The X11 Procedure

Effect of Backcast and Forecast Length

Based on a number of empirical studies (Dagum 1982a, 1982b, 1982c; Dagum and Laniel 1987), one year of forecasts minimize revisions when new data become available. Two and three years of forecasts show only small gains.

Backcasting improves seasonal adjustment but introduces permanent revisions at the beginning of the series and also at the end for series of length 8, 9, or 10 years. For series shorter than 7 years, the advantages of backcasting outweigh the disadvantages (Dagum 1988).

Other studies (Pierce 1980; Bobbit and Otto 1990; Buszuwski 1987) suggest "full forecasting"— that is, using enough forecasts to allow symmetric weights for the seasonal moving averages for the most current data. For example, if a $3\times 9$ seasonal moving average was specified for one or more months by using the MACURVES statement, five years of forecasts would be required. This is because the seasonal moving averages are performed on calendar months separately, and the $3\times 9$ is an 11-term centered moving average, requiring five observations before and after the current observation. Thus

   macurves dec='3x9';

would require five additional December values to compute the seasonal moving average.