HURST EFFECT UNDER TRENDS.

Rabindra N Bhattacharya, Vijay K. Gupta, Ed Waymire

Research output: Contribution to journalArticle

126 Citations (Scopus)

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) equals c(m plus n)** beta , where m is an arbitrary non-negative parameter and c is not 0. For minus one-half less than beta less than 0 the Hurst exponent is shown to be precisely given by 1 plus beta . For beta less than equivalent to minus one-half and for beta equals 0 the Hurst exponent is 0. 5, while for beta greater than 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.

Original languageEnglish (US)
Pages (from-to)649-662
Number of pages14
JournalJournal of Applied Probability
Volume20
Issue number3
StatePublished - Sep 1983
Externally publishedYes

Fingerprint

Hurst Exponent
Stationary Sequences
Dependent Random Variables
Monotonic
Random variable
Non-negative
Mathematical Model
Necessary Conditions
Dependent
Sufficient Conditions
Arbitrary
Demonstrate
Trends
Hurst exponent
Random variables
Evidence
Form
Empirical evidence
Mathematical model

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Bhattacharya, R. N., Gupta, V. K., & Waymire, E. (1983). HURST EFFECT UNDER TRENDS. Journal of Applied Probability, 20(3), 649-662.

HURST EFFECT UNDER TRENDS. / Bhattacharya, Rabindra N; Gupta, Vijay K.; Waymire, Ed.

In: Journal of Applied Probability, Vol. 20, No. 3, 09.1983, p. 649-662.

Research output: Contribution to journalArticle

Bhattacharya, RN, Gupta, VK & Waymire, E 1983, 'HURST EFFECT UNDER TRENDS.', Journal of Applied Probability, vol. 20, no. 3, pp. 649-662.
Bhattacharya RN, Gupta VK, Waymire E. HURST EFFECT UNDER TRENDS. Journal of Applied Probability. 1983 Sep;20(3):649-662.
Bhattacharya, Rabindra N ; Gupta, Vijay K. ; Waymire, Ed. / HURST EFFECT UNDER TRENDS. In: Journal of Applied Probability. 1983 ; Vol. 20, No. 3. pp. 649-662.
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