THE DECOMPOSITION OF ECONOMIC RELATIONSHIPS BY TIME-SCALE USING WAVELETS - EXPENDITURE AND INCOME

Economists have long known that time scale matters, in that the struct ure of decisions as to the relevant time horizon, degree of time aggre gation, strength of relationship, and even the relevant variables diff er by time scale. Unfortunately, until recently it was difficult to de compose economic time series into orthogonal time-scale components exc ept for the short and long run, in which the former is dominated by no ise. This paper uses wavelets to produce an orthogonal decomposition o f some economic variables by time scale over six different time scales . The relationship of interest is the permanent income hypothesis. We confirm that time-scale decomposition is very important for analyzing economic relationships and that a number of anomalies previously noted in the literature are explained by these means. The analysis indicate s the importance of recognizing variations in phase between variables when investigating the economic relationships.