TY  - JOUR
AU  - Calvet,Laurent
AU  - Fisher,Adlai
TI  - Regime-Switching and the Estimation of Multifractal Processes
JF  - National Bureau of Economic Research Working Paper Series
VL  - No. 9839
PY  - 2003
Y2  - July 2003
UR  - http://www.nber.org/papers/w9839
L1  - http://www.nber.org/papers/w9839.pdf
N1  - Author contact info:
Laurent E. Calvet
Department of Finance
HEC Paris
1 rue de la Libération
78351 Jouy en Josas
France
Tel: +33 13 967 9409
Fax: +33 13 967 7085
E-Mail: calvet@hec.fr

Adlai Fisher
Sauder School of Business
University of British Columbia
2053 Main Mall, Vancouver BC, CANADA
V6T 1Z2
Tel: 604 822 8331
Fax: 604 822 4695
E-Mail: adlai.fisher@sauder.ubc.ca
AB  - 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.
ER  -