Regression over Timescale Decompositions: A Sampling Analysis of Distributional Properties

In two previous papers, Ramsey and Lampart demonstrated that regression analyses between timescale decompositions provided important insight into the properties of economic relationships. The idea in those papers was that the relationship between any two variables, say consumption and income, was the union of the individual relationships between consumption and income at each timescale and that the regression relationship might, differ across timescales. This paper is dedicated to discovering the approximate distributional properties of the regression estimators and of the residuals in the context of such models. Sampling procedures are used to verify the distributional properties of the regression estimators at each timescale and those of the residuals. This analysis is necessary to provide the appropriate distributional information required to specify tests of hypotheses and confidence intervals.