A Bayesian time series model of multiple structural changes in level, trend, and variance

We consider a deterministically trending dynamic time series model in which multiple structural changes in level, trend, and error variance are modeled explicitly and the number, but not the timing, of the changes is known. Estimation of the model is made possible by the use of the Gibbs sampler. The determination of the number of structural breaks and the form of structural change is considered as a problem of model selection, and we compare the use of marginal likelihoods, posterior odds ratios, and Schwarz's Bayesian model-selection criterion to select the most appropriate model from the data. We evaluate the efficacy of the Bayesian approach using a small Monte Carlo experiment. As empirical examples, we investigate structural changes in the U.S. ex post real interest rate and in a long time series of U.S. real gross domestic product.