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

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  • Laurent E. Calvet

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. Copyright 2004, Oxford University Press.

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  • Laurent E. Calvet, 2004. "How to Forecast Long-Run Volatility: Regime Switching and the Estimation of Multifractal Processes," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 49-83.
  • Handle: RePEc:oup:jfinec:v:2:y:2004:i:1:p:49-83
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbh003
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