A Proof Of Consistency Of The Mle For Nonlinear Markov-Switching Ar Processes

We propose a new approach to demonstrate the consistency of the maximum likelihood estimator for nonlinear Markov-switching AR processes (abbreviated MS-NAR). We obtain a uniform exponential memory loss property for the prediction filter by approximating it by a filter with finite memory. From the α-mixing property for the MS-NAR process we obtain an ergodic theorem. Finally, we show that in the linear and Gaussian case our assumptions are fully satisfied.