Gibbs sampler to stochastic volatility models

A new technique for nonlinear state and parameter estimation of the discrete time stochastic volatility models in which the logarithm of the asset return conditional variance follows an autoregressive model has been developed. The Gibbs sampling algorithm is used to construct a Markov-chain simulation tool that reflects both inherent model variability and parameter uncertainty. The proposed chain converges to an equilibrium making it possible to summarize the distributions of the unobserved volatilities and the unknown model parameters. The non-Gaussian density of the log of squared innovations is advantageously modelled as a mixture of Gaussians.