Estimated variance of seasonally adjusted series

For model-based seasonal adjustment, there are explicit formulas for obtaining the variance of the seasonal factors or the seasonally adjusted series. For series adjusted with X-11 or X-12, variance estimates are generally based on a linear approximation of the seasonal adjustment procedure. The work of Pfeffermann (1992) extends earlier work by Wolter and Monseur. This study uses simulated series and comparisons of alternative seasonal adjustment results for a few economic series to assess the accuracy of variance estimates. Pfeffermann's method gives good results when the true seasonal is centered and follows a fairly smooth evolution from year to year. Comparisons with formula-based computations and estimates from the Tramo-Seats programs by Maravall and Gomez show the latter can give good variance results for series adjusted with X-11 even if the seasonal factors themselves differ from X-11 factors.