Calculating the Variance of Seasonally Adjusted Series

Abstract

Abstract This article considers the use of the Kalman filter to perform the seasonal adjustment and to calculate the variance of the signal extraction error in model-based seasonal adjustment procedures. The steady-state filter covariance is seen to provide a convenient basis for obtaining the variances not only of the current adjustment but also of subsequent revisions. The method is applied to the unobserved-components model we have recently proposed as a justification of the X-11 method and to a real economic time series.