Order selection for same-realization predictions in autoregressive processes

@article{Ing2005OrderSF,
  title={Order selection for same-realization predictions in autoregressive processes},
  author={Ching-Kang Ing and Ching-Zong Wei},
  journal={Annals of Statistics},
  year={2005},
  volume={33},
  pages={2423-2474}
}
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… 

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