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Lyapunov exponent for stochastic time series

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  • Weihs, Claus
  • Busse, Anja M.

Abstract

This paper deals with the problem of the discrimination between stable and unstable time series. One criterion for the seperation is given by the size of the Lyapunov exponent, which was originally defined for deterministic systems. However, this paper will show, that the Lyapunov exponent can also be analyzed and used for ergodic stochastic time series. Experimantal results illustrate the classification by the Lyapunov exponent. Although the Lyapunov exponent is a discriminatory parameter of the asymptotic behavior and can be interpreted as a parameter of the asymptotic distribution in the stochastic case, it has to be estimated from a given time series, where the process might still be in the transient state. Experimental results will show that in special cases the estimation leads to misclassifications of the time series and the underlying process due to the uncertainty of estimators for the Lyapunov exponent.

Suggested Citation

  • Weihs, Claus & Busse, Anja M., 2004. "Lyapunov exponent for stochastic time series," Technical Reports 2004,37, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200437
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    Cited by:

    1. Busse, Anja M., 2004. "Classification of Processes by the Lyapunov exponent," Technical Reports 2004,70, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. RIANE, Nizare, 2014. "Etude de la dynamique non-linéaire des rentabilités de la bourse de Casablanca [Study of the returns nonlinear dynamics of the Casablanca stock exchange]," MPRA Paper 61957, University Library of Munich, Germany, revised 06 Feb 2015.
    3. Busse, Anja M. & Theis, Winfried, 2004. "Comparing Time Series from Experiments with and without Spiralling," Technical Reports 2004,39, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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