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Forecasting chaotic systems: The role of local Lyapunov exponents

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  • Dominique Guegan

    (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, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • 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 exponents of a system. This information is used to correct for the inevitable bias of most non-parametric predictors. Using simulated data, we show that gains in prediction accuracy can be substantial.

Suggested Citation

  • Dominique Guegan & Justin Leroux, 2009. "Forecasting chaotic systems: The role of local Lyapunov exponents," PSE-Ecole d'économie de Paris (Postprint) halshs-00431726, HAL.
    • Handle: RePEc:hal:pseptp:halshs-00431726
    DOI: 10.1016/j.chaos.2008.09.017
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00431726v2
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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.
    3. Yousefi, Shahriar & Weinreich, Ilona & Reinarz, Dominik, 2005. "Wavelet-based prediction of oil prices," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 265-275.
    4. Chian, Abraham C.-L. & Rempel, Erico L. & Rogers, Colin, 2006. "Complex economic dynamics: Chaotic saddle, crisis and intermittency," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1194-1218.
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    Cited by:

    1. Dominique Guegan & Justin Leroux, 2009. "Local Lyapunov Exponents: A new way to predict chaotic systems," Post-Print halshs-00511996, HAL.
    2. Dominique Guegan & Justin Leroux, 2009. "Local Lyapunov Exponents: A new way to predict chaotic systems," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00511996, HAL.
    3. Vogl, Markus, 2022. "Controversy in financial chaos research and nonlinear dynamics: A short literature review," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    4. Dominique Guégan & Justin Leroux, 2008. "Local Lyapunov exponents: Zero plays no role in Forecasting chaotic systems," Cahiers de recherche 08-10, HEC Montréal, Institut d'économie appliquée.
    5. Miśkiewicz-Nawrocka Monika, 2014. "The Application of Random Noise Reduction By Nearest Neighbor Method To Forecasting of Economic Time Series," Folia Oeconomica Stetinensia, Sciendo, vol. 13(2), pages 1-13, July.
    6. Dominique Guegan, 2009. "Chaos in economics and finance," Post-Print halshs-00187885, HAL.
    7. Dominique Guegan, 2009. "Chaos in Economics and Finance," Post-Print halshs-00375713, HAL.
    8. Dominique Guegan, 2009. "Chaos in Economics and Finance," PSE-Ecole d'économie de Paris (Postprint) halshs-00375713, HAL.
    9. 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.

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