Central European currencies. Acta Oecon Prag 2016(2):3–17CrossRef

Vilasuso J (2002) Forecasting exchange rate volatility. Econ Lett 76:59–64CrossRefMATH

Wang X, Guo K, Lu X (2016) The long run dynamic relationship between exchange rate and its attention index: based on DDCA and TOP method. Phys A Stat Mech Appl 453:108–115CrossRef

Wang Z, Yan Y, Chen X (2016) Multifractal properties of interest rates in bond market. Procedia Comput Sci 91:432–441CrossRef

Xu S (2015) RMB exchange rate volatility research-based on models. Modern Econ Inf 08:344

Zhang H, Ke W (2015) The study of the dynamic characteristics of RMB exchange rate based on the GARCH model. Econ Math 04:93–98

Zhang A, Liu B (2014) The long-term memory and the system perfection of RMB exchange rate. Study Explor 01:114–117

Zumbach G (2002) Volatility processes and volatility forecast with long memory. Mimeo, New York City

Title: Measuring and forecasting the volatility of USD/CNY exchange rate with multi-fractal theory
Authors: Limei Sun
Lina Zhu
Alec Stephenson
Jinyu Wang
Publication date: 22-02-2018
Publisher: Springer Berlin Heidelberg
Published in: Soft Computing / Issue 16/2018
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-018-3079-z

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