Autocovariance and Linear Transformations of Markov Switching VARMA Processes

We study the autocovariance structure of a general Markov switching second-order stationary VARMA model. Then we give stable finite order VARMA(p*, q*) representations for those M-state Markov switching VARMA(p, q) processes where the observables are uncorrelated with the regime variables. This allows us to obtain sharper bounds for p* and q* with respect to the ones existing in literature. Our results provide new insights into stochastic properties and facilitate statistical inference about the orders of MS-VARMA models and the underlying number of hidden states.