摘要
The predictive capability of a modification of Rissanen's accumulated prediction error (APE) criterion, APE δn , is investigated in infinite-order autoregressive (AR(∞)) models. Instead of accumulating squares of sequential prediction errors from the beginning, APEδ n is obtained by summing these squared errors from stage nδ n , where n is the sample size and 1/n ≤ δ n ≤ 1 - (1/n) may depend on n. Under certain regularity conditions, an asymptotic expression is derived for the mean-squared prediction error (MSPE) of an AR predictor with order determined, by APEδ n . This expression shows that the prediction performance of APEδ n can vary dramatically depending on the choice of δ n . Another interesting finding is that when δ n approaches 1 at a certain rate, APEδ n can achieve asymptotic efficiency in most practical situations. An asymptotic equivalence between APEδ n and an information criterion with a suitable penalty term, is also established from the MSPE point of view. This offers new perspectives for understanding the information and prediction-based model selection criteria. Finally, we provide the first asymptotic efficiency result for the case when the underlying AR(∞) model is allowed to degenerate to a finite autoregression. © Institute of Mathematical Statistics, 2007.