Bayesian Selection of Threshold Autoregressive Models

An approach to Bayesian model selection in self-exciting threshold autoregressive (SETAR) models is developed within a reversible jump Markov chain Monte Carlo (RJMCMC) framework. Our approach is examined via a simulation study and analysis of the Zurich monthly sunspots series. We find that the method converges rapidly to the optimal model, whilst efficiently exploring suboptimal models to quantify model uncertainty. A key finding is that the parsimony of the model selected is influenced by the specification of prior information, which can be examined and subjected to criticism. This is a strength of the Bayesian approach, allowing physical understanding to constrain the model selection algorithm