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Metrika

, Volume 19, Issue 1, pp 178–184 | Cite as

Expolynomial smoothing of autocorrelated time series

  • M. Roubens
Article
  • 33 Downloads

Summary

In the following, causal pattern buried in autocorrelated noise is considered. The causal pattern may be described by models such as trends, polynomial trajectories, growing sines. Based on a new criterion — called expolynomial — estimators of coefficients of a polynomial model are obtained. Characteristic functions of the estimators are derived and the first two moments calculated. Continuous time series are briefly studied to show similarities between discrete and continuous observations. Popular exponential smoothing is a special case of the expolynomial smoothing.

Keywords

Time Series Stochastic Process Sine Characteristic Function Probability Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Brown, R. G.: Smoothing, Forecasting and Prediction of Discrete Time Series. Prentice-Hall, Inc. 1963.Google Scholar
  2. Erdelyi, A., et al.: Higher Transcendental Functions (Vol. 2.). McGraw-Hill, New York, 1953.Google Scholar
  3. Meyer, R. F.: An Adaptive Method for Routine Short-Term Forecasting. Paper presented at the 3rd International Conference on Operations Research, Oslo, July 1963.Google Scholar
  4. Roubens, M.: Sur le lissage exponentiel d'un signal polynomial brouillé. Paper presented at the European Meeting on Statistics, Econometrics and Management Science, Amsterdam, October 1968.Google Scholar
  5. Roubens, M.: Le lissage exponentiel d'un signal polynomial brouillé observé de manière discrète ou continue. Revue de Statistique Appliquée, 17, 1969.Google Scholar

Copyright information

© Physica-Verlag Rudolf Liebing KG 1972

Authors and Affiliations

  • M. Roubens
    • 1
  1. 1.Faculté Polytechnique de MonsMonsBelgium

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