A Reversible Jump Sampler for Autoregressive Time Series, Employing Full Conditionals to Achieve Efficient Model Space Moves

Introduction When fitting an autoregressive model to Gaussian time series data, often the correct order of the model is unknown. The model order cannot be estimated analytically by conventional Bayesian techniques when the excitation variance is unknown. We present MCMC methods for drawing samples from the joint posterior of all the unknowns, from which Monte Carlo estimates of the quantities of interest can be made, with the possibility of model mixing, if required, for tasks such as prediction, interpolation, smoothing or noise reduction. Previous work on MCMC autoregressive model selection has parameterised the model using partial correlation coefficients (Barnett, Kohn & Sheather 1996, Barbieri & O'Hagan 1996) or pole positions 1 (Huerta & West 1997). These have a simple physical interpretation for certain types of signal, and allow stationarity to be enforced in a straightforward manner. We use the AR parameters, a, directly. This allow