IDEAS home Printed from https://ideas.repec.org/p/hal/cesptp/halshs-01244239.html
   My bibliography  Save this paper

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

Author

Listed:
  • Matthieu Garcin

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, Natixis Asset Management - SAMS)

  • Dominique Guegan

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Matthieu Garcin & Dominique Guegan, 2015. "Optimal wavelet shrinkage of a noisy dynamical system with non-linear noise impact," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01244239, HAL.
    • Handle: RePEc:hal:cesptp:halshs-01244239
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01244239
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-01244239/document
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Antoniadis A. & Fan J., 2001. "Regularization of Wavelet Approximations," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 939-967, September.
    4. 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.
    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. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    7. D. Bosq & Dominique Guegan, 1995. "Nonparametric estimation of the chaotic function and the invariant measure of a dynamical system," Post-Print halshs-00199345, HAL.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Matthieu Garcin & Dominique Guegan, 2015. "Optimal wavelet shrinkage of a noisy dynamical system with non-linear noise impact," Post-Print halshs-01244239, HAL.
    3. Thilini V. Mahanama & Abootaleb Shirvani & Svetlozar Rachev, 2023. "The Financial Market of Indices of Socioeconomic Wellbeing," Papers 2303.05654, arXiv.org.
    4. Hee-Seok Oh & Donghoh Kim & Youngjo Lee, 2009. "Cross-validated wavelet shrinkage," Computational Statistics, Springer, vol. 24(3), pages 497-512, August.
    5. Alexandru Badescu & Robert J. Elliott & Juan-Pablo Ortega, 2012. "Quadratic hedging schemes for non-Gaussian GARCH models," Papers 1209.5976, arXiv.org, revised Dec 2013.
    6. Christian Gourieroux & Joanna Jasiak, 1999. "Nonlinear Innovations and Impulse Response," Working Papers 99-44, Center for Research in Economics and Statistics.
    7. Matthias R. Fengler & Alexander Melnikov, 2018. "GARCH option pricing models with Meixner innovations," Review of Derivatives Research, Springer, vol. 21(3), pages 277-305, October.
    8. Badescu, Alexandru & Cui, Zhenyu & Ortega, Juan-Pablo, 2016. "A note on the Wang transform for stochastic volatility pricing models," Finance Research Letters, Elsevier, vol. 19(C), pages 189-196.
    9. Badescu, Alexandru & Elliott, Robert J. & Ortega, Juan-Pablo, 2015. "Non-Gaussian GARCH option pricing models and their diffusion limits," European Journal of Operational Research, Elsevier, vol. 247(3), pages 820-830.
    10. Papantonis, Ioannis & Rompolis, Leonidas & Tzavalis, Elias, 2023. "Improving variance forecasts: The role of Realized Variance features," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1221-1237.
    11. Dominique Guegan & Guillaume Leorat, 1997. "Consistent estimation to determine the embedding dimension in financial data; with an application to the dollar/deutschmark exchange rate," The European Journal of Finance, Taylor & Francis Journals, vol. 3(3), pages 231-242.
    12. Thisari K. Mahanama & Abootaleb Shirvani & Svetlozar Rachev & Frank J. Fabozzi, 2023. "The Financial Market of Environmental Indices," Papers 2308.15661, arXiv.org.
    13. Youri Davydov & Ričardas Zitikis, 2007. "Deterministic Noises that can be Statistically Distinguished from the Random Ones," Statistical Inference for Stochastic Processes, Springer, vol. 10(2), pages 165-179, July.
    14. Yuan Hu & Svetlozar T. Rachev & Frank J. Fabozzi, 2019. "Modelling Crypto Asset Price Dynamics, Optimal Crypto Portfolio, and Crypto Option Valuation," Papers 1908.05419, arXiv.org.
    15. Joan del Castillo & Juan-Pablo Ortega, 2011. "Hedging of time discrete auto-regressive stochastic volatility options," Papers 1110.6322, arXiv.org.
    16. Seiler, Volker, 2024. "The relationship between Chinese and FOB prices of rare earth elements – Evidence in the time and frequency domain," The Quarterly Review of Economics and Finance, Elsevier, vol. 95(C), pages 160-179.
    17. Beran, Jan & Feng, Yuanhua, 1999. "Local Polynomial Estimation with a FARIMA-GARCH Error Process," CoFE Discussion Papers 99/08, University of Konstanz, Center of Finance and Econometrics (CoFE).
    18. Corbet, Shaen & Larkin, Charles & McMullan, Caroline, 2020. "The impact of industrial incidents on stock market volatility," Research in International Business and Finance, Elsevier, vol. 52(C).
    19. Minot, Nicholas, 2014. "Food price volatility in sub-Saharan Africa: Has it really increased?," Food Policy, Elsevier, vol. 45(C), pages 45-56.
    20. Lahmiri, Salim & Bekiros, Stelios, 2017. "Disturbances and complexity in volatility time series," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 38-42.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:cesptp:halshs-01244239. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.