Time Varying Transition Probabilities for Markov Regime Switching Models

We propose a new Markov switching model with time varying probabilities for the transitions. The novelty of our model is that the transition probabilities evolve over time by means of an observation driven model. The innovation of the time varying probability is generated by the score of the predictive likelihood function. We show how the model dynamics can be readily interpreted. We investigate the performance of the model in a Monte Carlo study and show that the model is successful in estimating a range of different dynamic patterns for unobserved regime switching probabilities. We also illustrate the new methodology in an empirical setting by studying the dynamic mean and variance behaviour of U.S. Industrial Production growth. We find empirical evidence of changes in the regime switching probabilities, with more persistence for high volatility regimes in the earlier part of the sample, and more persistence for low volatility regimes in the later part of the sample. Some key words: Hidden Markov Models; observation driven models; generalized autoregressive score dynamics. JEL classification: C22, C32. ∗The authors thank participants of the “2014 Workshop on Dynamic Models driven by the Score of Predictive Likelihoods”, La Laguna, and seminar participants and VU University Amsterdam for useful comments and discussions. Blasques and Lucas thank the Dutch Science Foundation (NWO, grant VICI45309-005) for financial support. Koopman acknowledges support from CREATES, Center for Research in Econometric Analysis of Time Series (DNRF78), funded by the Danish National Research Foundation.