Variance Measures for X-11 Seasonal Adjustment: A Summing Up of Empirical Work

1. Introduction Pfeffermann (1994) has proposed a solution to the long-standing problem of variance measures for time series seasonally adjusted by the X-11 method (Ladiray & Quenneville, 2001). Pfeffermann's approach builds from a method suggested by Wolter & Monsour (1981), using sampling error information and the linear approximation to X-11. The present paper pulls together results across the last decade, plus new results for variance estimation of seasonally adjusted change. The U.S. Bureau of Labor Statistics (BLS) is considering use of these measures for the analysis of employment and unemployment statistics as early as 2007. After a brief preview of results in this section, methodology will be reviewed in Section 2. Section 3 presents basic results, both for pure X-11 seasonal adjustment and for the case of ARIMA extrapolation, with highlights from Pfeffermann & Scott (1997) and Pfeffermann, Scott, & Tiller (2000). Next, we compare our method with a method proposed by Bell & Kramer (1999), first treated in Scott & Pfeffermann (2003). Section 4 contains results for employment change, which expand and improve results presented in Scott, Sverchkov, & Pfeffermann (2004). The final section summarizes additional past work, outlines next steps to be taken, and offers conclusions. We begin with the usual notion that an economic time series consists of a trend or trend-cycle, a seasonal component, and an irregular term,