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Local Lyapunov exponents: Zero plays no role in Forecasting chaotic systems



We propose a novel 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 simulated data on the nearest-neighbor predictor, we show that accuracy gains can be substantial and that the candidate selection problem identified in Guégan and Leroux (2009) can be solved irrespective of the value of LLEs. An important corollary follows: the focal value of zero, which traditionally distinguishes order from chaos, plays no role whatsoever when forecasting deterministic systems.

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  • 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.
  • Handle: RePEc:iea:carech:0810

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    References listed on IDEAS

    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. 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.
    3. Dominique Guegan & L. Mercier, 1998. "Stochastic or chaotic dynamics in high frequency financial data," Post-Print halshs-00199167, HAL.
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    More about this item


    Chaos theory; Lyapunov exponent; Lorenz attractor Rössler attractor; Monte Carlo Simulations.;

    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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