A Markov-switching regression model with non-Gaussian innovations: estimation and testing

In this paper we propose a very general multivariate Markov-switching regression (MSR) model considering the Normal Inverse Gaussian (NIG) distribution as conditional form of financial returns and model innovations. It is indeed well-known that the Gaussian distribution is not able to capture many stylized facts of the return series such as negative skewness, excess kurtosis and heavy tails. Through a large simulation study and an empirical analysis of the U.S. stock market, we show that a NIG-based MSR model allows to adequately account for both skewness and fat tails in the data and, according to model selection criteria, is the best overall model in the majority of cases considered, even preferred over other popular distributional assumptions such as Student-t and GED. We develop an EM algorithm which allows the estimation of the model parameters in closed form. As a natural byproduct of the algorithm we also derive the scores of the model estimators that allows us to perform dynamic specification tests to check for autocorrelation and for the violation of the first-order Markov assumption.