Effect of noise filtering on predictions : on the routes of chaos
AbstractThe detection of chaotic behaviors in commodities, stock markets and weather data is usually complicated by large noise perturbation inherent to the underlying system. It is well known, that predictions, from pure deterministic chaotic systems can be accurate mainly in the short term. Thus, it will be important to be able to reconstruct in a robust way the attractor in which evolves the data, if this attractor exists. In chaotic theory, the deconvolution methods have been largely studied and there exist different approaches which are competitive and complementary. In this work, we apply two methods : the singular value method and the wavelet approach. This last one has not been investigated a lot of filtering chaotic systems. Using very large Monte Carlo simulations, we show the ability of this last deconvolution method. Then, we use the de-noised data set to do forecast, and we discuss deeply the possibility to do long term forecasts with chaotic 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 b08008.
Length: 17 pages
Date of creation: Jan 2008
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Deconvolution; chaos; SVD; state space method; Wavelets method.;
Find related papers by JEL classification:
- C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
- C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics
- C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-02-16 (All new papers)
- NEP-ECM-2008-02-16 (Econometrics)
- NEP-ETS-2008-02-16 (Econometric Time Series)
- NEP-FOR-2008-02-16 (Forecasting)
- NEP-ORE-2008-02-16 (Operations Research)
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- Matthieu Garcin & Dominique Guegan, 2013. "Probability density of the wavelet coefficients of a noisy chaos," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) hal-00800997, HAL.
- Matthieu Garcin & Dominique Guegan, 2013. "Probability density of the wavelet coefficients of a noisy chaos," Documents de travail du Centre d'Economie de la Sorbonne 13015, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
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