  An autoregressive process with Markov regime is an autoregressive process for
which the regression function at each time point is given by a nonobservable
Markov chain. In this paper we consider the asymptotic properties of the
maximum likelihood estimator in a possibly nonstationary process of this kind
for which the hidden state space is compact but not necessarily finite.
Consistency and asymptotic normality are shown to follow from uniform
exponential forgetting of the initial distribution for the hidden Markov chain
conditional on the observations.
