FIN-02-064 |
NYU Stern School of Business |
Regime-Switching and the Estimation of Multifractal Processes
December 2002
Laurent Calvet and 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 gen-erate
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 de-veloped
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 favor-ably
to earlier specifications both in- and out-of-sample. Multifractal
forecasts slightly improve on GARCH(1,1) at daily and weekly inter-vals,
and provide considerable gains in accuracy at horizons of 10 to
50 days.
Laurent Calvet
Institution: Stern School of Business, New York University, 44 West 4th Street, New York, NY 10012
Email: lcalvet@stern.nyu.edu
Homepage:http://www.stern.nyu.edu/~lcalvet
Adlai Fisher
Institution: Faculty of Commerce, Department of British Columbia
Email: adlai.fisher@commerce.ubc.ca
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