Wavelet shrinkage of a noisy dynamical system with non-linear noise impact

Autor: Matthieu Garcin, Dominique Guegan
Přispěvatelé: Centre d'économie de la Sorbonne (CES), Université Paris 1 Panthéon-Sorbonne (UP1)-Centre National de la Recherche Scientifique (CNRS), Natixis Asset Management
Rok vydání: 2016
Předmět:
Dynamical systems theory
02 engineering and technology
Wavelets
01 natural sciences
010305 fluids & plasmas
Non-linear noise impact
symbols.namesake
Wavelet
[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]
Nonequispaced design
Dynamical systems
0103 physical sciences
0202 electrical engineering
electronic engineering
information engineering
Mathematics
[SHS.STAT]Humanities and Social Sciences/Methods and statistics
Noise (signal processing)
020206 networking & telecommunications
Statistical and Nonlinear Physics
Filter (signal processing)
[SHS.ECO]Humanities and Social Sciences/Economics and Finance
Condensed Matter Physics
Minimax
Thresholding
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
Filter design
Gaussian noise
symbols
[SHS.GESTION]Humanities and Social Sciences/Business administration
Algorithm
Zdroj: Physica D: Nonlinear Phenomena
Physica D: Nonlinear Phenomena, Elsevier, 2016, 325, pp.126-145. ⟨10.1016/j.physd.2016.03.013⟩
ISSN: 0167-2789
DOI: 10.1016/j.physd.2016.03.013
Popis: International audience; By filtering wavelet coefficients, it is possible to construct a good estimate of a pure signal from noisy data. Especially, for a simple linear noise influence, Donoho and Johnstone (1994) have already defined an optimal filter design in the sense of a minimization of the error made when estimating the pure signal. We set here a different framework where the influence of the noise is non-linear. In particular, we propose a method to filter the wavelet coefficients of a discrete dynamical system disrupted by a weak noise, in order to construct good estimates of the pure signal, including Bayes’ estimate, minimax estimate, oracular estimate or thresholding estimate. We present the example of a logistic and a Lorenz chaotic dynamical system as well as an adaptation of our technique in order to show empirically the robustness of the thresholding method in presence of leptokurtic noise. Moreover, we test both the hard and the soft thresholding and also another kind of smoother thresholding which seems to have almost the same reconstruction power as the hard thresholding. Finally, besides the tests on an estimated dataset, the method is tested on financial data: oil prices and NOK/USD exchange rate.
Databáze: OpenAIRE
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