Hurst Exponents for Non-Precise Data
Mayer Alvo, François Theberge
Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada; Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada

Non-precise data arise naturally in several contexts and in particular when one is interested in measuring the water level of a river. Non-precise data have been well described through the use of characterizing functions (Viertl, 1997). Consider a series of data of fixed length n, and define the sample variance and the sequence of centered partial sums. Hurst regressed the logarithm of the adjusted range of the centered partial sums divided by the sample standard deviation against the logarithm of one half the sample size, forcing a line through the origin. He observed that the resulting slope H > 0.5 for several natural ecological series. On the other hand, Feller showed that for any sequence of independent identically distributed random variables having finite variance, the limiting value of the slope H=0.5. Series for which H > 0.5 exhibit long term dependence. This implies such series are trend reinforcing: the direction of the next value is more likely the same as the current value. Our interest in this paper is to report the value of the Hurst coefficient within the context of non-precise data described by symmetric characterizing functions having finite support.

Keywords: Hurst exponent; Non-precise data; Adjusted range; Characterizing function

Biography: Mayer Alvo is a professor in the Department of Mathematics and Statistics at the University of Ottawa, Canada. His interests have been in the areas of non-parametric statistics, Bayesian statistics and the study of non-precise data.