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

Zheng Yan Lin, Sung Chul Lee

Research output: Contribution to journalArticlepeer-review

7 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

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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