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.
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
