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X-13ARIMA-SEATS Seasonal Adjustment Program

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Generalizations of the Box-Jenkins Airline Model with Frequency-Specific Seasonal Coefficients and a Generalizaton of Akaike’s MAIC

John Aston(1), David F. Findley(2), Kellie Wills(3) and Donald Martin(4)


The Box-Jenkins “airline” model is the most widely used ARIMA model for seasonal time series. Findley, Martin and Wills (2002) examined a generalization of the airline model with a more restricted seasonal moving average factor that models only seasonal effects and with a second-order nonseasonal moving average factor. Here, we generalize the seasonal factor further by associating a subset of the frequencies 1, 2, 3, 4, 5 and 6 cycles per year (in the case of monthly data) with one coefficient and the complementary subset with a second coefficient. A generalization of Akaike’s Minimum AIC criterion is presented for choosing among subsets of a given size or, more generally, among generalizations of the airline model having the same number of coefficients. Properties of modelbased seasonal adjustment filters obtained from the new models are considered as well as forecasting performance relative to the airline model.


Time series, seasonal adjustment, forecasting, model selection, 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) Kellie C. Wills is currently a doctoral student.

(4) 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: April 02, 2015