The Hurst parameter for two-dimensional (2-D) fractional Brownian motion (fBm) provides a single number that completely characterizes isotropic textured surfaces whose roughness is scale-invariant. Extended self-similar (ESS) processes were previously introduced in order to provide a generalization of fBm. These new processes are described by a number of multiscale Hurst parameters. In contrast...

A fractional Fourier transform (FrFT) based estimation method is introduced in this paper to analyze the long range dependence (LRD) in time series. The degree of LRD can be characterized by the Hurst parameter. The FrFT-based estimation of Hurst parameter proposed in this paper can be implemented efficiently allowing very large data set. We used fractional Gaussian noises (FGN) which typically...

We estimated Hurst exponent of twelve stock index series from across the glove using daily values of for past ten years and found that the Hurst exponent value of the full series is around 0.50 confirming market efficiency. But the Hurst exponent value is found to vary widely when the full series is split into smaller series of 60 trading days. Later, we tried to find relationship between Hurst...

This paper deals with the analysis of sunspot number time series using the Hurst exponent. We use the rescaled range (R/S) analysis to estimate the Hurst exponent for 259-year and 11 360-year sunspot data. The results show a varying degree of persistence over shorter and longer time scales corresponding to distinct values of the Hurst exponent. We explain the presence of these multiple Hurst ex...

Hurst exponents depict the long memory of a time series. For human-dependent phenomena, as in finance, this feature may vary in the time. It justifies modelling dynamics by multifractional Brownian motions, which are consistent with time-varying Hurst exponents. We improve the existing literature on estimating time-dependent Hurst exponents by proposing a smooth estimate obtained by variational...

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

The Hurst exponent (H) is a statistical measure used to classify time series. H=0.5 indicates a random series while H>0.5 indicates a trend reinforcing series. The larger the H value is, the stronger trend. In this paper we investigate the use of the Hurst exponent to classify series of financial data representing different periods of time. Experiments with backpropagation Neural Networks show ...

Estimation of the Hurst parameter provides information about the memory range or correlations (long vs. short) of processes (time-series). A new application for the Hurst parameter, real-time event detection, is identified. Hurst estimates using rescaled range, dispersional and bridgedetrended scaled windowed variance analyses of seizure time-series recorded from human subjects reliably detect ...

In this paper, we show how the sampling properties of Hurst exponent methods of estimation change with the presence of heavy tails. We run extensive Monte Carlo simulations to find out how rescaled range analysis (R/S), multifractal detrended fluctuation analysis (MF − DFA), detrending moving average (DMA) and generalized Hurst exponent approach (GHE) estimate Hurst exponent on independent seri...

The Hurst Exponent is a dimensionless estimator for the self-similarity of a time series. Initially defined by Harold Edwin Hurst to develop a law for regularities of the Nile water level, it now has applications in medicine and finance. Meaningful values are in the range [0, 1]. Different methods for estimating the Hurst Exponent have been evaluated: The classical “Rescaled Range” method devel...