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Generalized adaptive exponential smoothing procedures

Published online by Cambridge University Press:  14 July 2016

Ulrich Herkenrath
Ulrich Herkenrath*
Affiliation:
University of Duisburg
*
∗ Postal address: Fachbereich 11 Mathematik, Universität Duisburg, Postfach 10 15 03, D-47048 Duisburg, Germany.
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Abstract

The classical exponential smoothing procedure to be applied to a sequence of observations is modified into some adaptive variants and also generalized to the recursive scheme

This means that given the history of observations and smoothed values up to time n, the updated smoothed value Wn +1 is given by a function u of Wn and Xn, which satisfies only certain structural properties. We study these procedures within the framework of random systems with complete connections and exploit results from Markov process theory to study the sequence . A broad class of ‘smoothing functions' u, which induce sequences with nice statistical properties, is presented. A method to estimate the limit of the expected smoothed values is also developed.,

Keywords

ADAPTIVE SMOOTHINGEXPONENTIAL SMOOTHINGRANDOM SYSTEMS WITH COMPLETE CONNECTIONSMARKOV CHAINS
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 3 , September 1994 , pp. 673 - 690
Copyright
Copyright © Applied Probability Trust 1994 

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References

Bonsdorff, H. (1989) A comparison of the ordinary and a varying parameter exponential smoothing. J. Appl. Prob. 26, 784–792.CrossRefGoogle Scholar
Brown, R. G. (1963) Smoothing, Forecasting and Prediction of Discrete Time Series. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
Doob, J. L. (1953) Stochastic Processes. Wiley, New York.Google Scholar
Gardner, E. S. Jr. (1985) Exponential smoothing: the state of the art. J. Forecasting 4, 1–28.CrossRefGoogle Scholar
Iosifescu, M. and Grigorescu, S. (1990) Dependence with Complete Connections and its Applications. Cambridge University Press.Google Scholar
Iosifescu, M. and Theodorescu, R. (1969) Random Processes and Learning. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Norman, M. F. (1972) Markov Processes and Learning Models. Academic Press, New York.Google Scholar
Nummelin, E. (1984) General Irreducible Markov Chains and Non-negative Operators. Cambridge University Press.CrossRefGoogle Scholar
Richter, H. (1956) Wahrscheinlichkeitstheorie. Springer-Verlag, Berlin.CrossRefGoogle Scholar