2004/04/01 by Ching‐Kang Ing, Ching-Kang Ing · 1 citation
Engineering · Mathematics · #Advanced Control Systems Optimization #Control Systems and Identification #Fault Detection and Control Systems #math.ST #msc:60F15. #msc:62M10 #msc:62M20 #stat.TH
paper · pdf · doi:10.1214/009053604000000148
published as Annals of Statistics 2004, Vol. 32, No. 2, 693-722
openalex publication_date 2004/04/01 · arxiv created 2004/06/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of choosing the optimal (in the sense of mean-squared prediction error) multistep predictor for an autoregressive (AR) process of finite but unknown order. If a working AR model (which is possibly misspecified) is adopted for multistep predictions, then two competing types of multistep predictors (i.e., plug-in and direct predictors) can be obtained from this model. We provide some interesting examples to show that when both plug-in and direct predictors are considered, the optimal multistep prediction results cannot be guaranteed by correctly identifying the underlying model”s order. This finding challenges the traditional model (order) selection criteria, which usually aim to choose the order of the true model. A new prediction selection criterion, which attempts to seek the best combination of the prediction order and the prediction method, is proposed to rectify this difficulty. When the underlying model is stationary, the validity of the proposed criterion is justified theoretically. To obtain this result, asymptotic properties of accumulated squares of multistep prediction errors are investigated. In addition to overcoming the above difficulty, some other advantages of the proposed criterion are also mentioned.