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Wavelet Analysis and Denoising: New Tools for Economists

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  • 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
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    File URL: https://www.qmul.ac.uk/sef/media/econ/research/workingpapers/2007/items/wp600.pdf
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    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)

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    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

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