Duration Dependent Markov-Switching Vector Autoregression: Properties, Bayesian Inference and Application to the Analysis of the U.S. Business Cycle

Duration dependent Markov-switching VAR (DDMS-VAR) models are time series models with data generating process consisting in a mixture of two VAR processes. The switching between the two VAR processes is governed by a two state Markov chain with transition probabilities that depend on how long the chain has been in a state. In the present paper we analyze the second order properties of such models and propose a Markov chain Monte Carlo algorithm to carry out Bayesian inference on the model's unknowns. The methodology is then applied to the analysis of the U.S. business cycle. The model replicates rather well the NBER dating, and we find strong evidence against duration dependence in expansion phases. As for contractions, there is a very weak evidence in favor of duration dependence. This uncertainty is, however, coherent with the low number of recessions (seven) present in our dataset.