Econometrica: Jul 1964, Volume 32, Issue 3
Spectral Analysis of Seasonal Adjustment Procedures
Marc NerloveThis paper discusses one of the uses to which two powerful techniques of modern time series analysis may be put in economics: namely, the study of the precise effects of seasonal adjustment procedures on the characteristics of the series to which they are applied. Since most economic data appearing at intervals of less than a year are to a greater or lesser extent "manufactured" from more basic time series, the problem of assessing the effects of the "manufacturing" processes upon the essential characteristics of the raw material to which they are applied is not unimportant. Perhaps the most common type of adjustment applied to raw economic time series is that designed to eliminate so-called seasonal fluctuations. The precise nature of seasonality is not easy to define, but an attempt is made in Section 2.1 below. The techniques employed to study the effects of seasonal adjustment procedures are those of spectral and cross-spectral analysis. In somewhat oversimplified terms the basic idea behind these types of analysis is that a stochastic time series may be decomposed into an infinite number of sine and cosine waves with infinitesimal random amplitudes. Spectral analysis deals with a single time series in terms of its frequency "content": cross-spectral analysis deals with the relation between two time series in terms of their respective frequency "contents." The two techniques are discussed in both theoretical and practical terms. Spectral analyses have been made for about seventy-five time series of United States employment, unemployment, labor force, and various categories thereof. Cross-spectral analyses have been made of the relations between these series and the corresponding series as seasonally adjustment by the procedures used by the Bureau of Labor Statistics. Two major conclusions regarding the effects of the BLS seasonal adjustment procedures emerge from these emerge from these analyses. First, these procedures remove far more from the series to which they are applied than can properly be considered as seasonal. Second, if the relation between two seasonally adjusted series in time is compared with the corresponding relation between the original series in time, it is found that there is a distortion due to the process of seasonal adjustment itself. Both defects impair the usefulness of the seasonally adjusted series as indicators of economic conditions, but, of the two, temporal distortion is the more serious defect. Examples of some of these results are discussed below in Section 3.3.
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