Related papers: Estimation of the Hurst Exponent Using Trimean Est…
We propose a new method for (global) Hurst exponent determination based on wavelets. Using this method, we analyze synthetic data with predefined Hurst exponents, fracture surfaces and data from economy. The results are compared with those…
To improve diagnostic accuracy of breast cancer detection, several researchers have used the wavelet-based tools, which provide additional insight and information for aiding diagnostic decisions. The accuracy of such diagnoses, however, can…
High-frequency measurements and images acquired from various sources in the real world often possess a degree of self-similarity and inherent regular scaling. When data look like a noise, the scaling exponent may be the only informative…
Understanding signal behavior across scales is vital in areas such as natural phenomena analysis and financial modeling. A key property is self-similarity, quantified by the Hurst exponent (H), which reveals long-term dependencies.…
We study the scaling behavior of the fluctuations, as extracted through wavelet coefficients based on discrete wavelets. The analysis is carried out on a variety of physical data sets, as well as Gaussian white noise and binomial…
The wavelet spectra is a common starting point for estimating the Hurst exponent of a self-similar signal using wavelet-based techniques. The decay of the $\log_2$ average energy of the detail wavelet coefficients as a function of the level…
It is proposed a class of statistical estimators $\hat H =(\hat H_1, \ldots, \hat H_d)$ for the Hurst parameters $H=(H_1, \ldots, H_d)$ of fractional Brownian field via multi-dimensional wavelet analysis and least squares, which are…
We define an asymptotically normal wavelet-based strongly consistent estimator for the Hurst parameter of any Hermite processes. This estimator is obtained by considering a modified wavelet variation in which coefficients are wisely chosen…
Hurst Exponent has been widely used in different fields as a measure of long range dependence in time series. It has been studied in hydrology and geophysics, economics and finance, and recently, it is still a hot topic in the different…
We propose an algorithm to estimate the Hurst exponent of high-dimensional fractals, based on a generalized high-dimensional variance around a moving average low-pass filter. As working examples, we consider rough surfaces generated by the…
In this paper, we show how the sampling properties of the 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…
In the paper, we address parametric and non-parametric estimation for nonlinear stochastic differential equations with additive Hermite noise with possibly nonlinear scaling. We assume that a single trajectory of the solution is observed…
Density estimation is a classical problem in statistics and has received considerable attention when both the data has been fully observed and in the case of partially observed (censored) samples. In survival analysis or clinical trials, a…
This paper is concerned with a semiparametric partially linear regression model with unknown regression coefficients, an unknown nonparametric function for the non-linear component, and unobservable Gaussian distributed random errors. We…
Scale invariance (fractality) is a prominent feature of the large-scale behavior of many stochastic systems. In this work, we construct an algorithm for the statistical identification of the Hurst distribution (in particular, the scaling…
This article explores the required amount of time series points from a high-speed computer network to accurately estimate the Hurst exponent. The methodology consists in designing an experiment using estimators that are applied to time…
We estimate the Hurst parameter $H \in (0,1)$ of a fractional Brownian motion from discrete noisy data, observed along a high frequency sampling scheme. When the intensity $\tau_n$ of the noise is smaller in order than $n^{-H}$ we establish…
Quaternion wavelets are redundant wavelet transforms generalizing complex-valued non-decimated wavelet transforms. In this paper we propose a matrix-formulation for non-decimated quaternion wavelet transforms and define spectral tools for…
In [Han \& Schied, 2023, \textit{arXiv 2307.02582}], an easily computable scale-invariant estimator $\widehat{\mathscr{R}}^s_n$ was constructed to estimate the Hurst parameter of the drifted fractional Brownian motion $X$ from its…
In this paper we develop a nonparametric regression method that is simultaneously adaptive over a wide range of function classes for the regression function and robust over a large collection of error distributions, including those that are…