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A numerical comparison of non-linear with linear prediction for the transformed Ornstein-Uhlenbeck process

  • K. Helmes
Part II: Research Reports
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 16)

Abstract

For a class of stationary processes which are defined by polynomial functions of the Ornstein-Uhlenbeck process we investigate what advantages can be expected in passing from optimal linear prediction to non-linear prediction. By "optimal" we mean the square error of prediction to be minimized. Using the SUMT algorithm as well as the VF02AD program of the Harwell Subroutine Library we computed the maximum relative error difference between both kinds of prediction. It turned out that it may be possible to achieve an improvement of up to 20% by using the best non-linear predictor.

Keywords

Covariance Function Linear Prediction Hermite Polynomial Maximum Relative Error Error Improvement 
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. [1]
    Donelson, J. and Maltz, F.: A comparison of linear versus non-linear prediction for polynomial functions of the Ornstein-Uhlenbeck process, J. Appl. Prob. 9, 725–744 (1972).Google Scholar
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    Magnus, W., Oberhettinger, F. and Soni, R.P.: Formulas and theorems for the special functions of mathematical physics, 3. ed., Berlin, Heidelberg: Springer Verlag 1966.Google Scholar
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    Yaglom, A.M.: Optimal non-linear extrapolation, Selected Translation in Mathematical Statistics and Probability, 273–298, Amer. Math. Soc., Providence, R.I. 1971.Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • K. Helmes
    • 1
  1. 1.Institut für Angewandte MathematikUniversität BonnGermany

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