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Prediction of Chaotic Time Series in the Presence of Measurement Error: the Importance of Initial Conditions

Author

Listed:
  • Dominique Guegan

    (Département Mathématiques Mécanique et Informatique - URCA - Université de Reims Champagne-Ardenne)

  • Rolf Tschernig

    (HU Berlin - Humboldt-Universität zu Berlin = Humboldt University of Berlin = Université Humboldt de Berlin)

Abstract

n this paper we argue that even if a dynamic relationship can be well described by a deterministic system, retrieving this relationship from an empirical time series has to take into account some, although possibly very small measurement error in the observations. Therefore, measuring the initial conditions for prediction may become much more difficult since one now has a combination of deterministic and stochastic elements. We introduce a partial smoothing estimator for estimating the unobserved initial conditions. We will show that this estimator allows to reduce the effects of measurement error for predictions although the reduction may be small in the presence of strong chaotic dynamics. This will be illustrated using the logistic map.

Suggested Citation

  • Dominique Guegan & Rolf Tschernig, 2001. "Prediction of Chaotic Time Series in the Presence of Measurement Error: the Importance of Initial Conditions," Post-Print halshs-00194303, HAL.
    • Handle: RePEc:hal:journl:halshs-00194303
    DOI: 10.1023/A:1016608506110
    as

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