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Multifractal detrended fluctuation analysis: Practical applications to financial time series

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  • Thompson, James R.
  • Wilson, James R.
Abstract
To analyze financial time series exhibiting volatility clustering or other highly irregular behavior, we exploit multifractal detrended fluctuation analysis (MF-DFA). We summarize the use of local Hölder exponents, generalized Hurst exponents, and the multifractal spectrum in characterizing the way that the sample paths of a multifractal stochastic process exhibit light- or heavy-tailed fluctuations as well as short- or long-range dependence on different time scales. We detail the development of a robust, computationally efficient software tool for estimating the multifractal spectrum from a time series using MF-DFA, with special emphasis on selecting the algorithm’s parameters. The software is tested on simulated sample paths of Brownian motion, fractional Brownian motion, and the binomial multiplicative process to verify the accuracy of the resulting multifractal spectrum estimates. We also perform an in-depth analysis of General Electric’s stock price using conventional time series models, and we contrast the results with those obtained using MF-DFA.

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  • Thompson, James R. & Wilson, James R., 2016. "Multifractal detrended fluctuation analysis: Practical applications to financial time series," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 126(C), pages 63-88.
    • Handle: RePEc:eee:matcom:v:126:y:2016:i:c:p:63-88
    DOI: 10.1016/j.matcom.2016.03.003
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    1. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    2. Laurent Calvet & Adlai Fisher, 2002. "Multifractality In Asset Returns: Theory And Evidence," The Review of Economics and Statistics, MIT Press, vol. 84(3), pages 381-406, August.
    3. Mandelbrot, Benoit B, 1971. "When Can Price Be Arbitraged Efficiently? A Limit to the Validity of the Random Walk and Martingale Models," The Review of Economics and Statistics, MIT Press, vol. 53(3), pages 225-236, August.
    4. Barbara Olbermann & Sílvia Lopes & Valdério Reisen, 2006. "Invariance of the first difference in ARFIMA models," Computational Statistics, Springer, vol. 21(3), pages 445-461, December.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Baillie, Richard T & Chung, Ching-Fan & Tieslau, Margie A, 1996. "Analysing Inflation by the Fractionally Integrated ARFIMA-GARCH Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(1), pages 23-40, Jan.-Feb..
    7. Etheridge,Alison, 2002. "A Course in Financial Calculus," Cambridge Books, Cambridge University Press, number 9780521890779, October.
    8. Michael E. Kuhl & Sachin G. Sumant & James R. Wilson, 2006. "An Automated Multiresolution Procedure for Modeling Complex Arrival Processes," INFORMS Journal on Computing, INFORMS, vol. 18(1), pages 3-18, February.
    9. Michel Beine & Sébastien Laurent & Christelle Lecourt, 2002. "Accounting for conditional leptokurtosis and closing days effects in FIGARCH models of daily exchange rates," ULB Institutional Repository 2013/10443, ULB -- Universite Libre de Bruxelles.
    10. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    11. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
    12. Greene, Myron T. & Fielitz, Bruce D., 1977. "Long-term dependence in common stock returns," Journal of Financial Economics, Elsevier, vol. 4(3), pages 339-349, May.
    13. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
    14. Kantelhardt, Jan W & Koscielny-Bunde, Eva & Rego, Henio H.A & Havlin, Shlomo & Bunde, Armin, 2001. "Detecting long-range correlations with detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 441-454.
    15. Etheridge,Alison, 2002. "A Course in Financial Calculus," Cambridge Books, Cambridge University Press, number 9780521813853, October.
    16. Fama, Eugene F, 1991. "Efficient Capital Markets: II," Journal of Finance, American Finance Association, vol. 46(5), pages 1575-1617, December.
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