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

A. Fisher, L. E. CALVET

Journal of Financial Econometrics

Spring 2004, vol. 2, n°1, pp.49-83

Departments: Finance

Keywords: Forecasting, Long Memory, Markov-switching multifractal (MSM), Closed-form likelihood, Scaling , Stochastic volatility, Volatility component, Vuong test

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