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 \( (\max _{{1 \leqslant k \leqslant n}} ({\sum\nolimits_{j = 1}^k {(X_{j} - \bar{X}_{n} )) - \min _{{1 \leqslant k \leqslant n}} ({\sum\nolimits_{j = 1}^k {(X_{j} - \bar{X}_{n} )))/(n^{{ - 1}} {\sum\nolimits_{j = 1}^n {(X_{j} - \bar{X}_{n} )^{2} )^{{1/2}} } }} }} } \)where \( \bar{X}_{n} = n^{{ - 1}} {\sum\nolimits_{j = 1}^n {X_{j} .} } \)In this paper we show a law of iterated logarithm for rescaled range statistics Q(n) for AR(1) model.
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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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Lin, Z.Y., Lee, S.C. The Law of Iterated Logarithm of Rescaled Range Statistics for AR(1) Model. Acta Math Sinica 22, 535–544 (2006). https://doi.org/10.1007/s10114-005-0553-1
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DOI: https://doi.org/10.1007/s10114-005-0553-1