A General Method for Estimating the Variances of X‐11 Seasonally Adjusted Estimators

Abstract

The X-11 procedure with its various variants is the commonly used procedure for seasonal adjustment throughout the world. A well-known problem with the use of this procedure, however, is the estimation of the variances of its output such as, for example, the variances of the seasonally adjusted data or the month to month changes in these data. In this paper we propose a simple general procedure for estimating the variances of the X-11 estimators. The variances account for the sampling distribution of the survey estimators around the corresponding population values and for the distribution of the component series included in the decomposition of the population values. The procedure is applicable to general sampling designs, including partially overlapping surveys. Empirical results illustrating the performance of the procedure when applied to simulated and real series are presented.

A Data-Driven Selection of an Appropriate Seasonal Adjustment Approach

“…Within the non-parametric X-11 framework, such comparisons cannot be achieved since the theoretical properties of UC estimators cannot be derived in an analogous way. Nevertheless, various variance measures have been constructed to quantify different sources of error in X-11 seasonal adjustments, see Pfeffermann (1994) and Scott, Pfeffermann, and Sverchkov (2012).…”

Estimation of Mean Squared Error of X-11-ARIMA and Other Estimators of Time Series Components

“…G t ¼ T t þ S t , e t ¼ I t þ 1 t . In this case e t is the combined error of the time series irregular term and the sampling error (Pfeffermann 1994); GE2. G t ¼ T t þ S t þ I t , e t ¼ 1 t .…”

“…By (5), the variance of the X-11-ARIMA trend estimator is in this case a linear combination of the covariances v tm ¼ Covðe t ; e m Þ; t; m ¼ 1; : : : ; N. Following Pfeffermann (1994) and Pfeffermann and Scott (1997) …”

Producing Monthly Estimates of Unemployment and Employment According to the International Labour Office Definition

“…One issue is whether to take the series of values Y t as ®xed or as the realization of some stochastic process (Wolter and Monsour, 1981). Pfeermann (1994) proposed a method of estimating the variances of seasonally adjusted estimates obtained from X-11 which accounts for the sampling errors and the variability of the time series components of Y t . Applying this method to the series of total unemployment for Canada for 1981± 89 Pfeermann (1994) obtained standard deviations of the adjusted estimator of level less than those of the unadjusted estimator, except towards the end of the series where they were a little higher.…”

“…Pfeermann (1994) proposed a method of estimating the variances of seasonally adjusted estimates obtained from X-11 which accounts for the sampling errors and the variability of the time series components of Y t . Applying this method to the series of total unemployment for Canada for 1981± 89 Pfeermann (1994) obtained standard deviations of the adjusted estimator of level less than those of the unadjusted estimator, except towards the end of the series where they were a little higher. Using a dierent approach based on a linear approximation to X-11, Sutclie and Lee (1995) studied the standard errors of seasonally adjusted estimates of level and movement under dierent rotation schemes assuming a simple geometric decay model for the correlations between survey estimates.…”