We consider two modifcations of SEATS' diagnostics for determining whether, for an estimated seasonal decomposition component, there is underestimation or overestimation, meaning inadequate or excessive suppression of the other components. The diagnostic of SEATS depends on variance estimates that assume an infinitely long filter has been applied. This results in substantial bias toward indicating underestimation. Our modified diagnostics are calculated from time-varying variances associated with the finite-length filters actually used. Tests for the statistical significance of any indicated misestimation are presented and analyzed. Our diagnostics and tests also apply to structural model- based approaches to seasonal decomposition.
Signal Extraction, Auto Regressive Integrated Moving Average model, Wiener-Kolmogorov Filtering
David F. Findley was the Senior Mathematical Statistican for Time Series
and is now retired from the U. S. Census Bureau.
Kellie C. Wills is currently a senior research associate at the University of Washington.
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