Bayesian Student-T Stochastic Volatility Models Via Scale Mixtures

The normal error distribution for the observations and log-volatilities in a stochastic volatility (SV) model is replaced by the Student-t distribution for robustness consideration. The model is then called the t-t SV model throughout this paper. The objectives of the paper are two-fold. Firstly, we introduce the scale mixtures of uniform (SMU) and the scale mixtures of normal (SMN) representations to the Student-t density and show that the setup of a Gibbs sampler for the t-t SV model can be simplified. For example, the full conditional distribution of the log-volatilities has a truncated normal distribution which enables an efficient Gibbs sampling algorithm. These representations also provide a means for outlier diagnostics. Secondly, we consider the so-called t SV model with leverage where the observations and log-volatilities follow a bivariate t distribution. Returns on exchange rates of Australian dollar to ten currencies are fitted by the t-t SV model and the t SV model with leverage, respectively