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.