| The Law of Iterated Logarithm of Rescaled Range Statistics for AR（1） Model |
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| 引用本文： | Zheng Yan LIN Sung Chul LEE.The Law of Iterated Logarithm of Rescaled Range Statistics for AR（1） Model[J].数学学报(英文版),2006,22(2):535-544. |
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| 作者姓名： | Zheng Yan LIN Sung Chul LEE |
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| 作者单位： | [1]Department of Mathematics, Zhejiang University, Hangzhou 310028, P. R. China [2]Department of Mathematics, Yonsei University, Seoul 120 749, Korea |
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| 基金项目： | The first author is supported by NSFC （10071072） and SRFDP（200235090）. The second author is supported by the BK21 Project of the Department of Mathematics, Yonsei University, the Interdisciplinary Research Program of K0SEF 1999-2-103-001-5 and Com^2MaC in P0STECH |
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| 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.
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| 关 键 词： | 迭代算法 值域统计 AR（1）模型 时间序列 |
| 收稿时间： | 2003-03-21 |
| 修稿时间： | 2003-03-212004-02-09 |
The Law of Iterated Logarithm of Rescaled Range Statistics
for AR(1) Model |
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| Zheng Yan Lin,Sung Chul Lee.The Law of Iterated Logarithm of Rescaled Range Statistics
for AR(1) Model[J].Acta Mathematica Sinica,2006,22(2):535-544. |
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| Authors: | Zheng Yan Lin Sung Chul Lee |
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| Institution: | Sungchul;LEE |
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| Abstract: | 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
where
In this paper we show a law of iterated
logarithm for rescaled range statistics Q(n) for AR(1) model.
The first author is supported by NSFC (10071072) and SRFDP(200235090). The second author is supported 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 |
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| Keywords: | Rescaled range statistics Law of iterated logarithm AR(1) model |
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