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Error Estimate for Retrieving Parameters of a Nonlinear Map from Noisy Chaotic Time Series

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Radiophysics and Quantum Electronics Aims and scope

Abstract

We consider the problems of accuracy in retrieving nonlinear maps from noisy data and the quality of prediction based on the retrieved low-dimensional models. It is shown that there exists an optimal sample length which minimizes the map-retrieval error and, hence, maximizes the forecast period. General conclusions are illustrated by the example of retrieving a fourth-power polynomial map using the “exact,” truncated, and excessive models.

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Authors and Affiliations

  1. Vladimir State University, Vladimir, Russia

    O. Ya. Butkovsky & M. Yu. Logunov

  2. Space Research Institute of the Russian Academy of Sciences, Moscow, Russia

    Yu. A. Kravtsov

  3. Space Research Center of the Polish Academy of Sciences, Warsaw, Poland

    Yu. A. Kravtsov

Authors
  1. O. Ya. Butkovsky
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  2. Yu. A. Kravtsov
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  3. M. Yu. Logunov
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Butkovsky, O.Y., Kravtsov, Y.A. & Logunov, M.Y. Error Estimate for Retrieving Parameters of a Nonlinear Map from Noisy Chaotic Time Series. Radiophysics and Quantum Electronics 45, 48–58 (2002). https://doi.org/10.1023/A:1015244623440

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