Regime-Switching and the Estimation of Multifractal Processes

42 Pages Posted: 3 Nov 2008

See all articles by Laurent E. Calvet

Laurent E. Calvet

SKEMA Business School; CEPR

Adlai J. Fisher

University of British Columbia (UBC) - Sauder School of Business

Multiple version iconThere are 4 versions of this paper

Date Written: March 2002


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.

Keywords: Forecasting, long memory, Markov regime-switching, maximum likelihood estimation, scaling, stochastic volatility, time deformation, volatility component, Vuong test

Suggested Citation

Calvet, Laurent E. and Fisher, Adlai J., Regime-Switching and the Estimation of Multifractal Processes (March 2002). NYU Working Paper No. FIN-02-064, Available at SSRN:

Laurent E. Calvet (Contact Author)

SKEMA Business School ( email )

5 Quai Marcel Dassault
Suresnes, 92150

CEPR ( email )

33 Great Sutton Street
London, EC1V 0DX
United Kingdom

Adlai J. Fisher

University of British Columbia (UBC) - Sauder School of Business ( email )

2053 Main Mall
Vancouver, BC V6T 1Z2
604-822-8331 (Phone)
604-822-4695 (Fax)


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