WORKSHOP
IN STATISTICAL MIXTURES AND LATENT-STRUCTURE MODELLING
International Centre
for Mathematical Sciences, Edinburgh, March 28 - March 30,
2000
E. Moulines, Ecole Nationale Supérieure
des Télécommunications (ENST), Paris
`Asymptotic properties of the maximum likelihood
estimator in autoregressive models with Markov regime'
An autoregressive
process with Markov regime 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 for a possibly non-stationary autoregressive process with Markov
regime where the hidden state space is separable and compact but not necessarily
finite. Consistency and asymptotic normality are shown to follow from the
uniform exponential forgetting of the initial distribution for the hidden
Markov chain conditional on the observations. Numerical implementations
of the maximum likelihood estimators based on Markov chain Monte Carlo
and the particle filters will also be discussed.
