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Forecasting chaotic systems : the role of local Lyapunov exponents

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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, CIRPEE - Centre interuniversitaire sur le risque, les politiques économiques et l'emploi [Montréal] - UQAM - Université du Québec à Montréal = University of Québec in Montréal)

Abstract

We propose a novel methodology for forecasting chaotic systems which is based on the nearest-neighbor predictor and improves upon it by incorporating local Lyapunov exponents to correct for its inevitable bias. Using simulated data, we show that gains in prediction accuracy can be substantial. The general intuition behind the proposed method can readily be applied to other non-parametric predictors.

Suggested Citation

  • Dominique Guegan & Justin Leroux, 2008. "Forecasting chaotic systems : the role of local Lyapunov exponents," Post-Print halshs-00259238, HAL.
    • Handle: RePEc:hal:journl:halshs-00259238
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00259238v2
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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, October.
    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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