Infinite hidden markov switching VARs with application to macroeconomic forecast

Abstract

This paper develops vector autoregressive models with infinite hidden Markov structures, motivated by the recent empirical success of hierarchical Dirichlet process mixture models in financial and macroeconomic applications. We begin by developing a new Markov chain Monte Carlo (MCMC) method that is built upon precision-based algorithms, in order to improve the computational efficiency. We then investigate the forecast performances of these infinite hidden Markov switching models. Our forecasting results suggest that (1) models with separate infinite hidden Markov processes for the VAR coefficients and the volatilities generally forecast better than other specifications of infinite hidden Markov switching models; (2) using a single infinite hidden Markov process to govern all model parameters tends to result in poor forecasts; (3) most of the gains obtained when forecasting the inflation rate and GDP growth seem to come from allowing for time-variation in the volatilities rather than in the conditional mean coefficients. In contrast, when forecasting the short-term interest rate it is important to allow time-variation in all model parameters.