Bayes regression with autoregressive errors. A Gibbs sampling approach

This paper develops a practical framework for the Bayesian analysis of Gaussian and Student-t regression models with autocorrelated errors. As is customary in classical estimation procedures, the posteriors are conditioned on the initial observations. Recourse is taken to the method of Gibbs sampling, an iterative Markovian sampling method, and it is shown that the proposed approach can readily deal with high-order autoregressive processes without requiring an importance sampling function or other tuning constants. Several examples, including one with AR(4) errors, are used to illustrate the ideas.