we provide a framework for the study of statistical quantitiesrelated to the hurst phenomenon when the data are non-precise with boundedsupport.

We provide a framework for the study of statistical quantitiesrelated to the Hurst phenomenon when the data are non-precise with boundedsupport.

The Hurst phenomenon, which characterizes hydrological and other geophysical time series, is formulated and studied in an easy manner in terms of the variance and autocorrelation of a stochastic process on multiple temporal scales. In addition, a simple explanation of the Hurst phenomenon based on the fluctuation of a hydrological process upon different temporal scales is presented. The stochas...

In the last few years the discovery of the self-similar nature of packet traac has highlighted the need for the estimation of parameters quantifying scaling phenomenon, such as the Hurst parameter. An important practical question concerns the variation of the Hurst parameter with time. The on-line real-time version of the wavelet based estimator of Abry and Veitch, which allows data of unlimite...

Fractal behavior and long-range dependence have been observed in an astonishing number of physical, biological, geological, and socio-economic systems. Time series, profiles, and surfaces have been characterized by their fractal dimension, a measure of roughness, and by the Hurst coefficient, a measure of long-memory dependence. Either phenomenon has been modeled and explained by self-affine ra...

Let D(n) and H(n) be the fractal dimension and the Hurst parameter of traffic in the nth interval, respectively. Thus, this paper gives the experimental variance analysis of D(n) and H(n) of network traffic based on the generalized Cauchy (GC) process on an interval-by-interval basis. We experimentally infer that traffic has the phenomenon Var[D(n)] > Var[H(n)]. This suggests a new way to descr...