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Nonparametric estimation of the chaotic function and the invariant measure of a dynamical system

Author

Listed:
  • D. Bosq

    (LSTA - Laboratoire de Statistique Théorique et Appliquée - UPMC - Université Pierre et Marie Curie - Paris 6 - CNRS - Centre National de la Recherche Scientifique)

  • 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 - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique)

Abstract

Let (Xt), Image be Image valued stochastic process defined by a discrete time dynamical system as Xt = phi(Xt−1, T = 1,2,..., where phi is some nonlinear function preserving a probability measure say μ, we estimate phi and the density -f of μ without using special condition on the analytical form of phi, with nonparametric methods and some convergence rates are given.

Suggested Citation

  • D. Bosq & Dominique Guegan, 1995. "Nonparametric estimation of the chaotic function and the invariant measure of a dynamical system," Post-Print halshs-00199345, HAL.
    • Handle: RePEc:hal:journl:halshs-00199345
    DOI: 10.1016/0167-7152(94)00223-U
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    Citations

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    Cited by:

    1. Christian Gourieroux & Joanna Jasiak, 1999. "Nonlinear Innovations and Impulse Response," Working Papers 99-44, Center for Research in Economics and Statistics.
    2. Matthieu Garcin & Dominique Guegan, 2015. "Optimal wavelet shrinkage of a noisy dynamical system with non-linear noise impact," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01244239, HAL.
    3. Dominique Guegan & Guillaume Leorat, 1997. "Consistent estimation to determine the embedding dimension in financial data; with an application to the dollar/deutschmark exchange rate," The European Journal of Finance, Taylor & Francis Journals, vol. 3(3), pages 231-242.
    4. Matthieu Garcin & Dominique Guegan, 2015. "Optimal wavelet shrinkage of a noisy dynamical system with non-linear noise impact," Documents de travail du Centre d'Economie de la Sorbonne 15085, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    5. Matthieu Garcin & Dominique Guegan, 2015. "Optimal wavelet shrinkage of a noisy dynamical system with non-linear noise impact," Post-Print halshs-01244239, HAL.
    6. Youri Davydov & Ričardas Zitikis, 2007. "Deterministic Noises that can be Statistically Distinguished from the Random Ones," Statistical Inference for Stochastic Processes, Springer, vol. 10(2), pages 165-179, July.

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