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X-13ARIMA-SEATS Seasonal Adjustment Program

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New ARIMA Models for Seasonal Time Series and Their Application to Seasonal Adjustment and Forecasting

John A.D. Aston(1), David F. Findley(2), Tucker S. McElroy(3), Kellie C. Wills(4), Donald E. K. Martin(5)


Focusing on the widely-used Box-Jenkins "airline" model, we show how the class of seasonal ARIMA models with a seasonal moving average factor can be parsimoniously generalized to model time series with heteroskedastic seasonal frequency components. Our frequency-specific models decompose this factor by associating one moving average coefficient with a proper subset of the seasonal frequencies 1, 2, 3, 4, 5 and 6 cycles per year and a second coefficient with the complementary subset. A generalization of Akaike's AIC is presented to determine these subsets. Properties of seasonal adjustment filters and adjustments obtained from the new models are examined as are forecasts.


Airline model; Frequency-Specific Model; Generalized Airline Model; Model selection; AIC; F-AIC

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

(2) 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 :

(3) Tucker S. McElroy is Mathematical Statistican, Center for Statistical Research and Methodology U. S. Census Bureau, 4600 Silver Hill Road, Washington, DC 20233. email :

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

(5) Donald E. K. Martin is currently a professor at North Carolina State University.

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Source: U.S. Census Bureau | Center for Statistical Research and Methodology | (301) 763-1649 (or |  Last Revised: August 07, 2015