We develop an approach to estimating variances for X-11 seasonal adjustments that recognizes the effects of sampling error and revisions (the latter result from errors in forecast extension). We assume that both the true underlying series and the sampling errors follow known time series models. In practice these models are estimated using the time series data and estimates of the variances and lagged co-variances of the sampling errors. The model is used to extend the series with forecasts and backcasts, allowing use of the symmetric X-11 filter. 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 (assuming an additive or log-additive decomposition and using a linear approximation to X-11). This agrees with an approach suggested by Wolter and Monsour (1981).

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WORKING PAPER

Statistical Research Reports and Studies

Time Series and Seasonal Adjustment Working Papers

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