The Law of Iterated Logarithm of Rescaled Range Statistics for AR(1) Model

Authors
Lin, Yan Zheng Lee, Sung Chul
Citation
Lin, Yan Zheng et Lee, Sung Chul, The Law of Iterated Logarithm of Rescaled Range Statistics for AR(1) Model, Acta mathematica Sinica. English series (Print) , 22(2), 2006, pp. 535-544
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
22
Issue
2
Year of publication
2006
Pages
535 - 544
Database
ACNP
SICI code
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(.kj=1(Xj.X.n)).min1.k.n(.kj=1(Xj.X.n)))/(n.1.nj=1(Xj.X.n)2)1/2where X.n=n.1.nj=1Xj.In this paper we show a law of iterated logarithm for rescaled range statistics Q(n) for AR(1) model