Economists have long known that timescale matters in that the structure ofdecisions 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 economictime series into orthogonal timescale components except for the short orlong run in which the former is dominated by noise. Wavelets are usedto produce an orthogonal decomposition of some economic variables by timescale over six different timescales. The relationship of interest is thatbetween money and income, i.e., velocity. We confirm that timescaledecomposition is very important for analyzing economic relationships. Theanalysis indicates the importance of recognizing variations in phase betweenvariables when investigating the relationships between them and throwsconsiderable light on the conflicting results that have been obtained in theliterature using Granger causality tests.
