Inference in hidden Markov models I: Local asymptotic normality in the stationary case

Following up on work by Baum and Petrie published 30 years ago, we study likelihood-based methods in hidden Markov models, where the hiding mechanism can lead to continuous observations and is itself governed by a parametric model. We show that procedures essentially equivalent to maximum likelihood estimates are asymptotically normal as expected and consistent estimates of their variance can be constructed, so that the usual inferential procedures are asymptotically valid.