The Hurst phenomenon and the rescaled range statistic

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Mason, David M.¹ 

[1] Univ Delaware, Dept Appl Econ & Stat, 213 Townsend Hall, Newark, DE 19716 USA

关键词: Resealed range statistic;    Hurst phenomenon;    Subgaussian;   

DOI  :  10.1016/j.spa.2016.04.008

来源: Elsevier

【 摘 要 】

In his 1951 study of Nile River data, H.E. Hurst introduced the resealed range statistic-the R/S statistic. He argued via a small simulation study that if X-i, i = 1,...,n, are i.i.d. normal then the R/S statistic should grow in the order of root n. However, Hurst found that for the Nile River data, the R/S statistic increased not in the order of root n, but in the order n(H), where H ranged between 0.75 and 0.80. He discovered that the effect also appeared in other sets of data. This is now called the Hurst phenomenon. We shall establish some unexpected universal asymptotic properties of the R/S statistic, which show conclusively that the Hurst phenomenon can never appear for i.i.d. data. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

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