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.