Change detection of hidden Markov models

Let θˆ_N denote the maximum-likelihood estimator of the true parameter θ* of a hidden Markov Model with fixed gain or forgetting rate λ. We establish an explicit formula for the error term θˆ_N - θ*. Using the representation of the error term we investigate the effect of parameter uncertainty on the performance of an adaptive encoding procedure. Using this result and ideas from the theory of stochastic complexity a change point detection method for HMM-s will be developed.