Specific Markov-switching behaviour for ARMA parameters

We propose an estimation method that circumvents the path dependence problem existing in Change-Point (CP) and Markov Switching (MS) ARMA models. Our model embeds a sticky infinite hidden Markov-switching structure (sticky IHMM), which makes possible a self-determination of the number of regimes as well as of the specification : CP or MS. Furthermore, 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 on moderate samples (300 observations), the sticky IHMM-ARMA algorithm detects which model parameters change over time. Applications to the U.S. GDP growth and the DJIA realized volatility highlight the relevance of estimating different structural breaks for the mean and variance parameters.