Calculating the Variance of Seasonally Adjusted Series

This paper considers the use of the Kalam 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 the current adjustment but also 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.