How to Forecast Long-Run Volatility: Regime Switching and the Estimation of Multifractal Processes
Posted: 29 Feb 2008
Date Written: 2004
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
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