Stationnarité des modèles ARMA à changement de régime markovien

In this Note we consider multivariate ARMA models subject to Markov-switching. In these models, the parameters are allowed to depend on the state of an unobserved Markov chain. The methods developed in the statistical literature for estimating these models, typically impose local stationarity conditions, i.e., stationarity within each regime. We show that the local stationarity of the observed process is neither sufficient nor necessary to obtain the global stationarity. We derive stationarity conditions and we compute the autocovariance function of this nonlinear process. Some examples are proposed to illustrate the stationarity conditions.