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

Posted: 29 Feb 2008

See all articles by Laurent E. Calvet

Laurent E. Calvet

EDHEC Business School - Department of Economics & Finance; CEPR

Adlai J. Fisher

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

Date Written: 2004

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.

Keywords: forecasting, long memory, Markov-switching multifractal (MSM), closed-form likelihood, scaling, stochastic volatility, volatility component, Vuong test

Suggested Citation

Calvet, Laurent E. and Fisher, Adlai J., How to Forecast Long-Run Volatility: Regime Switching and the Estimation of Multifractal Processes ( 2004). Journal of Financial Econometrics, Vol. 2, Issue 1, pp. 49-83, 2004. Available at SSRN: https://ssrn.com/abstract=821714

Laurent E. Calvet (Contact Author)

EDHEC Business School - Department of Economics & Finance ( email )

France

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
Canada
604-822-8331 (Phone)
604-822-4695 (Fax)

HOME PAGE: http://finance.sauder.ubc.ca/~fisher

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