M-estimation for Moderate Deviations From a Unit Root

被引:3
作者
Kong, Xin-Bing [1 ,2 ]
机构
[1] Soochow Univ, CASER, Suzhou, Peoples R China
[2] Soochow Univ, Sch Math, Suzhou, Peoples R China
关键词
M-estimation; Unit root; Local to unit root; Moderately deviated root; Bahadur representation; TIME-SERIES;
D O I
10.1080/03610926.2012.751114
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
Phillips and Magdalinos (2007) introduced a larger neighborhoods of one (called moderate deviations) than the conventional local to unity roots in autoregression models. Least square estimates (LSE) of the serial correlation coefficient were studied and asymptotics were provided. In this article, we investigate the M-estimation of the serial correlation coefficient having moderate deviations from the unit root. For both the near stationary case and explosive case, the Bahadur representations and limits in distribution are given for the M-estimators of the serial correlation coefficient. The limit theory demonstrates that the convergence rates of the M-estimators are the same as that for LSE hence bridging the very different convergence rates of the stationary and unit root cases. The limit theory also facilitates the comparison of the relative asymptotic efficiency among different estimators within the family of M-estimators.
引用
收藏
页码:476 / 485
页数:10
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