IDEAS home Printed from https://ideas.repec.org/p/qmw/qmwecw/600.html
   My bibliography  Save this paper

Wavelet Analysis and Denoising: New Tools for Economists

Author

Listed:
  • Iolanda Lo Cascio

    (Queen Mary, University of London)

Abstract

This paper surveys the techniques of wavelets analysis and the associated methods of denoising. The Discrete Wavelet Transform and its undecimated version, the Maximum Overlapping Discrete Wavelet Transform, are described. The methods of wavelets analysis can be used to show how the frequency content of the data varies with time. This allows us to pinpoint in time such events as major structural breaks. The sparse nature of the wavelets representation also facilitates the process of noise reduction by nonlinear wavelet shrinkage, which can be used to reveal the underlying trends in economic data. An application of these techniques to the UK real GDP (1873-2001) is described. The purpose of the analysis is to reveal the true structure of the data - including its local irregularities and abrupt changes - and the results are surprising.

Suggested Citation

  • Iolanda Lo Cascio, 2007. "Wavelet Analysis and Denoising: New Tools for Economists," Working Papers 600, Queen Mary University of London, School of Economics and Finance.
  • Handle: RePEc:qmw:qmwecw:600
    as

    Download full text from publisher

    File URL: https://www.qmul.ac.uk/sef/media/econ/research/workingpapers/2007/items/wp600.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Duck, N W, 1992. "UK Evidence on Breaking Trend Functions," Oxford Economic Papers, Oxford University Press, vol. 44(3), pages 426-439, July.
    2. Terence Mills, 1994. "Segmented trends and the stochastic properties of UK output," Applied Economics Letters, Taylor & Francis Journals, vol. 1(8), pages 132-133.
    3. 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.
    4. Iain M. Johnstone & Bernard W. Silverman, 1997. "Wavelet Threshold Estimators for Data with Correlated Noise," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 319-351.
    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. Iolanda Lo Cascio, 2007. "Wavelet Analysis and Denoising: New Tools for Economists," Working Papers 600, Queen Mary University of London, School of Economics and Finance.
    2. Beran, Jan & Heiler, Mark A., 2008. "A nonparametric regression cross spectrum for multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 99(4), pages 684-714, April.
    3. Capobianco Enrico & Marras Elisabetta & Travaglione Antonella, 2011. "Multiscale Characterization of Signaling Network Dynamics through Features," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-32, November.
    4. Beran, Jan, 2008. "A nonparametric regression cross spectrum for multivariate time series," CoFE Discussion Papers 08/01, University of Konstanz, Center of Finance and Econometrics (CoFE).
    5. Beran, Jan & Shumeyko, Yevgen, 2012. "Bootstrap testing for discontinuities under long-range dependence," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 322-347.
    6. Marco Di Zio & Arnoldo Frigessi, 1999. "Smoothness in Bayesian Non-parametric Regression with Wavelets," Methodology and Computing in Applied Probability, Springer, vol. 1(4), pages 391-405, December.
    7. Wishart, Justin Rory, 2011. "Minimax lower bound for kink location estimators in a nonparametric regression model with long-range dependence," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1871-1875.
    8. ILHAN Gullu, 2015. "An Application On The Efficiency Of Customs Union: Turkey-Eu Customs Union," Revista Economica, Lucian Blaga University of Sibiu, Faculty of Economic Sciences, vol. 67(6), pages 158-177, December.
    9. Antonio E. Noriega & Araceli Ramírez-Zamora, 1999. "Unit roots and multiple structural breaks in real output," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 14(2), pages 163-188.
    10. Linyuan Li & Yimin Xiao, 2007. "Mean Integrated Squared Error of Nonlinear Wavelet-based Estimators with Long Memory Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(2), pages 299-324, June.
    11. A. Antoniadis, 1997. "Rejoinder," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 6(2), pages 143-144, August.
    12. Luan, Yihui & Xie, Zhongjie, 2001. "The wavelet identification for jump points of derivative in regression model," Statistics & Probability Letters, Elsevier, vol. 53(2), pages 167-180, June.
    13. McGinnity, K. & Varbanov, R. & Chicken, E., 2017. "Cross-validated wavelet block thresholding for non-Gaussian errors," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 127-137.
    14. 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.
    15. Fryzlewicz, Piotr & Nason, Guy P., 2004. "Smoothing the wavelet periodogram using the Haar-Fisz transform," LSE Research Online Documents on Economics 25231, London School of Economics and Political Science, LSE Library.
    16. repec:jss:jstsof:12:i08 is not listed on IDEAS
    17. Yu Yue & Paul Speckman & Dongchu Sun, 2012. "Priors for Bayesian adaptive spline smoothing," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 577-613, June.
    18. Nilotpal Sanyal & Marco A. R. Ferreira, 2017. "Bayesian Wavelet Analysis Using Nonlocal Priors with an Application to fMRI Analysis," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(2), pages 361-388, November.
    19. Vo Thi Hong Tuyet, 2016. "Adaptive filter and threshold for image denoising in new generation wavelet," HO CHI MINH CITY OPEN UNIVERSITY JOURNAL OF SCIENCE - ENGINEERING AND TECHNOLOGY, HO CHI MINH CITY OPEN UNIVERSITY JOURNAL OF SCIENCE, HO CHI MINH CITY OPEN UNIVERSITY, vol. 6(2), pages 89-96.
    20. Mak Kaboudan, 2006. "Computational Forecasting of Wavelet-converted Monthly Sunspot Numbers," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(9), pages 925-941.
    21. Hee-Seok Oh & Donghoh Kim & Youngjo Lee, 2009. "Cross-validated wavelet shrinkage," Computational Statistics, Springer, vol. 24(3), pages 497-512, August.

    More about this item

    Keywords

    Wavelets; Denoising; Structural breaks; Trend estimation;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

    Statistics

    Access and download statistics

    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:qmw:qmwecw:600. 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: Nicholas Owen (email available below). General contact details of provider: https://edirc.repec.org/data/deqmwuk.html .

    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.