Bayesian Inference for Generalized Autoregressive Score Models

In this thesis I explore the benefits of adopting a Bayesian methodology when doing inference for generalized autoregressive score (GAS) models. Although analytical results regarding the form of the posterior or its conditional will generally not be available for this class of models, I show that for most simple GAS models several novel Markov chain Monte Carlo methods can be applied to enable accurate Bayesian inference in very reasonable time frames. I consider three illustrative empirical applications of GAS models where particular emphasize is placed on contrasting Bayesian inferences with those stemming from the traditional approach of estimating GAS models using the Maximum Likelihood (ML) method. I argue that there are certain complexities intrinsic to models in the GAS framework that can be dealt with far more naturally under a Bayesian methodology, such as (i) the non-nestedness of comparable models that arises as a consequence of the freedom of choice in scaling matrices and parametrization of GAS models and (ii) the “curse of dimensionality” problem that occurs primarily for multivariate GAS models. The logical Bayesian solution to the former is to apply Bayesian model comparison techniques - which I explore in the context of dynamic intensity factor models applied to credit rating data - whereas the later can be addressed by imposing additional structure on the parameter space using hierarchical prior setups - which I illustrate on a time-varying covariance GAS Student-t model. Additionally, I demonstrate how the typically high degree of non-linearity with which parameters enter the likelihood for GAS models cause slow convergence to the normal distribution for the parameters - as is highlighted for the Beta-Gen-t-EGARCH volatility model. Implying that considerable sample sizes are necessary to allow for valid appeals to the asymptotic convergence arguments used in ML estimation.