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Forecasting chaotic systems: the role of local Lyapunov exponents

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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 to 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," Documents de travail du Centre d'Economie de la Sorbonne b08014, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Sep 2008.
    • Handle: RePEc:mse:cesdoc:b08014
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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. 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.
    3. Barnett,William A. & Kirman,Alan P. & Salmon,Mark, 1997. "Nonlinear Dynamics and Economics," Cambridge Books, Cambridge University Press, number 9780521471411.
    4. Dominique Guegan & L. Mercier, 1998. "Stochastic or chaotic dynamics in high frequency financial data," Post-Print halshs-00199167, HAL.
    5. Dominique Guegan, 2003. "Les chaos en finance: approche statistique," Post-Print halshs-00180849, HAL.
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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 Guégan, 2007. "Chaos in economics and finance," Documents de travail du Centre d'Economie de la Sorbonne b07054, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Jan 2009.
    3. Dominique Guegan, 2008. "Effect of noise filtering on predictions : on the routes of chaos," Post-Print halshs-00235448, HAL.
    4. 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.
    5. Vogl, Markus, 2022. "Controversy in financial chaos research and nonlinear dynamics: A short literature review," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    6. 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.
    7. Dominique Guegan & Justin Leroux, 2010. "Predicting chaos with Lyapunov exponents: Zero plays no role in forecasting chaotic systems," Post-Print halshs-00462454, HAL.
    8. 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.
    9. Dominique Guegan, 2009. "Chaos in economics and finance," Post-Print halshs-00187885, HAL.
    10. Dominique Guegan, 2009. "Chaos in Economics and Finance," Post-Print halshs-00375713, HAL.
    11. Dominique Guegan, 2009. "Chaos in Economics and Finance," PSE-Ecole d'économie de Paris (Postprint) halshs-00375713, HAL.
    12. 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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    More about this item

    Keywords

    Chaos theory; Lyapunov exponent; logistic map; 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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