The hurst effect and its implications for extrapolating process rates

1987 ◽  
Vol 12 (1) ◽  
pp. 57-67 ◽  
Author(s):  
M. J. Kirkby
Keyword(s):  
Hurst Effect

The Hurst effect under trends

1983 ◽  
Vol 20 (3) ◽  
pp. 649-662 ◽  
Author(s):  
R. N. Bhattacharya ◽  
Vijay K. Gupta ◽  
Ed Waymire
Keyword(s):  
Hurst Exponent ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Stationary Sequence ◽  
Monotonic Trend ◽  
Weakly Dependent Random Variables ◽  
Necessary And Sufficient ◽  
Hurst Effect ◽  
Weakly Dependent ◽  
Negative Parameter

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 < ß < 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 > 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.

Skew inputs and the Hurst effect

1975 ◽  
Vol 26 (1-2) ◽  
pp. 39-53 ◽  
Author(s):  
A.A. Anis ◽  
E.H. Lloyd
Keyword(s):  
Hurst Effect

Renewal processes and the Hurst effect

2002 ◽  
Vol 35 (20) ◽  
pp. 4395-4412 ◽  
Author(s):  
Thierry Huillet
Keyword(s):  
Renewal Processes ◽  
Hurst Effect

scholarly journals The Hurst Effect: The scale of fluctuation approach

1993 ◽  
Vol 29 (12) ◽  
pp. 3995-4002 ◽  
Author(s):  
Oscar J. Mesa ◽  
German Poveda
Keyword(s):  
Scale Of Fluctuation ◽  
Hurst Effect

On the variance of the maximum of partial sums of n-exchangeable random variables with applications

1980 ◽  
Vol 17 (02) ◽  
pp. 432-439
Author(s):  
A. A. Anis ◽  
M. Gharib
Keyword(s):  
General Formula ◽  
Random Variables ◽  
Partial Sums ◽  
Direct Relevance ◽  
Exchangeable Random Variables ◽  
Hurst Effect

A general formula is obtained for the variance of the maximum of partial sums of n-exchangeable random variables, derived from a result of Spitzer's. The formula is applied in particular to obtain the variance of the maximum of adjusted rescaled partial sums of normal summands. This is of direct relevance to the Hurst effect.

Skew inputs and the Hurst effect — A reply

1976 ◽  
Vol 31 (1-2) ◽  
pp. 193-194
Author(s):  
E.H. Lloyd
Keyword(s):  
Hurst Effect

On the variance of the maximum of partial sums of n-exchangeable random variables with applications

1980 ◽  
Vol 17 (2) ◽  
pp. 432-439
Author(s):  
A. A. Anis ◽  
M. Gharib
Keyword(s):  
General Formula ◽  
Random Variables ◽  
Partial Sums ◽  
Direct Relevance ◽  
Exchangeable Random Variables ◽  
Hurst Effect

A general formula is obtained for the variance of the maximum of partial sums of n-exchangeable random variables, derived from a result of Spitzer's. The formula is applied in particular to obtain the variance of the maximum of adjusted rescaled partial sums of normal summands. This is of direct relevance to the Hurst effect.

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