New Models for Seasonal Time Series and a Modification of Akaike's AIC for Associated Multiple Comparisons
David F. Findley,
John A. Aston, Institute of Statistical Science,
Donald E. K. Martin,
Kellie C. Wills, Corporate Executive Board
Abstract
I will present joint work on a class of generalizations of the "airline" model of Box and Jenkins (1969), a remarkably successful model for seasonal time series, with one "nonseasonal" and one "seasonal" coefficient. For series observed s times a year (typically s = 4 or 12), the main focus will be on generalizations that use one additional seasonal coefficient, modeling the situation in which two complementary subsets of k and s-k seasonal frequency components have different stochastic behavior. For a given k, there are s!/k!(s - k)! models to be compared to the airline model. To deal with this multiplicity of comparisons, we developed a simulation-based modification of Akaike's minimum AIC model selection criterion (MAIC) that will be described. The new models were fit to sixty-five Census Bureau Foreign Trade and Manufacturing series for which an airline model had previously been selected. For about a third of the series, one of the new models is preferred by the modified MAIC criterion. Often this preferred model provides better out-of-sample forecasts and/or a more appealing seasonal adjustment than the airline model. Some relevant basic time series concepts will be briefly reviewed.