Efficient Bayesian Inference for Stochastic Volatility Models

This talk considers Bayesian inference for stochastic volatility (SV) models using efficient MCMC inference. Our method is based on the popular approximation of the log $\chi^2$-distribution by a mixture of 10 normal distributions which allows to sample the latent volatilities simultaneously, however, we introduce several improvements. First, rather than using standard forward-filtering-backward-sampling to draw the volatilities, we apply a sparse Cholesky factor algorithm to the high-dimensional joint density of all volatilities. This reduces computing time considerably because it allows joint sampling without running a filter. Second, we consider various reparameterizations of the augmented SV model. Under the standard parameterization, augmented MCMC estimation turns out to be inefficient, especially if the volatility of volatility parameter in the latent state equation is small. By considering a non-centered version of the SV model, this parameter is moved to the observation equation. Using MCMC estimation for this transformed model reduces the inefficiency factor in particular for the volatility of volatility parameter considerably.