The continuous wavelet transform : a primer

Wavelet analysis is becoming more popular in the Economics discipline. Until re- cently, most works have made use of tools associated with the Discrete Wavelet Trans- form. However, after 2005, there has been a growing body of work in Economics and Finance that makes use of the Continuous Wavelet Transform tools. In this article, we give a self-contained summary on the most relevant theoretical results associated with the Continuous Wavelet Transform, the Cross-Wavelet Transform, the Wavelet Coherency and the Wavelet Phase-Dierence. We describe how the transforms are usually implemented in practice and provide some examples. We also introduce the Economists to a new class of analytic wavelets, the Generalized Morse Wavelets, which have some desirable properties and provide an alternative to the Morlet Wavelet. Fi- nally, we provide a user friendly toolbox which will allow any researcher to replicate our results and to use it in his/her own research.