Bayesian Estimation in Autoregressive Models Using Reversible Jump Markov Chain Monte Carlo

In most applications, there is uncertainty about the statistical model to be considered. In this paper, we consider a particular class of autoregressive time series models where the order of the model---which determines the dimension of parameter---is uncertain. A common approach for model selection is to balance model fit with model complexity using, say, an AIC criterion. However, such an approach provides no meaningful measure of uncertainty about the selected model. A Bayesian approach, on the other hand, which treats the model and model parameters as random variables, can directly accommodate model uncertainty. The challenge is that the Bayesian posterior distribution is supported on a union of spaces of different dimensions, which makes computation difficult. We review a reversible jump Markov chain Monte Carlo method for sampling from the posterior, and apply this method to provide a Bayesian analysis of simulated and real data