Pfeffermann (1994) and Bell & Kramer (1999) have proposed solutions to the long-standing problem of variance measures for time series seasonally adjusted with the X-11 method. The starting point is X-11's use of linear filters to decompose the observed series into trend, seasonal, and irregular. My interest is application to economic time series derived from surveys, where sampling error is present. The Bell-Kramer method relies on models for the sampling error and the overall series. The Pfeffermann method makes more extensive use of the data and X-11 results, and is assisted by having a model for the sampling error. In addition, the variances are defined and calculated differently.

A simulation experiment is carried out to evaluate performance of the methods, including a comparison of the underlying variance definitions. The models used in the simulation are based on a labor force series from the U.S. Current Population Survey for which sampling error information is available.

The talk should be accessible to nonspecialists, since I will begin with a brief discussion of seasonal adjustment and the X-11 method.

Bell, William R. & Matthew Kramer (1999), "Toward Variances for X-11 Seasonal Adjustments," Survey Methodology 25, 13-29.
Ladiray, Dominique & Benoit Quenneville (2001), Seasonal Adjustment with the X-11 Method, Springer, New York.
Pfeffermann, D. (1994), "A General Method for Estimating the Variances of X-11 Seasonally Adjusted Estimators," Journal of Time Series Analysis 15, 85-116.
Scott, Stuart & Danny Pfeffermann (2003), "Evaluation of Two Variance Methods for X-11 Seasonally Adjusted Series", Proceedings of the ASA Section on Business & Economic Statistics, forthcoming.