A Bayesian Analysis of Multiple Changes in the Variance of First-Order Autoregressive Time Series Models

The problem of a change in the mean of a sequence of random variables at an unknown time point has been addressed extensively in the literature. But, the problem of a change in the variance at an unknown time point has, however, been covered less widely. Hsu examines the problem of testing whether there has been a change in the variance at an unknown time point using sampling theory, and applies to stock return data and also give a Bayesian treatment of a similar problem. This paper analyses a sequence of first order autoregressive time series model in which the variance may have subjected to multiple changes at an unknown time points. Posterior distributions are found both for the unknown points of time at which the changes occurred and for the parameters of the model. A numerical example is discussed.