Estimation and forecasting in models with multiple breaks

This paper develops a new approach to change-point modelling that allows the number of change-points in the observed sample to be unknown. The model we develop assumes that regime durations have a Poisson distribution. It approximately nests the two most common approaches: the time-varying parameter (TVP) model with a change-point every period and the change-point model with a small number of regimes. We focus considerable attention on the construction of reasonable hierarchical priors both for regime durations and for the parameters that characterize each regime. A Markov chain Monte Carlo posterior sampler is constructed to estimate a version of our model, which allows for change in conditional means and variances. We show how real-time forecasting can be done in an efficient manner using sequential importance sampling. Our techniques are found to work well in an empirical exercise involving U.S. GDP growth and inflation. Empirical results suggest that the number of change-points is larger than previously estimated in these series and the implied model is similar to a TVP (with stochastic volatility) model.