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| HAL : halshs-00462454, version 1 |
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| Predicting chaos with Lyapunov exponents : Zero plays no role in forecasting chaotic systems |
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| Dominique Guegan 1, 2Justin Leroux 3 |
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| (01/2010) |
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| 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. |
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| 1 : | Centre d'économie de la Sorbonne (CES) |
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CNRS : UMR8174 – Université Paris I - Panthéon Sorbonne |
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| 2 : | Ecole d'Économie de Paris - Paris School of Economics (EEP-PSE) |
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Ecole d'Économie de Paris |
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| 3 : | Institute for Applied Economics |
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HEC MONTRÉAL |
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| Axe Finance |
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| Discipline | : | Sciences de l'Homme et Société/Economie et finances Sciences de l'Homme et Société/Méthodes et statistiques Mathématiques/Analyse fonctionnelle Mathématiques/Probabilités Mathématiques/Statistiques Statistiques/Théorie |
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| Chaos theory – forecasting – Lyapunov exponent – Lorenz attractor – Rössler attractor – Chua attractor – Monte Carlo simulations. |
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| Liste des fichiers attachés à ce document : | |||||
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| halshs-00462454, version 1 | |
| http://halshs.archives-ouvertes.fr/halshs-00462454 | |
| oai:halshs.archives-ouvertes.fr:halshs-00462454 | |
| Contributeur : Lucie Label | |
| Soumis le : Mardi 9 Mars 2010, 17:15:03 | |
| Dernière modification le : Mercredi 10 Mars 2010, 08:54:14 | |
