Investigation of rescaled range analysis, the Hurst exponent, and long-time correlations in plasma turbulence

2002 ◽  
Vol 9 (4) ◽  
pp. 1312-1317 ◽  
Author(s):  
M. Gilmore ◽  
C. X. Yu ◽  
T. L. Rhodes ◽  
W. A. Peebles
2014 ◽  
Vol 687-691 ◽  
pp. 1668-1671
Author(s):  
Bin Luo ◽  
Tong Zhou Zhao ◽  
De Hua Li ◽  
Dun Bo Cai

In this paper, we study long-range dependence of hydrological records with high frequent and massive data set. For detecting breakpoints, we apply the Evolutionary Wavelet Spectrum (EWS) to provide a segmentation of the original time series. And rescaled range analysis (R/S) for estimating the Hurst exponent that describe the long-range dependence phenomenon are used. The results affirm that the hydrological records have long-range dependent (LRD) behaviors.


2020 ◽  
pp. 153-164
Author(s):  
Costas Siriopoulos ◽  
Maria Skaperda

This study analyses the performance of US Mutual Funds, from the perspective of Long Memory (LM), exploring if the returns of MFs are systematic due to their active management or they are random. The sample was 200 US equity MFs, from four categories, Large Cap, Middle Cap, Small Cap and World Stock, both 1- and 5-stars rating funds according to Morning Star rating. The time period was starting between 1981 and 2006 and ending 2016. Rescaled Range Analysis (R/S) employed for the Hurst exponent estimation, so to detect LM. Using Surrogate Data Analysis (SDA), the study was extended to Hurst exponent estimation for surrogate time series. The findings suggest that the selection of a MF presents a lot of complexity for investors. The 5-star MFs, with high qualified, and so expensive managers, tend to achieve random returns, while the returns of 1-star MFs, are more systematic. These MFs have higher fees than the 5-star MFs, but the management fees paid are quite inferior. This leads to the conclusion, that it might be preferable to pay for gaining an almost the same, but systematic return than to pay for the ties of the manager.


Fractals ◽  
2008 ◽  
Vol 16 (03) ◽  
pp. 259-265 ◽  
Author(s):  
YUSUF H. SHAIKH ◽  
A. R. KHAN ◽  
M. I. IQBAL ◽  
S. H. BEHERE ◽  
S. P. BAGARE

The record of the sunspot number visible on the sun is regularly collected over the centuries by various observatories for studying the different factors influencing the sunspot cycle and solar activity. Sunspots appear in cycles, and last several years. These cycles follow a certain pattern which is well known. We analyzed monthly and yearly averages of sunspot data observed from year 1818 to 2002 using rescaled range analysis. The Hurst exponent calculated for monthly data sets are 0.8899, 0.8800 and 0.8597 and for yearly data set is 0.7187. Fractal dimensions1 calculated are 1.1100, 1.1200, 1.1403 and 1.2813. From the study of Hurst exponent and fractal dimension, we conclude that time series of sunspots show persistent behavior. The fundamental tool of signal processing is the fast Fourier transform technique (FFT). The sunspot data is also analyzed using FFT. The power spectrum of monthly and yearly averages of sunspot shows distinct peaks at 11 years confirming the well known 11-year cycle. The monthly sunspot data is also analyzed using FFT to filter the noise in the data.


2012 ◽  
Vol 4 (8) ◽  
pp. 457-466
Author(s):  
Sanjay Rajagopal

We analyze the daily returns on 63 real estate investment trusts (REITs) that comprise five US Small Cap REIT indices, and test for weak-form efficiency by estimating the Hurst exponent and fractal dimension. Fourteen of the 63 firms (or roughly 22% of the firms studied) fail to exhibit weak-form efficiency, based on Classical Rescaled Range Analysis. Two additional self-affine fractal analysis techniques (Roughness-Length and Variogram analyses) provide some support for this finding. In particular, it is found that a majority of the series for which weak-form efficiency is rejected are anti-persistent, with estimated Hurst exponents below 0.50.These results are further confirmed by Lo’s (1991) modified rescaled range analysis, which reveals significant memory at long lags. Overall, the results suggest inefficient pricing for a significant subset of REITs, with important implications for trading and for the modeling of REIT returns. .Some aspects of their returns behavior warrant further study.


GIS Business ◽  
2018 ◽  
Vol 13 (6) ◽  
pp. 21-28
Author(s):  
Vijaya Kumar

Long range memory in share indices show temporal dependence between observations spaced by long intervals of time and has distinct non-periodic cycles. This paper examines the presence of long memory of various indices of National Stock Exchange (NSE). The data consists of closing values of indices over different periods of time. The tests applied to examine long memory are Hurst exponent, Manderbolt-Hurst exponent, Lo’s rescaled-range analysis and Geweke and Porter-Hudak (GPH) test. The results of the estimated Hurst exponent, Manderbolt-Hurst exponent and GPH test show that invariably all NSE indices series have long memory. However, the results of Lo’s rescaled-range analysis indicate the absence of long memory for all indices. Key words: Long memory, rescaled range analysis, fractional dimension, Hurst exponent, GPH test, NSE indices


2019 ◽  
Vol 118 ◽  
pp. 02061
Author(s):  
Yunzhi Fei ◽  
Xufang Shao ◽  
Gang Wang ◽  
Li Zhou ◽  
Xue Xia ◽  
...  

The Rescaled Range Analysis method (R/S Analysis method) is applied to analyze the PJM electricity derivatives market through calculating V statistics and Hurst Exponent of three types of products. The study finds that there is no obvious average cycle in the PJM electricity derivatives market. The price fluctuation of various products is not a non-random walk process but has a long-term memory. It shows that the PJM electricity derivatives market is not completely effective. The study also finds that PJM electricity option market is more effective than PJM electricity futures market.


Fractals ◽  
2004 ◽  
Vol 12 (02) ◽  
pp. 235-241 ◽  
Author(s):  
MICHAEL R. KING

White blood cells slowly roll along the walls of blood vessels, due to the coordinated formation and breakage of chemical selectin-carbohydrate bonds. Using detailed computer simulations of cells rolling on a selectin surface under flow, we show the time series of the cell translational velocity to be fractal in nature over time scales ranging from 22–211 ms. A rescaled range analysis was performed to determine the Hurst exponent of the velocity time series, for simulations of cells rolling on either a uniform or punctate distribution of P-selectin molecules. The rolling behavior was found to exhibit two very distinct regimes, with a negative Hurst exponent ranging from -(1.2-0.6) over time scales of 23-27 ms, and a positive Hurst exponent of +0.47±0.03 over time scales of 27-211 ms. The short-time Hurst exponent was found to be a strong function of the molecular distribution and also a function of average molecular density, while the long-time Hurst exponent was unchanged over all conditions studied. The implication is that the short-time adhesive behavior of cells interacting with a reactive surface is sensitive to the spatial arrangement of molecules, and the total number of molecules on the surface.


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