Asymptotic smoothing errors for hidden Markov models

In this paper, the asymptotic smoothing error for hidden Markov models (HMM s) is investigated using hypothesis testing ideas. A family of HMMs is stud ied parametrised by a positive constant epsilon, which is a measure of the frequency of change. Thus, when epsilon --> 0, the HMM becomes increasingly slower moving. We show that the smoothing error is O(epsilon). These theor etical predictions ate confirmed by a series of simulations.