Author:
Bhattacharya R. N.,Gupta Vijay K.,Waymire Ed
Abstract
Necessary and sufficient conditions for the so-called Hurst effect are given in the case of a weakly dependent stationary sequence of random variables perturbed by a trend. As a consequence of this general result it is shown that the Hurst effect is present in the case of weakly dependent random variables with a small monotonic trend of the formf(n) =c(m+n)ß, where m is an arbitrary non-negative parameter andcis not 0. For – ½ <ß< 0 the Hurst exponent is shown to be precisely given by 1 +ß.Forß≦ – ½ and forß= 0 the Hurst exponent is 0.5, while forß > 0it is 1. This simple mathematical model, motivated by empirical evidence in various geophysical records, demonstrates the presence of the Hurst effect in a direction not explored before.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Reference21 articles.
1. On the range of cumulative sums
2. Burton R. and Waymire E. (1983) Limit theorems for point random fields. J. Math. Anal.
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138 articles.
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