This paper describes, in detail, techniques for measuring the Hurst parameter. Measurements are given on artificial data both in a raw form and corrupted in various ways to check the robustness of the tools in question. Measurements are also given on real data, both new data sets and well-studied data sets. All data and tools used are freely available for download along with simple “recipes” wh...

We consider the role of finite size effects on the value of the effective Hurst exponent H . This problem is motivated by the properties of the high frequency daily stock-prices. For a finite size random walk we derive some exact results based on Spitzer’s identity. The conclusion is that finite size effects strongly enhance the value of H and the convergency to the asymptotic value (H = 1/2) i...

Multifractional Brownian motions have become popular as flexible models in describing real-life signals of high-frequency features in geoscience, microeconomics, and turbulence, to name a few. The time-changing Hurst exponent, which describes regularity levels depending on time measurements, and variance, which relates to an energy level, are two parameters that characterize multifractional Bro...

In this study we propose a bayesian approach to the estimation of the Hurst exponent in terms of linear mixed models. Even for unevenly sampled signals and signals with gaps, our method is applicable. We test our method by using artificial fractional brownian motion of different length and compare it with the detrended fluctuation analysis technique. The estimation of the Hurst exponent of a Ro...

We apply the Hurst exponent idea for investigation of DJIA index time-series data. The behavior of the local Hurst exponent prior to drastic changes in financial series signal is analyzed. The optimal length of the time-window over which this exponent can be calculated in order to make some meaningful predictions is discussed. Our prediction hypothesis is verified with examples of '29 and '87 c...

In order to estimate the Hurst exponent of long-range dependent time series numerous estimators such as based e.g. on rescaled 9 range statistic (R/S) or detrended fluctuation analysis (DFA) are traditionally employed. Motivated by empirical behaviour of the bias of R/S estimator, its bias-corrected version is proposed. It has smaller mean squared error than DFA and behaves comparably 11 to wav...

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...

Methods of assessing the fractal characteristics of time-varying signals like the heart rate, Electroencephalogram, respiratory rate, seismology signal, and so on, which vary apparently irregularly, are random. Hurst (1951) defined an empirical descriptor, the Hurst exponent, of temporal signals describing natural phenomena. This was based on the statistical assessment of the observation of man...

This paper investigates the effect of the 2008 financial crisis on informational efficiency by carrying out a long-memory analysis of European corporate bond markets. We compute the Hurst exponent for fifteen sectorial indices to scrutinise the time-varying behaviour of long-range memory, applying a shuffling technique to avoid short-term correlation. We find that the financial crisis has uneve...