We investigate frequency domain properties of seasonal adjustment filters of the model-based signal extraction method of SEATS, using corresponding properties of X-11/12-ARIMA filters as a convenient reference. One-sided and symmetric filters determined by Box and Jenkins’ airline models for time series of lengths 49 and 109 are considered. Our analyses are preceded by a discussion of three approaches to filter design: the Digital Signal Processing approach, the Optimal Filtering approach motivating SEATS, and a synthesis that we find appropriate for SEATS. Our most important conclusion is that the frequency domain diagnostics of SEATS are inadequate. In particular, the gain function of the infinite symmetric model-based filter provided by SEATS can fail to show significant features of the finite filter gain function, and it provides virtually no insight into the properties of the one-sided concurrent filter, whose gain and phase delay offer more relevant information for most users of seasonally adjusted data.
