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X-13ARIMA-SEATS Seasonal Adjustment Program

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A Non-Gaussian Airline Model for Seasonal Adjustment

John A. D. Aston (1), Statistica Sinicia
Siem Jan Koopman (2), Free University Amsterdam


The Airline model, introduced by Box and Jenkins in their seminal book Time Series Analysis: Forecasting and Control, is routinely used to model economic time series. This model is parameterized by two factors, and gaussianity is usually assumed for the underlying noise component. Here, this model is generalised to include a non-Gaussian component to model outliers in the data. The model is examined using a state-space modelling approach, and importance sampling (see Durbin and Koopman). It utilises the decomposition method for ARIMA models developed by Hillmer and Tiao. This is necessary in order to preserve the airline structure whilst allowing a flexibility to include non-Gaussian noise terms for different components in the model. Different forms for the generalisation of the noise term are investigated. The models are interrogated through the use of a real series, the US Automobile Retail Series. The new models allow outliers to be accounted for, whilst keeping the underlying structures that are currently used to aid reporting of economic data.


airline model, ARIMA, non-gaussian models, seasonal adjustment, importance sampling.

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

(2) Siem Jan Koopman is professor, Free University of Amsterdam.

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