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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 1999-7
February 1999

Asymptotic normality of the maximum likelihood estimator in state space models


Jens Ledet Jensen

Niels Væver Petersen


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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This paper has now been published in Ann. Statist. 27 (1999), no. 2, 514--535