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Multi-Fractality in Foreign Currency Markets

In: Economic Uncertainty, Instabilities And Asset Bubbles Selected Essays

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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-Lévy 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, 2005. "Multi-Fractality in Foreign Currency Markets," World Scientific Book Chapters, in: Economic Uncertainty, Instabilities And Asset Bubbles Selected Essays, chapter 11, pages 151-184, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812701015_0011
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    1. Marco Corazza & A.G. Malliaris & Carla Nardelli, 1997. "Searching for fractal structure in agricultural futures markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 17(4), pages 433-473, June.
    2. Lobato, Ignacio N & Savin, N E, 1998. "Real and Spurious Long-Memory Properties of Stock-Market Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 261-268, July.
    3. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
    4. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    5. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    6. Hsing Fang & Kon S. Lai & Michael Lai, 1994. "Fractal structure in currency futures price dynamics," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 14(2), pages 169-181, April.
    7. Cornell, Bradford, 1977. "Spot rates, forward rates and exchange market efficiency," Journal of Financial Economics, Elsevier, vol. 5(1), pages 55-65, August.
    8. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    9. Zhou, Bin, 1996. "High-Frequency Data and Volatility in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 45-52, January.
    10. Hsieh, David A., 1992. "A nonlinear stochastic rational expectations model of exchange rates," Journal of International Money and Finance, Elsevier, vol. 11(3), pages 235-250, June.
    11. Bong-Chan, Kho, 1996. "Time-varying risk premia, volatility, and technical trading rule profits: Evidence from foreign currency futures markets," Journal of Financial Economics, Elsevier, vol. 41(2), pages 249-290, June.
    12. Chiang, Thomas C. & Jiang, Christine X., 1995. "Foreign exchange returns over short and long horizons," International Review of Economics & Finance, Elsevier, vol. 4(3), pages 267-282.
    13. Hsieh, David A, 1989. "Testing for Nonlinear Dependence in Daily Foreign Exchange Rates," The Journal of Business, University of Chicago Press, vol. 62(3), pages 339-368, July.
    14. repec:nys:sunysb:93-02 is not listed on IDEAS
    15. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105, January.
    16. Fama, Eugene F, 1991. "Efficient Capital Markets: II," Journal of Finance, American Finance Association, vol. 46(5), pages 1575-1617, December.
    17. Levich, Richard M. & Thomas, Lee III, 1993. "The significance of technical trading-rule profits in the foreign exchange market: a bootstrap approach," Journal of International Money and Finance, Elsevier, vol. 12(5), pages 451-474, October.
    18. Taylor, Stephen J, 1992. "Rewards Available to Currency Futures Speculators: Compensation for Risk or Evidence of Inefficient Pricing?," The Economic Record, The Economic Society of Australia, vol. 0(0), pages 105-116, Supplemen.
    19. van de Gucht, Linda M. & Dekimpe, Marnik G. & Kwok, Chuck C. Y., 1996. "Persistence in foreign exchange rates," Journal of International Money and Finance, Elsevier, vol. 15(2), pages 191-220, April.
    20. Lobato, I. & Robinson, P. M., 1996. "Averaged periodogram estimation of long memory," Journal of Econometrics, Elsevier, vol. 73(1), pages 303-324, July.
    21. Lobato, Ignacio N & Savin, N E, 1998. "Real and Spurious Long-Memory Properties of Stock-Market Data: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 280-283, July.
    22. Alexakis, Panayotis & Apergis, Nicholas, 1996. "ARCH effects and cointegration: Is the foreign exchange market efficient?," Journal of Banking & Finance, Elsevier, vol. 20(4), pages 687-697, May.
    23. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    24. Jacobsen, Ben, 1996. "Long term dependence in stock returns," Journal of Empirical Finance, Elsevier, vol. 3(4), pages 393-417, December.
    25. Stephen J. Taylor, 1992. "Rewards Available to Currency Futures Speculators: Compensation for Risk or Evidence of Inefficient Pricing?," The Economic Record, The Economic Society of Australia, vol. 68(S1), pages 105-116, December.
    26. Cheung, Yin-Wong & Lai, Kon S, 1993. "Do Gold Market Returns Have Long Memory?," The Financial Review, Eastern Finance Association, vol. 28(2), pages 181-202, May.
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    3. 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.
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    9. 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.
    10. Cornelis A. Los & Rossitsa M. Yalamova, 2004. "Multi-Fractal Spectral Analysis of the 1987 Stock Market Crash," Finance 0409050, University Library of Munich, Germany.
    11. Truong Ngoc Cuong & Sam-Sang You & Le Ngoc Bao Long & Hwan-Seong Kim, 2022. "Seaport Resilience Analysis and Throughput Forecast Using a Deep Learning Approach: A Case Study of Busan Port," Sustainability, MDPI, vol. 14(21), pages 1-25, October.
    12. Rossitsa Yalamova, 2012. "Fractal Measures in Market Microstructure Research," Multinational Finance Journal, Multinational Finance Journal, vol. 16(1-2), pages 137-154, March - J.
    13. Cerqueti, Roy & Fanelli, Viviana & Rotundo, Giulia, 2019. "Long run analysis of crude oil portfolios," Energy Economics, Elsevier, vol. 79(C), pages 183-205.
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    20. 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.
    21. 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].

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    More about this item

    Keywords

    Asymptotic Economic Growth; Inflation; Interest Rates; Asset Pricing; Equity Markets; Foreign Currency; Monetary Policy; Crash;
    All these keywords.

    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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