Univariate and Multivariate Stochastic Volatility Models : Estimation and Diagnostics

A Maximum Likelihood (ML) approach based upon an Efficient Importance Sampling (EIS) procedure is used to estimate several extensions of the standard Stochastic Volatility (SV) model for daily financial return series. EIS provides a highly generic procedure for a very accurate Monte Carlo evaluation of the marginal likelihood which depends upon high-dimensional interdependent integrals. Extensions of the standard SV model being analyzed only require minor modifications in the ML-EIS procedure. Furthermore, EIS can also be applied for filtering which provides the basis for several diagnostic tests. Our empirical analysis indicates that extensions such as a semi-nonparametric specification of the error term distribution in the return equation dominate the standard SV model. Finally, we also apply the ML-EIS approach to a multivariate factor model with stochastic volatility