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How to Forecast Long-Run Volatility: Regime Switching and the Estimation of Multifractal Processes

Author

Listed:
  • Laurent-Emmanuel Calvet

    () (Department of Economics, Harvard University - Harvard University [Cambridge])

  • Adlai J. Fisher

    (Faculty of Commerce, University of British Columbia - UBC - University of British Columbia)

Abstract

We propose a discrete-time stochastic volatility model in which regime switching serves three purposes. First, changes in regimes capture low-frequency variations. Second, they specify intermediate-frequency dynamics usually assigned to smooth autoregressive transitions. Finally, high-frequency switches generate substantial outliers. Thus a single mechanism captures three features that are typically viewed as distinct in the literature. Maximum-likelihood estimation is developed and performs well in finite samples. Using exchange rates, we estimate a version of the process with four parameters and more than a thousand states. The multifractal outperforms GARCH, MS-GARCH, and FIGARCH in- and out-of-sample. Considerable gains in forecasting accuracy are obtained at horizons of 10 to 50 days.

Suggested Citation

  • Laurent-Emmanuel Calvet & Adlai J. Fisher, 2004. "How to Forecast Long-Run Volatility: Regime Switching and the Estimation of Multifractal Processes," Post-Print hal-00478472, HAL.
  • Handle: RePEc:hal:journl:hal-00478472
    DOI: 10.1093/jjfinec/nbh003
    Note: View the original document on HAL open archive server: https://hal-hec.archives-ouvertes.fr/hal-00478472
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