Estimating and forecasting structural breaks in financial time series

We present an algorithm, based on a differential evolution MCMC method, for Bayesian inference in AR-GARCH models subject to an unknown number of structural breaks at unknown dates. Break dates are directly treated as parameters and the number of breaks is determined by the marginal likelihood criterion. We prove the convergence of the algorithm and we show how to compute marginal likelihoods. We allow for both pure change-point and recurrent regime specifications and we show how to forecast structural breaks. We illustrate the efficiency of the algorithm through simulations and we apply it to eight financial time series of daily returns over the period 1987-2011. We find at least three breaks in all series.