  The stochastic volatility model is a popular tool for modeling the volatility
of assets. The model is a nonlinear and non-Gaussian state space model, and
consequently is difficult to fit. Many approaches, both classical and Bayesian,
have been developed that rely on numerically intensive techniques such as
quasi-maximum likelihood estimation and Markov chain Monte Carlo (MCMC).
Convergence and mixing problems still plague MCMC algorithms when drawing
samples sequentially from the posterior distributions. While particle Gibbs
methods have been successful when applied to nonlinear or non-Gaussian state
space models in general, slow convergence still haunts the technique when
applied specifically to stochastic volatility models. We present an approach
that couples particle Gibbs with ancestral sampling and joint parameter
sampling that ameliorates the slow convergence and mixing problems when fitting
both univariate and multivariate stochastic volatility models. We demonstrate
the enhanced method on various numerical examples.
