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Predicting chaos with Lyapunov exponents : Zero plays no role in forecasting chaotic systems

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  • Dominique Guegan

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris 1 - Panthéon-Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)

  • Justin Leroux

    ()
    (HEC - Institute for Applied Economics - HEC MONTRÉAL)

Abstract

We propose a nouvel methodology for forecasting chaotic systems which uses information on local Lyapunov exponents (LLEs) to improve upon existing predictors by correcting for their inevitable bias. Using simulations of the Rössler, Lorenz and Chua attractors, we find that accuracy gains can be substantial. Also, we show that the candidate selection problem identified in Guégan and Leroux (2009a,b) can be solved irrespective of the value of LLEs. An important corrolary follows : the focal value of zero, which traditionally distinguishes order from chaos, plays no role whatsoever when forecasting deterministic systems.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00462454.

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Date of creation: Jan 2010
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Handle: RePEc:hal:cesptp:halshs-00462454

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Related research

Keywords: Chaos theory; forecasting; Lyapunov exponent; Lorenz attractor; Rössler attractor; Chua attractor; Monte Carlo simulations.;

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