The Law of Iterated Logarithm of Rescaled Range Statistics for AR(1) Model  

作　　者：Zheng Yan LIN Sung Chul LEE 

机构地区：[1]Department of Mathematics, Zhejiang University [2]Department of Mathematics, Yonsei University

出　　处：《Acta Mathematica Sinica,English Series》2006年第2期535-544,共10页数学学报（英文版）

基　　金：supported by NSFC(10071072) ;supported by SRFDP(200235090);support by the BK21 Project of the Department of Mathematics,Yonsei University;the Interdisciplinary Research Program of KOSEF 1999-2-103-001-5 and com2MaC in POSTECH

摘　　要：Let {Xn,n ≥ 0} be an AR（1） process. Let Q（n） be the rescaled range statistic, or the R/S statistic for {Xn} which is given by （max1≤k≤n（∑j=1^k（Xj - ^-Xn）） - min 1≤k≤n（∑j=1^k（ Xj - ^Xn ））） /（n ^-1∑j=1^n（Xj -^-Xn）^2）^1/2 where ^-Xn = n^-1 ∑j=1^nXj. In this paper we show a law of iterated logarithm for rescaled range statistics Q（n） for AR（1） model.Let {Xn,n ≥ 0} be an AR（1） process. Let Q（n） be the rescaled range statistic, or the R/S statistic for {Xn} which is given by （max1≤k≤n（∑j=1^k（Xj - ^-Xn）） - min 1≤k≤n（∑j=1^k（ Xj - ^Xn ））） /（n ^-1∑j=1^n（Xj -^-Xn）^2）^1/2 where ^-Xn = n^-1 ∑j=1^nXj. In this paper we show a law of iterated logarithm for rescaled range statistics Q（n） for AR（1） model.

关 键 词：Rescaled range statistics Law of iterated logarithm AR（1） model 

分 类 号：O212.1[理学—概率论与数理统计]