On X-11 Seasonal Adjustment and Estimation of its MSE

Most official seasonal adjustments are based on the X-11 method and its extensions. An important problem with the use of this method is how to estimate the mean square error (MSE) of the estimators of the seasonal effects and other components. Wolter and Monsour (1981) assumed that the estimators are unbiased and proposed an approach for variance estimation that uses the linear approximation to X-11 and accounts for the variability of the sampling errors. Pfeffermann (1994) and Bell and Kramer (1999) extend this approach (see below). In this paper we show that the seasonal and trend components can be defined in such a way that the X-11 estimators of these components are almost unbiased at the center of the series and consequently, Pfeffermann (1994) method produces unbiased estimators for the MSE of the X-11 estimators at the center of the series but not at the two ends. We propose, therefore, bias corrections for the MSE estimates at the ends of the series. Similar bias corrections are proposed for Bell and Kramer (1999) method.