The Continuous Wavelet Transform: Moving Beyond Uni‐ and Bivariate Analysis

Abstract

A body of work using the continuous wavelet transform has been growing. We provide a self‐contained summary on its most relevant theoretical results, describe how such transforms can be implemented in practice, and generalize the concept of simple coherency to partial wavelet coherency and multiple wavelet coherency, moving beyond bivariate analysis. We also describe a family of wavelets, which emerges as an alternative to the popular Morlet wavelet, the generalized Morse wavelets. A user‐friendly toolbox, with examples, is attached to this paper.

Keywords: Continuous wavelet transform, Economic fluctuations, Multiple wavelet coherency, Partial wavelet coherency, Wavelet coherency, Wavelet partial phase‐difference