MCMC methods for comparing stochastic volatility and GARCH models

This paper presents Markov chain Monte Carlo and importance sampling techniques for volatility estimation, model misspecification testing and comparisons for general volatility models, including GARCH and stochastic volatility formulations. Integrated model likelihoods are estimated and employed to compare among competing classes of volatility model. The performance of some GARCH and stochastic volatility models, incorporating fat-tailed errors and Markov switching, is compared for the S&P500 daily return index and the US/Canadian dollar exchange rate. The comparison is made using integrated likelihoods and residuals, incorporating parameter uncertainty and some model uncertainty. Simulation studies are carried out to confirm that the Bayesian approach is reliable for these models.