Nonlinear Smoother for Stochastic Volatility Model

A new technique for nonlinear state and parameter estimation of the discrete time stochastic volatility models in the state space form is developed. The Gibbs sampler is used to construct a Markov-chain simulation tool that reflects both inherent model variability and parameter uncertainty. The Gibbs sampling algorithm is derived from the generalized data-augmentation method and the iterative Monte Carlo simulation procedures to calculating marginal state and parameters probability density functions. The design algorithm generates a loop where samples from the correspondent data augmented probability density functions are drawn. The proposed chain converges to equilibrium enabling to summarize the unobserved variance states and unknown model parameters distributions. The non-Gaussian density of the log of squared innovations is advantageously modelled as a mixture of Gaussians.