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

Zheng Yan Lin, Sung Chul Lee

Research output: Contribution to journalArticle

6 Citations (Scopus)

### 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 - 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.

Original language English 535-544 10 Acta Mathematica Sinica, English Series 22 2 https://doi.org/10.1007/s10114-005-0553-1 Published - 2006 Apr 1

### Fingerprint

Law of the Iterated Logarithm
Statistic
Law of Iterated Logarithm
Statistics
Range of data
Model

### All Science Journal Classification (ASJC) codes

• Mathematics(all)
• Applied Mathematics

### Cite this

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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 - 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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In: Acta Mathematica Sinica, English Series, Vol. 22, No. 2, 01.04.2006, p. 535-544.

Research output: Contribution to journalArticle

TY - JOUR

T1 - The law of iterated logarithm of rescaled range statistics for AR(1) model

AU - Lin, Zheng Yan

AU - Lee, Sung Chul

PY - 2006/4/1

Y1 - 2006/4/1

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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