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清華大學統計學研究所
國立清華大學統計學研究所
2016-09-30(五),主講人:俞淑惠 副教授 (國立高雄大學 統計所)

清華大學、交通大學

統 計 學 研 究 所

專 題 演 講

 


講 題: Order selection for predictions in high-dimensional AR models: the cases of I(d) processes   
演講者: 俞淑惠 副教授 (國立高雄大學 統計所)
時 間: 105年09月30日(星期五)10:40 - 12:00  (上午10:20 - 10:40茶會於統計所821室舉行)
地 點: 綜合三館837室
摘 要: Most order selection methods in high-dimensional autoregressive models are devised for processes of integrated of order 0 (I(d) processes, d = 0). We consider in this paper an I(d) autoregressive (AR) process, d ≥ 0 is an unknown integer and the lag order may be finite or infinite. The number of lags considered, Pn, goes to infinity, when the sample size, n, does. While Sin and Yu (2016) show that Akaike’s information criterion (AIC) is asymptotically inefficient (in terms of prediction) when the lag order is finite; this paper shows that when the lag order is infinite with algebraically decaying AR coefficients, neither Bayesian information criterion (BIC) nor Hanan Quninn information criterion (HQIC) is asymptotically inefficient. These results motivate us to combine the strengths of AIC and BIC/HQIC, yielding a so-called two-stage information criterion (TSIC) for a general I(d) AR process. We show that TSIC is asymptotically efficient in the aforementioned two scenarios, as well as the scenario of exponentially decaying AR coefficients. This paper concludes with a simulation study which compares various information criteria with the least absolute shrinkage and selection operator (Lasso) and the adaptive Lasso. Although the (modified) Lasso-type methods perform comparably with, if not marginally outperform, the TSIC for some processes, the TSIC performs substantially better for some other processes.

 

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