We develop an approach to estimating variances for X-11 seasonal adjustments that recognizes the effects of sampling error and errors from forecast extension. In our approach, seasonal adjustment error in the central values of a sufficiently long series results only from the effect of the X-11 filtering on the sampling errors. Towards either end of the series, we also recognize the contribution to seasonal adjustment error from forecast and backcast errors. We extend the approach to produce variances of errors in X-11 trend estimates, and to recognize error in estimation of regression coefficients used to model, e.g., calendar effects. In empirical results, the contribution of sampling error often dominated the seasonal adjustment variances. Trend estimate variances, however, showed large increases at the ends of series due to the effects of fore/backcast error. Nonstationarities in the sampling errors produced striking patterns in the seasonal adjustment and trend estimate variances.

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Time Series and Seasonal Adjustment Working Papers

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