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X-13ARIMA-SEATS Seasonal Adjustment Program

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Diagnostics for ARIMA-Model-Based Seasonal Adjustment

David F. Findley (1), Kellie C. Wills (2), John A. D. Aston (3), Roxanne M. Feldpausch (4) and Catherine C. H. Hood (5)


We present two types of diagnostics for SEATS and similar programs. We start with modifications of the diagnostic used by SEATS to detect underestimation or overestimation, meaning inadequate or excessive supression of frequency components near the target frequencies, e.g. the seasonal frequencies in the case of seasonal adjustment. The modifications use time-varying variances of the finite-length filter output instead of the constant variance associated with the infinite-length filter. The SEATS diagnostic is shown to be substantially biased toward indicating underestimation even when the estimation is optimal, a situation where the modified diagnostics are unbiased. The second type of diagnostic considered is an adaptation of the widely used sliding spans diagnostic of X-12-ARIMA. The adaptation is a method for determining the span length appropriate for model-based-adjustment as a function of the ARIMA model's seasonal moving average parameter.


Residual seasonality, spectrum, SEATS, underestimation, overestimation, sliding spans

(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 :

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

(3) John A. D. Aston is currently at the University of Warwick. email :

(4) Roxanne M. Feldpausch is currently a consultant.

(5) Catherine C. H. Hood is currently a consultant. email :

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Source: U.S. Census Bureau | Center for Statistical Research and Methodology | (301) 763-1649 (or |  Last Revised: April 02, 2015