Wavelet Analysis and Denoising: New Tools for Economists

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 show how the frequency content of the data varies with time. This allow 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 \textit{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.