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

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  • Dominique Guégan
  • Justin Leroux

    ()
    (IEA, HEC Montréal)

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://www.hec.ca/iea/cahiers/2008/iea0810_jleroux.pdf
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Bibliographic 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
Date of revision:
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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  1. Oliver Linton & Mototsugu Shintani, 2002. "Nonparametric Neutral Network Estimation of Lyapunov Exponents and a Direct Test for Chaos," STICERD - Econometrics Paper Series, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE /2002/434, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  2. Dominique Guégan & Justin Leroux, 2007. "Forecasting chaotic systems: The role of local Lyapunov exponents," Cahiers de recherche, HEC Montréal, Institut d'économie appliquée 07-12, HEC Montréal, Institut d'économie appliquée.
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