Decomposition of Economic Relationships by Timescale Using Wavelets

Economists have long known that timescale matters in that the structure of decisions as to the relevant time horizon, degree of time aggregation, strength of relationship, and even the relevant variables differ by timescale. Unfortunately, until recently it was difficult to decompose economic time series into orthogonal timescale components except for the short or long run in which the former is dominated by noise. Wavelets are used to produce an orthogonal decomposition of some economic variables by timescale over six different timescales. The relationship of interest is that between money and income, i.e., velocity. We confirm that timescale decomposition is very important for analyzing economic relationships. The analysis indicates the importance of recognizing variations in phase between variables when investigating the relationships between them and throws considerable light on the conflicting results that have been obtained in the literature using Granger causality tests.