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We consider alternative definitions of seasonal adjustment variances for both model-based and X-11 type seasonal adjustments. In particular, when we account for sampling error components of time series we can consider either the variance of the estimation error for the nonseasonal component of the true series, or the variance of the estimation error for the seasonally adjusted series (observed series minus estimated seasonal component). The magnitudes of these variances can be quite different. We examine the relative contributions of various error components to seasonal adjustment variances, and the effects on model-based seasonal adjustment variances of uncertainty about model parameters. The considerations are illustrated with several examples.
sampling error, canonical decomposition, forecast extension
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