Fractional Gaussian noise (fGn) is an important and widely used self-similar process, which is mainly parametrized by its Hurst exponent (H) . Many researchers have proposed methods for estimating the Hurst exponent of fGn. In this paper we put forward a modified periodogram method for estimating the Hurst exponent based on a refined approximation of the spectral density function. Generalizing ...

Within the scope of this study we test the Long Memory property on monthly average pig market prices including piglet, young pig, sow and slaughter pig. We also calculate the Hurst exponent using Detrended Fluctuation Analysis (DFA) method. DFA is a method for determining the statistical self-affinity of a time serie. It is a useful technique for investigating time series with long memory (dive...

We present the results of an experiment with light microscopy performed to capture the trajectories of live Nitzschia sp. diatoms. The time series corresponding to the motility of this kind of cells along ninety-five circularlike trajectories have been obtained and analyzed with the scaling statistical method of detrended fluctuation analysis optimized via a wavelet transform. In this way, we d...

[1] Geophysical time series sometimes exhibit serial correlations that are stronger than can be captured by the commonly used first‐order autoregressive model. In this study we demonstrate that a power law statistical model serves as a useful upper bound for the persistence of total ozone anomalies on monthly to interannual timescales. Such a model is usually characterized by the Hurst exponent...

The fluctuations of Internet traffic possess an intricate structure which cannot be simply explained by long–range dependence and self–similarity. In this work, we explore the use of the wavelet spectrum, whose slope is commonly used to estimate the Hurst parameter of long–range dependence. We show that much more than simple slope estimates are needed for detecting important traffic features. I...

Valve stiction is the most common root of oscillation faults in process control systems, and it can cause severe deterioration performance system instability, ultimately impacting product quality safety. A new method for detecting valve stiction, based on dynamic slow feature analysis (DSFA) Hurst exponent, proposed this paper. The first utilizes DSFA to extract features (SFs) from preprocessed...

We study the two-dimensional fractional Brownian motion with Hurst parameter H > 1 2. In particular, we show, using stochastic calculus , that this process admits a skew-product decomposition and deduce from this representation some asymptotic properties of the motion.

In this short note, we show how to use concentration inequalities in order to build exact confidence intervals for the Hurst parameter associated with a one-dimensional fractional Brownian motion.

Abstract. In this note, a diffusion approximation result is shown for stochastic differential equations driven by a (Liouville) fractional Brownian motion B with Hurst parameter H ∈ (1/3, 1/2). More precisely, we resort to the Kac-Stroock type approximation using a Poisson process studied in [4, 7], and our method of proof relies on the algebraic integration theory introduced by Gubinelli in [13].