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Local Lyapunov Exponents: A new way to predict chaotic systems

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  • Dominique Guegan

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Justin Leroux

    (HEC Montréal - HEC Montréal)

Abstract

We propose a novel methodology for forecasting chaotic systems which is based on exploiting the information conveyed by the local Lyapunov ex- ponent of a system. We show how our methodology can improve forecast- ing within the attractor and illustrate our results on the Lorenz system.

Suggested Citation

  • Dominique Guegan & Justin Leroux, 2009. "Local Lyapunov Exponents: A new way to predict chaotic systems," PSE-Ecole d'économie de Paris (Postprint) halshs-00511996, HAL.
    • Handle: RePEc:hal:pseptp:halshs-00511996
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00511996
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    References listed on IDEAS

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    1. Shintani, Mototsugu & Linton, Oliver, 2004. "Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos," Journal of Econometrics, Elsevier, vol. 120(1), pages 1-33, May.
    2. Barnett,William A. & Kirman,Alan P. & Salmon,Mark, 1997. "Nonlinear Dynamics and Economics," Cambridge Books, Cambridge University Press, number 9780521471411, September.
    3. Dominique Guégan & Justin Leroux, 2007. "Forecasting chaotic systems: The role of local Lyapunov exponents," Cahiers de recherche 07-12, HEC Montréal, Institut d'économie appliquée.
    4. Guégan, Dominique & Leroux, Justin, 2009. "Forecasting chaotic systems: The role of local Lyapunov exponents," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2401-2404.
    5. S. Yakowitz, 1987. "Nearest‐Neighbour Methods For Time Series Analysis," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(2), pages 235-247, March.
    6. Dominique Guegan & Justin Leroux, 2009. "Forecasting chaotic systems: The role of local Lyapunov exponents," PSE-Ecole d'économie de Paris (Postprint) halshs-00431726, HAL.
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    Cited by:

    1. Dominique Guegan, 2009. "Chaos in economics and finance," Post-Print halshs-00187885, HAL.
    2. Dominique Guegan, 2009. "Chaos in Economics and Finance," Post-Print halshs-00375713, HAL.
    3. Dominique Guegan, 2009. "Chaos in Economics and Finance," PSE-Ecole d'économie de Paris (Postprint) halshs-00375713, HAL.

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