Multivariate Wishart Stochastic Volatility Models

We generalize the basic Wishart multivariate stochastic volatility model of Philipov and Glickmann (2006) to encompass regime switching behavior. The latent state variable is driven by a first-order Markov process. In order to estimate the proposed model we use Bayesian Markov Chain Monte Carlo procedures. For the computation of filtered estimates of the latent variances and covariances we rely upon particle filter techniques. The model is applied to five European stock index returns. Our results show that our proposed regime-switching specification substantially improves the estimates of the conditional covariance matrix and the VaR performance relative to the basic model.