Generalized Adaptive Exponential Smoothing of Ergodic Markovian Observation Sequences
An exponential smoothing procedure applied to a homogeneous Markovian oberservation sequence generates an inhomogeneous Markov process as sequence of smoothed values. If the underlying observation sequence is moreover ergodic then for two classes of smoothing functions the strong ergodicity of the sequence of smoothed values is proved. As a consequence a central limit theorem and a law of large numbers hold true for the smoothed values. The proof uses general results for so-called convergent inhomogeneous Markov processes. In the literature a lot fo time series are discussed to which the smoothing procedures are applicable.