Generalizations of the Box-jenkins Airline Model with Frequency-specific Seasonal Coefficients and a Generalizaton of Akaike's Maic

Abstract

The Box-Jenkins ?€?airline?€? model is the most widely used univariate time series model for seasonal economic 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. Joint work with: John Aston, Tucker McElroy, Kellie Wills, and Donald Martin