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X-13ARIMA-SEATS Seasonal Adjustment Program

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Modifications of SEATS' Diagnostic for Detecting Over- or Underestimation of Seasonal Adjustment Decomposition Components

David F. Findley(1), Tucker S. McElroy(2) and Kellie Wills (3)


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

(1) David F. Findley was the Senior Mathematical Statistican for Time Series and is now a consultant, U. S. Census Bureau, 4600 Silver Hill Road, Washington, DC 20233. email : david.f.findley@census.gov

(2) Tucker S. McElroy is Mathematical Statistican, U. S. Census Bureau, 4600 Silver Hill Road, Washington, DC 20233. email : Tucker.S.McElroy@census.gov

(3) Kellie C. Wills is currently a doctoral student.

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Source: U.S. Census Bureau | Center for Statistical Research and Methodology | (301) 763-1649 (or x12@census.gov) |  Last Revised: November 19, 2012