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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 - 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 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.

Suggested Citation

  • Dominique Guegan & Justin Leroux, 2010. "Predicting chaos with Lyapunov exponents: Zero plays no role in forecasting chaotic systems," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00462454, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00462454
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00462454
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    Keywords

    prévisions Rössler; Chua; Lorenz; Chaos theory; forecasting; Lyapunov exponent; Lorenz attractor; Rössler attractor; Chua attractor; Monte Carlo simulations;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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