Estimation of Multivariate Stochastic Volatility Models: A Comparative Monte Carlo Study

In this paper, we compare the small sample performances of Quasi Maximum Likelihood (QML) and Monte Carlo Likelihood (MCL) methods through Monte Carlo studies for several multivariate stochastic volatility models, among which we consider two new models that account for leverage effects. Our results confirm previous findings within the literature, namely, that the MCL estimator has better finite sample performance compared to the QML estimator. QML estimator's performance is closer to that of MCL estimator when the volatility processes have higher variance or when the correlations are high and/or time varying, but it performs relatively worse when leverage is introduced. Finally, we include an empirical illustration by estimating an MSV model with leverage using a trivariate data from the major European stock markets.