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.
Source: U.S. Census Bureau, Statistical Research Division
Created: October 18, 2007
Last revised: October 18, 2007
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