In:
Journal of Applied Probability, Cambridge University Press (CUP), Vol. 20, No. 03 ( 1983-09), p. 649-662
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 form f ( n ) = c ( m + n ) ß , where m is an arbitrary non-negative parameter and c is not 0. For – ½ & lt; ß & lt; 0 the Hurst exponent is shown to be precisely given by 1 + ß. For ß ≦ – ½ and for ß = 0 the Hurst exponent is 0.5, while for ß & gt; 0 it 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.
Type of Medium:
Online Resource
ISSN:
0021-9002
,
1475-6072
DOI:
10.1017/S0021900200023895
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
1983
detail.hit.zdb_id:
1474599-9
detail.hit.zdb_id:
219147-7
SSG:
3,2
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