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
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