Specific Markov-switching behaviour for ARMA parameters

Change-point (CP) and Markov-switching (MS) Auto-regressive models have been intensively discussed over the last two decades due to their flexibility and their relatively simple estimations. Although CP- and MS-ARMA models constitute a natural extension, they have been barely studied. The main reason comes from that classical inference fails when estimating these models. In particular the CP- and MS-ARMA models exhibit path dependence problem that renders the likelihood out of reach. We propose an estimation method that circumvents the issue. Our MCMC algorithm resting on the sticky in.finite hidden Markov-switching model (sticky IHMM) self-determines the number of regimes as well as the specification : CP or MS. Furthermore, the CP and MS frameworks usually assume that all the model parameters vary from one regime to another. We relax this restrictive assumption. As illustrated by simulations realized on moderate samples (300 observations), the sticky IHMM-ARMA algorithm detects which parameters of the model change over regimes. Applications to the U.S. GDP growth and the DJIA realized volatility highlight this flexibility by estimating different structural breaks for the mean and the variance parameters.