Bayesian analysis of the conditional correlation between stock index returns with multivariate stochastic volatility models

In the paper we compare the modelling ability of discrete-time multivariate Stochastic Volatility (SV) models to describe the conditional correlations between stock index returns. We consider four tri-variate SV models, which differ in the structure of the conditional covariance matrix. Specifications with zero, constant and time-varying conditional correlations are taken into account. As an example we study tri-variate volatility models for the daily log returns on the WIG, S&P 500, and FTSE 100 indexes. In order to formally compare the relative explanatory power of SV specifications we use the Bayesian principles of comparing statistic models. Our results are based on the Bayes factors and implemented through Markov Chain Monte Carlo techniques. The results indicate that the most adequate specifications are those that allow for time-varying conditional correlations and that have as many latent processes as there are conditional variances and covariances. The empirical results clearly show that the data strongly reject the assumption of constant conditional correlations.