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Statistical estimation of the Embedding Dimension of a dynamical system

Author

Listed:
  • D. Boscq

    (ISUP - Institut de Statistique de Sorbonne Université - SU - Sorbonne Université)

  • Dominique Guegan

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique)

  • Guillaume Léorat

    (SLP Infoware - SLP Infoware)

Abstract

We consider a dynamical ergodic system defined as:Xt=ù(Xt-1,..., Xt-m0)where m0 is supposed to be unknown. X1,..., Xn being observed, we construct and study an estimate of m0 based on X1,..., XN, using the fact that m0 is a breaking point for the regularity of the distribution of (Xt-1,..., Xt-m0), m=1, 2,.... We present some simulations to illustrate our method and we discuss the computing problems.

Suggested Citation

  • D. Boscq & Dominique Guegan & Guillaume Léorat, 1999. "Statistical estimation of the Embedding Dimension of a dynamical system," Post-Print halshs-00194421, HAL.
    • Handle: RePEc:hal:journl:halshs-00194421
    DOI: 10.1142/S0218127499000456
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    Keywords

    Embedding Dimension; dynamical system;

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