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Multi-Fractality in Foreign Currency Markets

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  • Marco Corazza

    () (University Ca’ Foscari of Venice, Italy)

  • A. G. Malliaris

    (Loyola University Chicago, U.S.A.)

Abstract

Several empirical studies have shown the inadequacy of the standard Brownian motion (sBm) as a model of asset returns. To correct for this evidence some authors have conjectured that asset returns may be independently and identically Pareto-Levy stable (PLs) distributed, whereas others have asserted that asset returns may be identically - but not independently - fractional Brownian motion (fBm) distributed with Hurst exponents, in both cases, that differ from 0.5. In this article we empirically explore such non-standard assumptions for both spot and (nearby) futures returns for five foreign currencies: the British Pound, the Canadian Dollar, the German Mark, the Swiss Franc, and the Japanese Yen.

Suggested Citation

  • Marco Corazza & A. G. Malliaris, 2002. "Multi-Fractality in Foreign Currency Markets," Multinational Finance Journal, Multinational Finance Journal, vol. 6(2), pages 65-98, June.
  • Handle: RePEc:mfj:journl:v:6:y:2002:i:2:p:65-98
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    References listed on IDEAS

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    Cited by:

    1. Withanawasam, R.M. & Whigham, P.A. & Crack, Timothy Falcon, 2013. "Characterizing limit order prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5346-5355.
    2. Minjae Park & Mi Lim Lee & Jinpyo Lee, 2019. "Predicting Stock Market Indices Using Classification Tools," Asian Economic and Financial Review, Asian Economic and Social Society, vol. 9(2), pages 243-256, February.
    3. Jamdee, Sutthisit & Los, Cornelis A., 2007. "Long memory options: LM evidence and simulations," Research in International Business and Finance, Elsevier, vol. 21(2), pages 260-280, June.
    4. Mitra, S.K. & Bawa, Jaslene, 2017. "Can trade opportunities and returns be generated in a trend persistent series? Evidence from global indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 124-135.
    5. Kyaw, NyoNyo A. & Los, Cornelis A. & Zong, Sijing, 2006. "Persistence characteristics of Latin American financial markets," Journal of Multinational Financial Management, Elsevier, vol. 16(3), pages 269-290, July.
    6. Rossitsa Yalamova, 2012. "Fractal Measures in Market Microstructure Research," Multinational Finance Journal, Multinational Finance Journal, vol. 16(1-2), pages 137-154, March - J.
    7. Cerqueti, Roy & Fanelli, Viviana & Rotundo, Giulia, 2019. "Long run analysis of crude oil portfolios," Energy Economics, Elsevier, vol. 79(C), pages 183-205.
    8. Ladislav Kristoufek, 2012. "Fractal Markets Hypothesis And The Global Financial Crisis: Scaling, Investment Horizons And Liquidity," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 15(06), pages 1-13.
    9. Trinidad Segovia, J.E. & Fernández-Martínez, M. & Sánchez-Granero, M.A., 2012. "A note on geometric method-based procedures to calculate the Hurst exponent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(6), pages 2209-2214.
    10. Bo Qian & Khaled Rasheed, 2010. "Foreign exchange market prediction with multiple classifiers," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(3), pages 271-284.
    11. Sutthisit Jamdee & Cornelis A. Los, 2005. "Multifractal Modeling of the US Treasury Term Structure and Fed Funds Rate," Finance 0502021, University Library of Munich, Germany.
    12. Cornelis A. Los & Rossitsa M. Yalamova, 2004. "Multi-Fractal Spectral Analysis of the 1987 Stock Market Crash," Finance 0409050, University Library of Munich, Germany.
    13. Karuppiah, Jeyanthi & Los, Cornelis A., 2005. "Wavelet multiresolution analysis of high-frequency Asian FX rates, Summer 1997," International Review of Financial Analysis, Elsevier, vol. 14(2), pages 211-246.
    14. Kyrtsou, Catherine & Malliaris, Anastasios G., 2009. "The impact of information signals on market prices when agents have non-linear trading rules," Economic Modelling, Elsevier, vol. 26(1), pages 167-176, January.
    15. Samit Paul, 2020. "Time Varying Efficiency in Indian Sectors: An Event Study on Demonetization," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 18(1), pages 103-127, March.
    16. Guglielmo Maria Caporale & Luis Gil-Alana & Alex Plastun & Inna Makarenko, 2016. "Long memory in the Ukrainian stock market and financial crises," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 40(2), pages 235-257, April.
    17. Claudeci Da Silva & Hugo Agudelo Murillo & Joaquim Miguel Couto, 2014. "Early Warning Systems: Análise De Ummodelo Probit De Contágio De Crise Dos Estados Unidos Para O Brasil(2000-2010)," Anais do XL Encontro Nacional de Economia [Proceedings of the 40th Brazilian Economics Meeting] 110, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].

    More about this item

    Keywords

    exponent of Hurst; fractional Brownian motion; multi-fractal market hypothesis; Pareto-Levy stable process; R/S analysis;

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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