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 languageEnglish
Pages (from-to)535-544
Number of pages10
JournalActa Mathematica Sinica, English Series
Volume22
Issue number2
DOIs
Publication statusPublished - 2006 Apr 1

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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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The law of iterated logarithm of rescaled range statistics for AR(1) model. / Lin, Zheng Yan; Lee, Sung Chul.

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

Research output: Contribution to journalArticle

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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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