Multifractal detrended cross-correlation analysis in the MENA area

In this paper, we investigated multifractal cross-correlations qualitatively and quantitatively using a cross-correlation test and the Multifractal detrended cross-correlation analysis method (MF-DCCA) for markets in the MENA area. We used cross-correlation coefficients to measure the level of this correlation. The analysis concerns four stock market indices of Morocco, Tunisia, Egypt and Jordan. The countries chosen are signatory of the Agadir agreement concerning the establishment of a free trade area comprising Arab Mediterranean countries. We computed the bivariate generalized Hurst exponent, Rényi exponent and spectrum of singularity for each pair of indices to measure quantitatively the cross-correlations. By analyzing the results, we found the existence of multifractal cross-correlations between all of these markets. We compared the spectrum width of these indices; we also found which pair of indices has a strong multifractal cross-correlation.     

Multifractal detrended cross-correlation analysis between the Chinese stock market and surrounding stock markets

In this paper, we investigate the cross-correlations between the stock market in China and markets in Japan, South Korea and Hong Kong. We use not only the qualitative analysis of the cross-correlation test, but also the quantitative analysis of the MF-X-DFA. Our findings confirm the existence of cross-correlations between the stock market in China and markets in Japan, South Korea and Hong Kong, which have strongly multifractal features. We find that the cross-correlations display the characteristic of multifractality in the short term. Moreover, the cross-correlations of small fluctuations are persistent and those of large fluctuations are anti-persistent in the short term, while the cross-correlations of all kinds of fluctuations are persistent in the long term. Furthermore, based on the multifractal spectrum, we also find that the multifractality of cross-correlation between stock markets in China and Japan are stronger than those between China and South Korea, as well as between China and Hong Kong.     

毫米波辐照下大鼠脑电的长程相关性

通过脑电长程相关性的分析,定量研究了35 GHz毫米波辐照大鼠时产生的应激反应。通过退趋势分析法,得到反映高频成分的标度指数,显示在辐照前该成分具有布朗噪声的特性,辐照时具有长程相关性;而反映低频成分的标度指数显示在辐照前该成分具有长程相关性,辐照时成为布朗噪声。引进应激指标参量低频成份标度指标数/高频成份标度指标数,用其值的平均变化率来衡量大鼠在35 GHz毫米波作用下应激反应的剧烈程度。通过计算得到辐照时应激指标参量增加了49.9%±13.6%,说明35 GHz毫米波辐照使得大鼠脑电的高频部分变得更加有序,而低频成分变得更加无序,表明大鼠受35 GHz毫米波辐照而产生了剧烈应激反应。     

毫米波辐照下大鼠脑电的长程相关性

通过脑电长程相关性的分析,定量研究了35 GHz毫米波辐照大鼠时产生的应激反应.通过退趋势分析法,得到反映高频成分的标度指数.显示在辐照前该成分具有布朗噪声的特性,辐照时具有长程相关性;而反映低频成分的标度指数显示在辐照前该成分具有长程相关性,辐照时成为布朗噪声.引进应激指标参量低频成份标度指标数/高频成份标度指标数,...     

混合交通流时间序列的去趋势波动分析

应用去趋势波动分析法研究交通流时间序列的复杂性,探讨了混合交通流时间序列演变行为的标度指数.根据标度指数的变化特征,进而揭示交通流时间序列所具有的长程相关性和短程相关性.通过分析发现,存在一密度ρ,当ρ₁<ρ<ρ₂时,交通流时间序列具有长程相关性;而当ρ<ρ₁或ρ>ρ₂时,交通流时间序列具有短程相关性,即密度的变化影响着标度指数的变化.另外分析了在不同慢车比率条件下时间序列的标度指数,发现慢车比率的变化 关键词： 混合交通流 去趋势波动分析 时间序列 长程相关     

分波前干涉法中空间互相关函数的传输

在光学干涉技术中,被检信息主要包含在干涉波面的互相关函数中,并最终体现为干涉场强度分布的调制。由Fresnel衍射理论出发,运用Collins公式,分析了分波前干涉法中空间互相关函数的传递性质。得到了用光线矩阵元表示的空间互相关函数传输公式,并以此对迈克耳逊干涉仪和横向剪切干涉仪中的干涉图强度分布进行了分析。     

Crossover Phenomena in Detrended Fluctuation Analysis Used in Financial Markets

A systematic analysis of Shanghai and Japan stock indices for the period of Jan. 1984 to Dec. 2005 is performed. After stationarity is verified by ADF （Augmented Dickey-Fuller） test, the power spectrum of the data exhibits a power law decay as a whole characterized by 1/f^β processes with possible long range correlations. Subsequently, by using the method of detrended fluctuation analysis （DFA） of the general volatility in the stock markets, we find that the long-range correlations are occurred among the return series and the crossover phenomena exhibit in the results obviously.Further, Shanghai stock market shows long-range correlations in short time scale and shows short-range correlations in long time scale. Whereas, for Japan stock market, the data behaves oppositely absolutely. Last, we compare the varying of scale exponent in large volatility between two stock markets. All results obtained may indicate the possibility of characteristic of multifractal scaling behavior of the financial markets.     

Multifractal Detrended Fluctuation Analysis of Interevent Time Series in a Modified OFC Model

We use multifractal detrended fluctuation analysis(MF-DFA) method to investigate the multifractal behavior of the interevent time series in a modified Olami-Feder-Christensen(OFC) earthquake model on assortative scale-free networks.We determine generalized Hurst exponent and singularity spectrum and find that these fluctuations have multifractal nature.Comparing the MF-DFA results for the original interevent time series with those for shuffled and surrogate series,we conclude that the origin of multifractality is due to both the broadness of probability density function and long-range correlation.     

Detrended Fluctuation Analysis on Correlations of Complex Networks Under Attack and Repair Strategy

We analyze the correlation properties of the Erdos-Rényi random graph (RG) and the Barabási-Albert scale-free network (SF) under the attack and repair strategy with detrended fluctuation analysis (DFA). The maximum degree k representing the local property of the system, shows similar scaling behaviors for random graphs and scale-free networks. The fluctuations are quite random at short time scales but display strong anticorrelation at longer time scales under the same system size N and different repair probability pre. The average degree , revealing the statistical property of the system, exhibits completely different scaling behaviors for random graphs and scale-free networks. Random graphs display long-range power-law correlations. Scale-free networks are uncorrelated at short time scales; while anticorrelated at longer time scales and the anticorrelation becoming stronger with the increase of pre.     

脑电信号的标度分析及其在睡眠状态区分中的应用

脑电信号具有长程幂律相关性及多重分形的标度特性,并随生理病理状态改变.本文首次针对睡眠脑电信号应用单重分形去趋势波动分析(detrended fluctuation analysis,简记为DFA)方法与多重分形奇异谱对睡眠脑电信号的标度特征进行系统的对比研究.发现DFA标度指数α对于不同导联和样本组间的差异较为敏感,随睡眠状态的变化不规律;而多重分形奇异强度区间Δα随睡眠状态的变化更为规律,睡眠Ⅰ期至Ⅳ期不断增大,并且导联间差异和样本组间差异均较小.多重分形Δα参数更适合作为判定睡眠状态的定量参数.     

Generalized Structure Functions and Multifractal Detrended Fluctuation Analysis Applied to Vegetation Index Time Series: An Arid Rangeland Study

Estimates suggest that more than 70% of the world’s rangelands are degraded. The Normalized Difference Vegetation Index (NDVI) is commonly used by ecologists and agriculturalists to monitor vegetation and contribute to more sustainable rangeland management. This paper aims to explore the scaling character of NDVI and NDVI anomaly (NDVIa) time series by applying three fractal analyses: generalized structure function (GSF), multifractal detrended fluctuation analysis (MF-DFA), and Hurst index (HI). The study was conducted in four study areas in Southeastern Spain. Results suggest a multifractal character influenced by different land uses and spatial diversity. MF-DFA indicated an antipersistent character in study areas, while GSF and HI results indicated a persistent character. Different behaviors of generalized Hurst and scaling exponents were found between herbaceous and tree dominated areas. MF-DFA and surrogate and shuffle series allow us to study multifractal sources, reflecting the importance of long-range correlations in these areas. Two types of long-range correlation appear to be in place due to short-term memory reflecting seasonality and longer-term memory based on a time scale of a year or longer. The comparison of these series also provides us with a differentiating profile to distinguish among our four study areas that can improve land use and risk management in arid rangelands.     

On the Validity of Detrended Fluctuation Analysis at Short Scales

Detrended Fluctuation Analysis (DFA) has become a standard method to quantify the correlations and scaling properties of real-world complex time series. For a given scale ℓ of observation, DFA provides the function F(ℓ), which quantifies the fluctuations of the time series around the local trend, which is substracted (detrended). If the time series exhibits scaling properties, then F(ℓ)∼ℓα asymptotically, and the scaling exponent α is typically estimated as the slope of a linear fitting in the logF(ℓ) vs. log(ℓ) plot. In this way, α measures the strength of the correlations and characterizes the underlying dynamical system. However, in many cases, and especially in a physiological time series, the scaling behavior is different at short and long scales, resulting in logF(ℓ) vs. log(ℓ) plots with two different slopes, α1 at short scales and α2 at large scales of observation. These two exponents are usually associated with the existence of different mechanisms that work at distinct time scales acting on the underlying dynamical system. Here, however, and since the power-law behavior of F(ℓ) is asymptotic, we question the use of α1 to characterize the correlations at short scales. To this end, we show first that, even for artificial time series with perfect scaling, i.e., with a single exponent α valid for all scales, DFA provides an α1 value that systematically overestimates the true exponent α. In addition, second, when artificial time series with two different scaling exponents at short and large scales are considered, the α1 value provided by DFA not only can severely underestimate or overestimate the true short-scale exponent, but also depends on the value of the large scale exponent. This behavior should prevent the use of α1 to describe the scaling properties at short scales: if DFA is used in two time series with the same scaling behavior at short scales but very different scaling properties at large scales, very different values of α1 will be obtained, although the short scale properties are identical. These artifacts may lead to wrong interpretations when analyzing real-world time series: on the one hand, for time series with truly perfect scaling, the spurious value of α1 could lead to wrongly thinking that there exists some specific mechanism acting only at short time scales in the dynamical system. On the other hand, for time series with true different scaling at short and large scales, the incorrect α1 value would not characterize properly the short scale behavior of the dynamical system.     

互相关及高阶谱核材料富集度识别方法

针对基于传统核材料识别系统中特征值易受系统噪声影响且精确度不够的问题,将高阶统计特征概念引入252Cf源驱动核系统特征提取和识别之中,提出了一种基于互相关函数与高阶统计特征的252Cf源驱动核材料富集度识别方法。通过互相关运算及高阶统计分析,得到核系统信息的三维特征图像,并在此基础上开展了待测核材料(235U)的富集度实验研究与分析识别工作。实验研究结果表明,该识别方法能够较好地降低背景辐射噪声与电子学系统噪声。与传统识别方法相比,对于核部件富集度变化,该算法的敏感性与鲁棒性均有大幅提高。     

基于脑电图的大脑功能性网络分析

利用脑电图数据建立了大脑功能性网络.分析了该网络的复杂网络统计特征，发现它的聚类系数远大于相应随机网络，明显具有小世界网络的特征，其度分布也接近于无标度网络.进一步验证了大脑功能性网络的复杂网络特性，发现患者的各项复杂网络特征指数与正常人相比有明显不同.定义了大脑神经网络信息熵及神经网络标准信息熵的概念，发现脑病患者的大脑神经网络信息熵明显小于正常人.从一个全新的角度量度了大脑的复杂网络特征，并提示了临床脑病诊疗的判断依据. 关键词： 脑电图 大脑功能性网络 复杂网络统计特征 信息熵     

交叉色关联噪声驱动的单模激光系统统计性质研究

采用交叉色关联的加性色噪声和乘性色噪声驱动的单模激光立方模型,通过诺维科夫理论和福克斯近似以及斯特拉托诺维奇近似,得到反映激光统计性质的强度关联函数C的表达式;研究关联时间τ、净增益系数a₀和交叉关联强度λ对强度关联函数C的影响.数值模拟发现,在阈值以上（a₀>0）时,关联函数C随关联时间τ的增大而增大;在阈值以下（a₀<0）时,关联函数C随关联时间τ的增大而减小.无论在阈值以上还是阈值以下,关联函数C均随交叉关联强度λ的增大而减小.在C-a₀曲线上存在单峰. 关键词： 单模激光 交叉关联 强度涨落 强度关联函数     

光学薄膜界面互相关特性的确定

本文实验测量了光学薄膜的散射波场分布,根据多层光学薄膜的矢量散射理论,确定了膜层界面的互相关特性.当空间频率较低时,对于膜层层数较少的膜系,膜堆内的各界面是完全相关的;若空间频率较高,则逐渐趋于部分相关模型.实验指出,膜层界面的互相关特性亦与所采用的蒸发技术有关.     

Modified DFA and DCCA approach for quantifying the multiscale correlation structure of financial markets

We use multiscale detrended fluctuation analysis (MSDFA) and multiscale detrended cross-correlation analysis (MSDCCA) to investigate auto-correlation (AC) and cross-correlation (CC) in the US and Chinese stock markets during 1997–2012. The results show that US and Chinese stock indices differ in terms of their multiscale AC structures. Stock indices in the same region also differ with regard to their multiscale AC structures. We analyze AC and CC behaviors among indices for the same region to determine similarity among six stock indices and divide them into four groups accordingly. We choose S&P500, NQCI, HSI, and the Shanghai Composite Index as representative samples for simplicity. MSDFA and MSDCCA results and average MSDFA spectra for local scaling exponents (LSEs) for individual series are presented. We find that the MSDCCA spectrum for LSE CC between two time series generally tends to be greater than the average MSDFA LSE spectrum for individual series. We obtain detailed multiscale structures and relations for CC between the four representatives. MSDFA and MSDCCA with secant rolling windows of different sizes are then applied to reanalyze the AC and CC. Vertical and horizontal comparisons of different window sizes are made. The MSDFA and MSDCCA results for the original window size are confirmed and some new interesting characteristics and conclusions regarding multiscale correlation structures are obtained.     

Are Mobility and COVID-19 Related? A Dynamic Analysis for Portuguese Districts

In this research work, we propose to assess the dynamic correlation between different mobility indices, measured on a daily basis, and the new cases of COVID-19 in the different Portuguese districts. The analysis is based on global correlation measures, which capture linear and non-linear relationships in time series, in a robust and dynamic way, in a period without significant changes of non-pharmacological measures. The results show that mobility in retail and recreation, grocery and pharmacy, and public transport shows a higher correlation with new COVID-19 cases than mobility in parks, workplaces or residences. It should also be noted that this relationship is lower in districts with lower population density, which leads to the need for differentiated confinement policies in order to minimize the impacts of a terrible economic and social crisis.     

A multifractal detrended fluctuation analysis (MDFA) of the Chinese growth enterprise market (GEM)

A multifractal, detrended fluctuation approach is used to analyze the growth enterprise market (GEM) in China involving a range of correlations in fluctuations of share prices (fat tail), persistent and anti-persistent states. Our analysis exhibits company-specific multifractal characteristics, which vary among the companies listed in the same industry, e.g., the power-law cross-correlations between computer and electronics sectors. These results may help reduce the risk in complex financial markets.