NEW ARIMA MODELS FOR SEASONAL TIME SERIES AND THEIR
APPLICATION TO SEASONAL ADJUSTMENT AND FORECASTING
John A.D. Aston, David F. Findley,Tucker S. McElroy, Kellie C. Wills, and Donald E.K. Martin
KEY WORDS: Airline model; Frequency-Specific Model; Generalized Airline Model; Model selection; AIC; F-AIC
ABSTRACT
Focusing on the widely-used Box-Jenkins “airline” model, we show how the class
of seasonal ARIMA models with a seasonal moving average factor can be parsimoniously
generalized to model time series with heteroskedastic seasonal frequency components. Our
frequency-specific models decompose this factor by associating one moving average coefficient
with a proper subset of the seasonal frequencies 1, 2, 3, 4, 5 and 6 cycles per year and a second
coefficient with the complementary subset. A generalization of Akaike’s AIC is presented to
determine these subsets. Properties of seasonal adjustment filters and adjustments obtained
from the new models are examined as are forecasts.
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