Skip to main content
SpringerLink
Log in

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

  • Focus
  • Published:
Soft Computing Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

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

    Article  Google Scholar 

  • 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):56–69

    Article  Google Scholar 

  • 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 8:40–43

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  • 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

    Google Scholar 

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

    Book  MATH  Google Scholar 

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

    Google Scholar 

  • 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):1–9

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Caraiani P (2012) Evidence of multifractality from emerging European stock markets. PLoS ONE 7:e40693

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  • 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):323–334

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  • 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

    Google Scholar 

  • 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):286–294

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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

    Google Scholar 

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

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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):53–59

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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 60:615–630

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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):103–124

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

  • 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

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  • 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 453:108–115

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  • 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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

Download references

Acknowledgements

Funding was provided by Educational Ministry of China (Grant no. 17YJC630131).

Author information

Authors and Affiliations

  1. School of Economics and Management, Harbin Engineering University, Harbin, Heilongjiang Province, China

    Limei Sun, Lina Zhu & Jinyu Wang

  2. CSIRO, Clayton, Australia

    Alec Stephenson

Authors
  1. Limei Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lina Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alec Stephenson
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jinyu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Limei Sun.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interest with other organization or people on this article.

Additional information

Communicated by X. Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sun, L., Zhu, L., Stephenson, A. et al. Measuring and forecasting the volatility of USD/CNY exchange rate with multi-fractal theory. Soft Comput 22, 5395–5406 (2018). https://doi.org/10.1007/s00500-018-3079-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-018-3079-z

Keywords

Search

Navigation