The Prediction of Tik Series with Trends and Seasonalities*

Amaximization of the expected entropy of the predictive distribution interpretation of Akaike's minimum AIC procedure is exploited for the modeling and prediction of time series with trend and seasonal mean value functions and stationary covariances. The AIC criterion best one-step-ahead and best twelvestep-ahead prediction models are different. They exhibit the relative optimality properties for which they were designed. The results are related to open questions on optimal trend estimation and optimal seasonal adjustment of time series. *This paper was written when both authors were American Statistical Association Fellows in Time Series at the U.S. Bureau of the Census, 1981-1982.