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X-13ARIMA-SEATS Seasonal Adjustment Program

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Generalizations of the Box-Jenkins Airline Model

David F. Findley (1), Donald E. K. Martin (2) and Kellie C. Wills (3)


Two generalizations of the Box-Jenkins airline model were fit to a variety of time series, including two series identified by Fiorentini and Planas (2001) for which the fitted airline model does not have an admissible decomposition for model-based seasonal adjustment and one-hundred-eleven series for which an airline model had been chosen by an experienced modeler. One of the generalizations has admissible decompositions for both Fiorentini and Planas series and at least one of the generalizations is preferred over the airline model by AIC for thirty-two of the one-hundred-eleven series. Some comparisons are made of the gain and phase delay properties of model-based seasonal adjustment filters of the preferred model and the airline model for some series for which both models have admissible decompositions.


time series, seasonal adjustment, forecasting, filters, phase delay, squared gain

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

(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 |  Last Revised: April 02, 2015