The Continuous Wavelet Transform: A Primer

Economists are already familiar with the Discrete Wavelet Transform. However, a body of work using the Continuous Wavelet Transform has also been growing. We provide a self-contained summary on continuous wavelet tools, such as the Continuous Wavelet Transform, the Cross-Wavelet, the Wavelet Coherency and the Phase-Difference. Furthermore, we generalize the concept of simple coherency to Partial Wavelet Coherency and Multiple Wavelet Coherency, akin to partial and multiple correlations, allowing the researcher to move beyond bivariate analysis. Finally, we describe the Generalized Morse Wavelets, a class of analytic wavelets recently proposed. A user-friendly toolbox, with examples, is attached to this paper.