Asymptotic smoothing errors for hidden Markov models

In this paper, the asymptotic smoothing error for hidden Markov models (HMMs) is investigated using hypothesis testing ideas. A family of HMMs is studied 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 theoretical predictions are confirmed by a series of simulations.