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

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Author Info
Dominique Guégan
Justin Leroux () (IEA, HEC Montréal)

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Abstract

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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File URL: http://www2.hec.ca/iea/cahiers/2008/iea0810_jleroux.pdf
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Publisher Info
Paper provided by HEC Montréal, Institut d'économie appliquée in its series Cahiers de recherche with number 08-10.

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Length: 16 pages
Date of creation: Sep 2008
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Handle: RePEc:iea:carech:0810

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Postal: Institut d'économie appliquée HEC Montréal 3000, Chemin de la Côte-Sainte-Catherine Montréal, Québec H3T 2A7
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Related research
Keywords: Chaos theory; Lyapunov exponent; Lorenz attractor Rössler attractor; Monte Carlo Simulations.;

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Find related papers by JEL classification:
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Other Model Applications
C65 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Miscellaneous Mathematical Tools

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  1. 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. [Downloadable!]
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  2. 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. [Downloadable!] (restricted)
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