Bayes Inference via Gibbs Sampling of Autoregressive Time Series Subject to Markov Mean and Variance Shifts.

The authors examine autoregressive time series models subject to regime switching. A Bayesian framework is develope d in which the unobserved.states, one for each time point, are treated as missing data and then analyzed using the Gibbs sampler. This approac h is straightforward because the conditional posterior distribution of the parameters given the states, and the conditional posterior distribution of the states given the parameters, are amenable to simulation. The authors are able to generate marginal posterior distributions for all parameters of interest. Posterior distributio ns of the states, future observations, and the residuals, averaged over the parameter space, are also obtained. They illustrate the methodol ogy in several examples.