Order selection for same-realization predictions in autoregressive processes
成果类型：
Article
署名作者：
Ing, CK; Wei, CZ
署名单位：
Academia Sinica - Taiwan; National Taiwan University
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/009053605000000525
发表日期：
2005
页码：
2423-2474
关键词：
least-squares predictors
model selection
variables
摘要：
Assume that observations are generated from ail infinite-order autoregressive [AR(infinity)] 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 ail 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 Oil 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 ill 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. Oil 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.