2005/10/01 by Ching-Kang Ing, Ching-Zong Wei · 7 citations
Decision Sciences · Mathematics · #Advanced Statistical Process Monitoring #Akaike information criterion #Algorithm #Applied mathematics #Artificial intelligence #Autoregressive model #Computer science #Econometrics #Mathematical optimization #Mathematics #Model selection #Order (exchange) #Realization (probability) #Selection (genetic algorithm) #Series (stratigraphy) #Statistical Distribution Estimation and Applications #Statistical Methods and Inference #Statistics #math.ST #msc:60M20 #msc:62M10 #stat.TH
paper · pdf · doi:10.1214/009053605000000525
published as Annals of Statistics 2005, Vol. 33, No. 5, 2423-2474 · Published at http://dx.doi.org/10.1214/009053605000000525 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2005/10/01 · arxiv created 2006/02/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Assume that observations are generated from an infinite-order autoregressive [AR(∞)] process. Shibata [Ann. Statist. 8 (1980) 147–164] considered the problem of choosing a finite-order AR model, allowing the order to become infinite as the number of observations does in order to obtain a better approximation. He showed that, for the purpose of predicting the future of an independent replicate, Akaike’s information criterion (AIC) and its variants are asymptotically efficient. Although Shibata’s concept of asymptotic efficiency has been widely accepted in the literature, it is not a natural property for time series analysis. This is because when new observations of a time series become available, they are not independent of the previous data. To overcome this difficulty, in this paper we focus on order selection for forecasting the future of an observed time series, referred to as same-realization prediction. We present the first theoretical verification that AIC and its variants are still asymptotically efficient (in the sense defined in Section 4) for same-realization predictions. To obtain this result, a technical condition, easily met in common practice, is introduced to simplify the complicated dependent structures among the selected orders, estimated parameters and future observations. In addition, a simulation study is conducted to illustrate the practical implications of AIC. This study shows that AIC also yields a satisfactory same-realization prediction in finite samples. On the other hand, a limitation of AIC in same-realization settings is pointed out. It is interesting to note that this limitation of AIC does not exist for corresponding independent cases.