The Seasonal Adjustment of Economic Time Series

THE SEASONAL ADJUSTMENT of economic time series has recently received a great deal of attention from statisticians. The reason for this is not hard to perceive. The economic policymaker faced with the problem of controlling the level of activity does not wish to mistake a seasonal movement for a long-term or medium-term change in the level of economic activity. Pressure is thus brought to bear on official statisticians for better estimates and this pressure filters through to the theorist. The paper by Shiskin and Eisenpress 9 describing methods of seasonal adjustment used by the U. S. Bureau of the Census provoked much of the ensuing discussion. The first paper to use modern spectral methods to discuss this problem seems to have been Hannan 2 and much recent work seems to have used these techniques. (See Hannan 3, 5, Nerlove 7, Nettheim 8 for example.) These methods seem particularly appropriate, for any model for the seasonal component will surely represent it as a sum of six narrow (frequency) band signals which are amplitude, phase, and possibly frequency modulated. (A more complete discussion of the model is, of course, given below.) To this is added and the narrow band nature of the signals means that, substantially, only the average noise level over these bands is of significant concern. Thus a spectral treatment of the noise will require the introduction of only relatively few parameters so that more special models add little or nothing in simplicity and efficiency, while they increase the risk of an invalid analysis. The main problem of seasonal adjustment undoubtedly arises from the fact that the seasonal pattern may be changing. The problem of estimating such a changing seasonal pattern is an aspect of one of the most immanent of all scientific problems. The difficulty of the problem is simple to perceive but must be understood. If we construct an estimation procedure which is sensitive to changes in the seasonal component, then we shall have one which is sensitive also to chance fluctuations, i.e., to noise effects. Given an initial model we can optimize. Such optimum solutions may be of great value both for their own sake and as standards against which to compare ad hoc procedures; however they should not be used uncritically as the unique optimal solutions, for no model upon which an optimization procedure can be based can represent the truth. In addition, of course, a suitable optimum criterion may not be easy to produce as it may have to reflect subjective elements difficult to quantify (e.g., the reluctance of an official institution to use methods which may require substantial later revisions of initial estimates). In the next section we describe a technique for dealing with a changing