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Regime-Switching and the Estimation of Multifractal Processes

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  • Laurent Calvet
  • Adlai Fisher

Abstract

We propose a discrete-time stochastic volatility model in which regimeswitching serves three purposes. First, changes in regimes capture low frequency variations, which is their traditional role. Second, they specify intermediate frequency dynamics that are usually assigned to smooth autoregressive processes. Finally, high frequency switches generate substantial outliers. Thus, a single mechanism captures three important features of the data that are typically addressed as distinct phenomena in the literature. Maximum likelihood estimation is developed and shown to perform well in finite sample. We estimate on exchange rate data a version of the process with four parameters and more than a thousand states. The estimated model compares favorably to earlier specifications both in- and out-of-sample. Multifractal forecasts slightly improve on GARCH(1,1) at daily and weekly intervals, and provide considerable gains in accuracy at horizons of 10 to 50 days.

Suggested Citation

  • Laurent Calvet & Adlai Fisher, 2003. "Regime-Switching and the Estimation of Multifractal Processes," Harvard Institute of Economic Research Working Papers 1999, Harvard - Institute of Economic Research.
  • Handle: RePEc:fth:harver:1999
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    Cited by:

    1. Calvet, Laurent E. & Fisher, Adlai J., 2008. "Multifrequency jump-diffusions: An equilibrium approach," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 207-226, January.
    2. Calvet, Laurent E. & Fisher, Adlai J., 2007. "Multifrequency news and stock returns," Journal of Financial Economics, Elsevier, vol. 86(1), pages 178-212, October.
    3. Barunik, Jozef & Aste, Tomaso & Di Matteo, T. & Liu, Ruipeng, 2012. "Understanding the source of multifractality in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(17), pages 4234-4251.
    4. M. Rypdal & O. L{o}vsletten, 2011. "Multifractal modeling of short-term interest rates," Papers 1111.5265, arXiv.org.
    5. Lux, Thomas & Kaizoji, Taisei, 2007. "Forecasting volatility and volume in the Tokyo Stock Market: Long memory, fractality and regime switching," Journal of Economic Dynamics and Control, Elsevier, vol. 31(6), pages 1808-1843, June.
    6. Joshua Angrist & Eric Bettinger & Michael Kremer, 2004. "Long-Term Consequences of Secondary School Vouchers: Evidence from Administrative Records in Colombia," NBER Working Papers 10713, National Bureau of Economic Research, Inc.
    7. Lux, Thomas, 2008. "The Markov-Switching Multifractal Model of Asset Returns: GMM Estimation and Linear Forecasting of Volatility," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 194-210, April.
    8. Rypdal, Martin & Sirnes, Espen & Løvsletten, Ola & Rypdal, Kristoffer, 2013. "Assessing market uncertainty by means of a time-varying intermittency parameter for asset price fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(16), pages 3335-3343.
    9. Lux, Thomas & Kaizoji, Taisei, 2004. "Forecasting volatility and volume in the Tokyo stock market: The advantage of long memory models," Economics Working Papers 2004-05, Christian-Albrechts-University of Kiel, Department of Economics.
    10. Eisler, Z. & Kertész, J., 2004. "Multifractal model of asset returns with leverage effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 603-622.
    11. Thomas Lux, 2003. "The Multi-Fractal Model of Asset Returns:Its Estimation via GMM and Its Use for Volatility Forecasting," Computing in Economics and Finance 2003 14, Society for Computational Economics.
    12. Calvet, Laurent E. & Fisher, Adlai J. & Thompson, Samuel B., 2006. "Volatility comovement: a multifrequency approach," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 179-215.
    13. Julien Idier, 2011. "Long-term vs. short-term comovements in stock markets: the use of Markov-switching multifractal models," The European Journal of Finance, Taylor & Francis Journals, vol. 17(1), pages 27-48.
    14. Zoltan Eisler & Janos Kertesz, 2004. "Multifractal model of asset returns with leverage effect," Papers cond-mat/0403767, arXiv.org, revised May 2004.
    15. repec:wsi:rpbfmp:v:10:y:2007:i:03:n:s0219091507001112 is not listed on IDEAS

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    JEL classification:

    • G0 - Financial Economics - - General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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