Asymptotical statistics of misspecified HMM

Deals with the fitting of hidden Markov models to data generated by ergodic stochastic processes. More specifically we consider the problem of fitting a family of partially observed finite state Markov chain parameters (or hidden Markov models, HMMs) with continuous output to an ergodic process, with continuous values, which is not necessarily a member of the family. In this context we derive the main asymptotic results: almost sure consistency, asymptotic normality and rate of convergence of the MLE estimator.