Some Techniques for Analyzing a Set of Time Series Subject to a Linear Restriction

Abstract

Techniques are presented for decomposing each series in a set of time series into trend, seasonal, and non-seasonal, short-run components. The decomposition is such that if the original set of series satisfy a linear condition, the set of components of each type satisfy the same linear condition. This makes it possible to assess the contributions of different industries, commodities, etc., to different types of movements of weighted or unweighted aggregates. Additional summary measures are proposed for describing the relative movements of individual series. Short-Cuts in the analysis are outlined, based on certain restrictive assumptions. Finally, a table of illustrative calculations is presented and discussed.