BUGS for a Bayesian analysis of stochastic volatility models

This paper reviews the general Bayesian approach to parameter estimation in stochastic volatility models with posterior computations performed by Gibbs sampling. The main purpose is to illustrate the ease with which the Bayesian stochastic volatility model can now be studied routinely via BUGS (Bayesian inference using Gibbs sampling), a recently developed, user-friendly, and freely available software package. It is an ideal software tool for the exploratory phase of model building as any modifications of a model including changes of priors and sampling error distributions are readily realized with only minor changes of the code. However, due to the single move Gibbs sampler, convergence can be slow. BUGS automates the calculation of the full conditional posterior distributions using a model representation by directed acyclic graphs. It contains an expert system for choosing an effective sampling method for each full conditional. Furthermore, software for convergence diagnostics and statistical summaries is available for the BUGS output. The BUGS implementation of a stochastic volatility model is illustrated using a time series of daily Pound/Dollar exchange rates.