The law of iterated logarithm of rescaled range statistics for AR(1) model

Zheng Yan Lin; Sung Chul Lee

doi:10.1007/s10114-005-0553-1

The law of iterated logarithm of rescaled range statistics for AR(1) model

Zheng Yan Lin, Sung Chul Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

Let { X_n, n ≥ 0} be an AR(1) process. Let Q(n) be the rescaled range statistic, or the R/S statistic for {X_n} which is given by (max1≥k≥n(Σ_j=1^k (X_j - X̄_n)) - min1≥k≥n(Σ_j=1^k (X _j - X̄_n)))/(n^-1 Σ_j=1 ⁿ (X_j - X̄_n)²)^1/2 where X̄_n = n^-1 Σ_j=1ⁿ X_j. In this paper we show a law of iterated logarithm for rescaled range statistics Q (n) for AR(1) model.

Original language	English
Pages (from-to)	535-544
Number of pages	10
Journal	Acta Mathematica Sinica, English Series
Volume	22
Issue number	2
DOIs	https://doi.org/10.1007/s10114-005-0553-1
Publication status	Published - 2006 Apr

Bibliographical note

Funding Information:
Received March 21, 2003, Accepted February 9, 2004 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

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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title = "The law of iterated logarithm of rescaled range statistics for AR(1) model",

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 (max1≥k≥n(Σj=1k (Xj - {\=X}n)) - min1≥k≥n(Σj=1k (X j - {\=X}n)))/(n-1 Σj=1 n (Xj - {\=X}n)2)1/2 where {\=X}n = n-1 Σj=1n Xj. In this paper we show a law of iterated logarithm for rescaled range statistics Q (n) for AR(1) model.",

author = "Lin, {Zheng Yan} and Lee, {Sung Chul}",

note = "Funding Information: Received March 21, 2003, Accepted February 9, 2004 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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doi = "10.1007/s10114-005-0553-1",

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AU - Lee, Sung Chul

N1 - Funding Information: Received March 21, 2003, Accepted February 9, 2004 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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N2 - 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(Σj=1k (Xj - X̄n)) - min1≥k≥n(Σj=1k (X j - X̄n)))/(n-1 Σj=1 n (Xj - X̄n)2)1/2 where X̄n = n-1 Σj=1n Xj. In this paper we show a law of iterated logarithm for rescaled range statistics Q (n) for AR(1) model.

AB - 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(Σj=1k (Xj - X̄n)) - min1≥k≥n(Σj=1k (X j - X̄n)))/(n-1 Σj=1 n (Xj - X̄n)2)1/2 where X̄n = n-1 Σj=1n Xj. In this paper we show a law of iterated logarithm for rescaled range statistics Q (n) for AR(1) model.

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JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

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ER -

The law of iterated logarithm of rescaled range statistics for AR(1) model

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