Predicting chaos with Lyapunov exponents: Zero plays no role in forecasting chaotic systems

Dominique Guegan () and Justin Leroux
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Dominique Guegan: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

Abstract: We propose a nouvel 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 simulations of the Rössler, Lorenz and Chua attractors, we find that accuracy gains can be substantial. Also, we show that the candidate selection problem identified in Guégan and Leroux (2009a,b) can be solved irrespective of the value of LLEs. An important corrolary follows: the focal value of zero, which traditionally distinguishes order from chaos, plays no role whatsoever when forecasting deterministic systems.

Keywords: prévisions Rössler; Chua; Lorenz; Chaos theory; forecasting; Lyapunov exponent; Lorenz attractor; Rössler attractor; Chua attractor; Monte Carlo simulations (search for similar items in EconPapers)
Date: 2010-01
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00462454v1
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Published in 2010

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Related works:
Working Paper: Predicting chaos with Lyapunov exponents: zero plays no role in forecasting chaotic systems (2011)
Working Paper: Predicting chaos with Lyapunov exponents: zero plays no role in forecasting chaotic systems (2010)
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