Asymptotic properties of the maximum likelihood estimator in autoregressive
models with Markov regime
Randal Douc, Èric Moulines and Tobias Rydén
Centre for Mathematical Sciences
Lund Institute of Technology,
An autoregressive process with Markov regimes is an autoregressive process
for which the regression function at each time point is given by a non-observable
Markov chain. In this paper we consider the asymptotic properties of the
maximum likelihood estimator in a possibly non-stationary process of this
kind for which the hidden state space in 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.
asymptotic normality, autoregressive process, consistency, geometric ergodicity,
hidden Markov model, identifiability, maximum likelihood, switching