报告人：Professor Chor-yiu (CY) SIN
National Tsing Hua University, Taiwan
题目：Asymptotic risk of order selection in high-dimensional autoregressive models
摘要：Most order selection methods in autoregressive (AR) models are devised for processes of integrated of order 0 (I(d) processes, d = 0). We consider in this paper an I(d) AR process, is an unknown integer and the lag order is finite. The number of lags considered, Pn(d), may be finite; and in view of the flourishing literature on high-dimensional models, Pn(d) may also go to infinity, when the sample size, n, does. This paper first shows that Akaike's information criterion (AIC) is asymptotically inefficient (in terms of prediction) in finite-order AR processes, while the Bayesian information criterion (BIC) or the Hannan Quninn information criterion (HQIC) is asymptotically efficient. In other words, our results give some warnings on inappropriate choices of the penalty term in an information criterion, should the true lag order is finite. At the same time, we extend the asymptotic risk of order selection in AR models in fourfold: (i) a general I(d) process; (ii) the same realization of the data; (iii) an information criterion that is more general than AIC; and (iv) or.