Controlling Revisions in Arima-Model-Based Seasonal Adjustment

The Statistical Office of the European Community (EUROSTAT) currently uses two different methods for seasonally adjusting macroeconomic indicators, through the implementations of the programs X-12-ARIMA ( Findley et al ., 1998 ) and TRAMO-SEATS ( Gómez and Maravall, 1996 ). A major difference between the two methodologies is that X-11 filters are of finite length while the signal extraction filters in TRAMO-SEATS are infinite whenever the observed series model embodies a MA part. In this paper, we show how infinite seasonal adjustment filters can be optimally approximated by finite ones, and we apply this result to the problem of controlling the length of the revision period. We also show how considering finite versions of the signal extraction filters improves the interpretation of the X-11 filters in the model-based framework.