  The advantages of sequential Monte Carlo (SMC) are exploited to develop
parameter estimation and model selection methods for GARCH (Generalized
AutoRegressive Conditional Heteroskedasticity) style models. It provides an
alternative method for quantifying estimation uncertainty relative to classical
inference. Even with long time series, it is demonstrated that the posterior
distribution of model parameters are non-normal, highlighting the need for a
Bayesian approach and an efficient posterior sampling method. Efficient
approaches for both constructing the sequence of distributions in SMC, and
leave-one-out cross-validation, for long time series data are also proposed.
Finally, an unbiased estimator of the likelihood is developed for the Bad
Environment-Good Environment model, a complex GARCH-type model, which permits
exact Bayesian inference not previously available in the literature.
