SPECTRAL PROPERTIES OF LINEAR CONCURRENT AND SYMMETRIC SEASONAL ADJUSTMENT FILTERS OF SEATS AND X-11/12-ARIMA FOR SHORT AND MODERATE-LENGTH TIME SERIES
David F. Findley, Donald E. K. Martin · 2001
1 The X-12-ARIMA program was used for the analysis, but only filters also available in X-11-ARIMA were (Findley, Monsell, Bell, Otto and Chen, 1998) and TRAMO/SEATS (Gomez and Maravall, 1994). For shorter series (4-9 years) and both methods, the filter coefficients for the adjustment at time t depend in a complicated way on time series model coefficients, the series length T , and the position of t relative to T . For these and possibly other reasons, published studies of frequency domain properties of such short series are scarce. SEATS provides graphs of gain functions of biinfinite symmetric seasonal adjustment filters, and in several articles, e.g. Maravall (1999) and Gomez and Maravall (2000), frequency domain properties of biinfinite model-based symmetric filters are compared to those of the default T -independent ( 169 T ≥ ) symmetric X-11 filter (without forecast extension). However, there is no frequency domain analysis in the literature of SEATS symmetric filters for finite T or concurrent SEATS filters of any length. For X-11 filters, there has been only one unpublished study of frequency domain properties of short series (Cholette, 1979), although there have been various studies of spectral properties of T -independent concurrent and symmetric X-11-ARIMA filters and their approximations (see, for example, Dagum, 1983 and Dagum, Chhab and Chui, 1996). In this paper we present and discuss frequency domain properties of some basic suites of both concurrent and symmetric seasonal adjustment filters of X-11/12-ARIMA (with 12 months of forecasts and backcasts) and SEATS for series of short lengths, 49 T = and 109 T = . We begin with background material.