Time-Varying Covariances: A Factor Stochastic Volatility Approach

We propose a factor model which allows a parsimonious representation of the time series evolution of covariances when the number of series being modelled becomes very large. The factors arise from a standard stochastic volatility model as does the idiosyncratic noise associated with each series. We use an efficient method for deriving the posterior distribution of the parameters of this model. In addition we propose an effective method of Bayesian model selection for this class of models. Finally, we consider diagnostic measures for specific models