Moments of Markov switching models

This paper derives the moments for a range of Markov switching models. We characterize in detail the patterns of volatility, skewness and kurtosis that these models can produce as a function of the transition probabilities and parameters of the underlying state densities entering the switching process. The autocovariance of the level and squares of time series generated by Markov switching processes is also derived and we use these results to shed light on the relationship between volatility clustering, regime switches and structural breaks in time series models.