Multivariate Wishart Stochastic Volatility and Changes in Regime

Abstract

This paper generalizes the basic Wishart multivariate stochastic volatility model of Philipov and Glickman (2006) and Asai and McAleer (2009) to encompass regime switching behavior. The latent state variable is driven by a first-order Markov process. The model allows for state-dependent (co)variance and correlation levels and state-dependent volatility spillover effects. Parameter estimates are obtained using Bayesian Markov Chain Monte Carlo procedures and filtered estimates of the latent variances and covariances are generated by particle filter techniques. The model is applied to five European stock index return series. The results show that the proposed regime-switching specification substantially improves the in-sample fit and the VaR forecasting performance relative to the basic model.