Hurst exponents for short time series

Abstract

A concept called balanced estimator of diffusion entropy is proposed to detect quantitatively scalings in short time series. The effectiveness is verified by detecting successfully scaling properties for a large number of artificial fractional Brownian motions. Calculations show that this method can give reliable scalings for short time series with length ~10(2). It is also used to detect scalings in the Shanghai Stock Index, five stock catalogs, and a total of 134 stocks collected from the Shanghai Stock Exchange Market. The scaling exponent for each catalog is significantly larger compared with that for the stocks included in the catalog. Selecting a window with size 650, the evolution of scaling for the Shanghai Stock Index is obtained by the window's sliding along the series. Global patterns in the evolutionary process are captured from the smoothed evolutionary curve. By comparing the patterns with the important event list in the history of the considered stock market, the evolution of scaling is matched with the stock index series. We can find that the important events fit very well with global transitions of the scaling behaviors.

Evaluation of scale invariance in physiological signals by means of balanced estimation of diffusion entropy

“…In a recent paper, Bonachela et al [10] review the efforts for improved estimators of entropy for small data sets and propose accordingly a balanced estimator that performs well when the data sets are small. In one of our recent papers, we propose a new concept called balanced estimator of diffusion entropy (BEDE) [11], in which the original form of entropy in diffusion entropy analysis is replaced with the balanced estimator of entropy. Calculations show that it gives reliable scaling exponents for short time series with length ∼ 10 2 .…”

The elliptic function waves and solitons in thermal nonlocal media

“…The set of equations is identical to what determines the profile of parametric spatial solitary waves in w (2) media [20,21] and what in a liquid crystalline medium exhibiting a nonlinearity with an arbitrary degree of effective nonlocality [19]. In the above normalized set of Eqs.…”

“…Snyder and Mitchell [1] simplified the nonlocal nonlinear Schrodinger equation (NNLSE) to a linear model in the strongly nonlocal case, and found an exact Gaussian-shaped stationary solution to the model called as an accessible soliton. Qi Guo et al confirmed the existence of spatially optical solitons in the strongly nonlocal nonlinear media with arbitrary response function by expanded response function in Taylor's series [2]. P. D. Rasmussen et al [3] investigated interaction between spatial nonlocal bright soliton in nematic liquid crystal(NLC) using the effective particle approach, they predict attraction of out-of-phase solitons and the existence of the stable bound state.…”

“…On the other hand the analytical bright and dark soliton solutions in many nonlocal nonlinearity media have been found in other Refs. [1,2,4,9]. In fact, in the Ref.…”

Long-Range Correlations and Characterization of Financial and Volcanic Time Series

“…A time series data which exhibits long-range correlations implies that the evolution of the system is affected by previous system states over long periods of time [1][2][3][4][5]. This makes the need to determine long-range correlations in time series data very important for various fields.…”