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.