For equidistant discretizations of fractional Brownian motion (fBm), the probabilities of ordinal patterns of order d = 2 are monotonically related to the Hurst parameter H. By plugging the sample relative frequency of those patterns indicating changes between up and down into the monotonic relation to H, one obtains the Zero Crossing (ZC) estimator of the Hurst parameter which has found consid...

A major issue in time series analysis and particularly in the study of meteorological time series behaviour is the long range dependence (LRD). Various estimators of LRD have been proposed. Their accuracy have been generally tested by using simulated time series since sometimes only their asymptotic property are known, or worse, no asymptotic property have been proved. It is well – known that t...

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...

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

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...

We discuss the link between uncorrelated noise and the Hurst exponent for one- and two-dimensional interfaces. We show that long range correlations cannot be observed using one-dimensional cuts through two-dimensional self-affine surfaces whose height distributions are characterized by a Hurst exponent H lower than -1/2. In this domain, fractional and white noise are not distinguishable. A meth...

We examined the Hurst exponent of heart rate time series and its relation with the subjective measures of valence and arousal in two groups of subjects. The electrocardiogram (ECG) and the subjective valence and arousal were measured during the administration of emotional film stimuli (happiness, sadness, anger and fear). The results showed that there is a difference in the Hurst exponent for t...

The modern high-speed network traffic exhibits the self-similarity. The degree of selfsimilarity is measured by the Hurst parameter. In this paper are used two graphical techniques for estimating Hurst parameter of pseudo-random self-similar sequences, based on the fractional Gaussian noise (FGN) method. The analyses show that the FGN method always produces self-similar sequences, with relative...

Long Range Dependent (LRD) network tra c does not behave like the tra c generated by the Poisson model or other Markovian models. From the network performance point of view, the main di erence is that LRD tra c increases queueing delays due to its burstiness over many time scales. LRD behavior has been observed in di erent types and sizes of networks, for di erent applications (eg. WWW) and di ...