MPS-RR 1999-7
February 1999

Asymptotic normality of the maximum likelihood estimator in state space models

Jens Ledet Jensen

Niels Væver Petersen

Abstract

State space models is a very general class of time series models capable of modeling dependent observations in a natural and interpretable way. Inference in such models have been studied by Bickel et al., who consider hidden Markov models, which are a special kind of state space models, and prove that the maximum likelihood estimator is asymptotically normal under mild regularity conditions. In this paper we generalize the results of Bickel et al. to state space models, where the latent process is a continuous state Markov chain satisfying regularity conditions, which are fulfilled if the latent process takes values in a compact space.

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