Generalized Adaptive Exponential Smoothing of Ergodic Markovian Observation Sequences

An exponential smoothing procedure applied to a homogeneous Markovian observation 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 of time series are discussed to which the smoothing procedures are applicable. Smoothing of non-linear time series; Generalized exponential smoothing; Convergent Inhomogeneous Markov processes AMS 1991 Subject Classification: Primary 60J20 Secondary 62M10 1Postal address: Fachbereich 11 Mathematik, Gerhard-Mercator-Universitat | GH Duisburg, Postfach 10 15 03, D-47048 Duisburg