Paul T. Troughton and Simon J. Godsill. A reversible jump sampler for autoregressive time series, employing full conditionals to achieve efficient model space moves. Technical Report CUED/F-INFENG/TR.304, Cambridge University Engineering Department, 1997.

We use reversible jump Markov chain Monte Carlo (MCMC) methods to address the problem of model order uncertainty in autoregressive (AR) time series within a Bayesian framework. Efficient model jumping is achieved by proposing model space moves from the the full conditional density for the AR parameters, which is obtained analytically. This is compared with an alternative method, for which the moves are cheaper to compute, in which proposals are made only for the new parameters in each move. Results are presented for both synthetic and audio time series.