Predicting chaos with Lyapunov exponents : zero plays no role in forecasting chaotic systems
AbstractWe 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.
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Bibliographic InfoPaper provided by Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number 10019.
Length: 20 pages
Date of creation: Jan 2010
Date of revision:
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Chaos theory; forecasting; Lyapunov exponent; Lorenz attractor; Rössler attractor; Chua attractor; Monte Carlo Simulations.;
Other versions of this item:
- Dominique Guegan & Justin Leroux, 2010. "Predicting chaos with Lyapunov exponents : Zero plays no role in forecasting chaotic systems," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00462454, HAL.
- 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 &bull 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-04-11 (All new papers)
- NEP-FOR-2010-04-11 (Forecasting)
- NEP-ORE-2010-04-11 (Operations Research)
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