Jb. Ramsey et C. Lampart, DECOMPOSITION OF ECONOMIC RELATIONSHIPS BY TIMESCALE USING WAVELETS -MONEY AND INCOME, MACROECONOMIC DYNAMICS, 2(1), 1998, pp. 49-71
Economists have long known that timescale matters in that the structur
e of decisions as to the relevant time horizon, degree of time aggrega
tion, strength of relationship, and even the relevant variables differ
by timescale. Unfortunately, until recently it was difficult to decom
pose economic time series into orthogonal timescale components except
for the shea or long run in which the former is dominated by noise. Wa
velets are used to produce an orthogonal decomposition of some economi
c variables by timescale over six different timescales. The relationsh
ip of interest is that between money and income, i.e., velocity. We co
nfirm that timescale decomposition is very important for analyzing eco
nomic relationships. The analysis indicates the importance of recogniz
ing variations in phase between variables when investigating the relat
ionships between them and throws considerable light on the conflicting
results that have been obtained in the literature using Granger causa
lity tests.