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Some Properties of "Optimal" Seasonal Adjustment

D. M. Grether
M. Nerlove

Abstract

In recent years spectral techniques have been used to assess the effects of applying various types of seasonal adjustment procedures to economic time series. Similar analyses using artificially generated time series have also been attempted. The effects, desirable or undesirable, of a particular method of seasonal adjustment can, however, only be assessed properly in the time domain and only in relation to the objectives of such adjustment. Despite the fact that such objectives have not been clearly formulated nor any definitive conception of the nature of seasonality developed, in this paper we do adopt a general approach consistent with what has been written on the subject since the time of Jevons. In terms of a simple three component model of an economic time series having properties similar to those found in many actual time series, we devise several "methods" of seasonal adjustments based on a minimum mean-square-error criterion of optimality. We show that such methods of seasonal adjustment produce seasonally adjusted series bearing the same relationship to the unadjusted series in spectral terms as that found by Nerlove and others in their studies of BLS and Census methods of adjustment. Our conclusion is not that spectral methods are useless, but rather that comparisons in the frequency domain must be interpreted with great care. Further research must emphasize objectives and models. Whether these are formulated in frequency terms or in the time domain is of secondary importance.