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Economists have long known that time scale 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 time scale. Unfortunately, until recently it was difficult to decompose economic time series into orthogonal time-scale components except for the short and long run, in which the former is dominated by noise. This paper uses wavelets to produce an orthogonal decomposition of 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 indicates the importance of recognizing variations in phase between variables when investigating the economic relationships.

The Decomposition of Economic Relationships by Time Scale Using Wavelets: Expenditure and Income