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Forecasting chaotic systems : the role of local Lyapunov exponents

Author

Listed:
  • Dominique Guegan

    () (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics)

  • Justin Leroux

    () (HEC Montréal - HEC Montréal, CIRPEE - Centre Interuniversitaire sur le Risque, les Politiques Economiques et l'Emploi)

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," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00259238, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00259238
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00259238v2
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    References listed on IDEAS

    as
    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 Guegan & L. Mercier, 1998. "Stochastic or chaotic dynamics in high frequency financial data," Post-Print halshs-00199167, HAL.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Miśkiewicz-Nawrocka Monika, 2014. "The Application of Random Noise Reduction By Nearest Neighbor Method To Forecasting of Economic Time Series," Folia Oeconomica Stetinensia, De Gruyter Open, vol. 13(2), pages 1-13, July.

    More about this item

    Keywords

    Monte Carlo simulations; Chaos theory; Lyapunov exponent; logistic map; Monte Carlo simulations.; Systèmes chaotiques; exposants de Lyapunov; fonction logistique; méthodes de simulations de Monte Carlo.;

    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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