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

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Abstract

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 good reconstruction of the pure signal. We set here a different framework where the influence of the noise is non-linear. In particular, we propose an optimal 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 simple 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

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  • Matthieu Garcin & Dominique Guegan, 2015. "Optimal wavelet shrinkage of a noisy dynamical system with non-linear noise impact," Documents de travail du Centre d'Economie de la Sorbonne 15085, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:15085
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    1. Christophe Chorro & Dominique Gu�gan & Florian Ielpo, 2012. "Option pricing for GARCH-type models with generalized hyperbolic innovations," Quantitative Finance, Taylor & Francis Journals, vol. 12(7), pages 1079-1094, April.
    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    3. Bosq, D. & Guégan, D., 1995. "Nonparametric estimation of the chaotic function and the invariant measure of a dynamical system," Statistics & Probability Letters, Elsevier, vol. 25(3), pages 201-212, November.
    4. J. Bardet & G. Lang & E. Moulines & P. Soulier, 2000. "Wavelet Estimator of Long-Range Dependent Processes," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 85-99, January.
    5. F. Abramovich & T. Sapatinas & B. W. Silverman, 1998. "Wavelet thresholding via a Bayesian approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(4), pages 725-749.
    6. D. Bosq & Dominique Guegan, 1995. "Nonparametric estimation of the chaotic function and the invariant measure of a dynamical system," Post-Print halshs-00199345, HAL.
    7. Antoniadis A. & Fan J., 2001. "Regularization of Wavelet Approximations," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 939-967, September.
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    Keywords

    wavelets; dynamical systems; chaos; Gaussian noise; Cauchy noise; thresholding; nonequispaced design; non-linear noise impact;
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