In this paper, Markov chain Monte Carlo sampling methods are exploited to provide a
unified, practical likelihood-based framework for the analysis of stochastic volatility models. A
highly effective method is developed that samples all the unobserved volatilities at once using an
approximating offset mixture model, followed by an importance reweighting procedure. This
approach is compared with several alternative methods using real data. The paper also develops
simulation-based methods for filtering, likelihood evaluation and model failure diagnostics. The
issue of model choice using non-nested likelihood ratios and Bayes factors is also investigated.
These methods are used to compare the fit of stochastic volatility and GARCH models. All the
procedures are illustrated in detail.
