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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 regime switching 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.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 9839.

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Date of creation: Jul 2003
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Publication status: published as Calvet, Laurent E. and Adlai J. Fisher. "How To Forecast Long-Run Volatility: Regime Switching And The Estimation Of Multifractal Processes," Journal of Financial Econometrics, 2004, v2(1,Winter), 49-83.
Handle: RePEc:nbr:nberwo:9839

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