Selection of a Multistep Linear Predictor for Short Time Series

We develop a version of the Corrected Akaike Information Criterion (AICC) suitable for selection of an h-step-ahead linear predictor for a weakly stationary time series in discrete time. A motivation for this criterion is provided in terms of a generalized Kullback-Leibler information which is minimized at the optimal h-step predictor, and which is equivalent to the ordinary Kullback-Leibler information when h = 1. In a simulation study, we find that if the sample size is small and the predictor coefficients are estimated by Burg’s method, then AICC typically outperforms both the ordinary Akaike Information Criterion (AIC) and the Final Prediction Error (FPE) for h-step prediction, and we present evidence to indicate that Burg estimation can produce much better selected predictors than Yule-Walker estimation.