Model Selection, AIC

Abstract. 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 model-based seasonal adjustment filters obtained from the new models are considered as well as forecasting performance relative to the airline model