Hidden Markov models (HMMs) have during the last decade become a widespread
tool for modeling sequences of dependent random variables. Inference for s
uch models is usually based on the maximum-likelihood estimator (MLE), and
consistency of the MLE for general HMMs was recently proved by Leroux. In t
his paper me show that under mild conditions the MLE is also asymptotically
normal and prove that the observed information matrix is a consistent esti
mator of the Fisher information.