Forecasting Volatility under Multivariate Stochastic Volatility Model via Reprojection

This paper evaluates the performance of volatility forecasting based on stochastic volatility (SV) models. We show that the choice of squared asset-return residuals as a proxy for ex-post volatility directly leads to extremely low explanatory power in the common regression analysis of volatility forecasting. We argue that, since the measure of volatility is always model dependent, the performance of volatility forecasting should be evaluated in a consistent modeling framework. This paper provides several main contributions. First, we apply the EMM estimation method proposed by Gallant and Tauchen (1996) to estimate the multivariate SV model of asset returns. Second, we extend implementation of the underlying volatility reprojection technique proposed by Gallant and Tauchen (1998) to the estimated multivariate SV model. Finally, we illustrate that the performance of volatility forecasting based on the reprojected volatility series can be substantially improved. Furthermore, we show that the volatility forecasting performance based on the multivariate SV model is an improvement over that of univariate SV models due to the correlated movements of asset return volatility.