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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 ε, which is a measure of the frequency of change. Thus, when ε→0, the HMM becomes increasingly slower moving. We show that the smoothing error is O(ε). These theoretical predictions are confirmed by a series of simulations.