股票市场多重分形性的统计描述

以上海股票市场为例,运用多重分形谱方法对其多重分形性进行了实证研究。分析了多重分形谱的两个参数(分形谱的宽度及最大、最小概率子集分形维数的差)与指数变化趋势的关系。并进一步研究了多重分形谱参数与时间序列对数收益率的关系。结果表明多重分形谱参数与指数的变化趋势及对数收益率具有明显的关联性,这说明多重分形分析能够揭示更多关于市场变化的有用信息,有望以一定概率预测股价的涨落。

基于OSW-MF-DFA的外汇市场多重分形性研究

运用改进的多重分形消除趋势波动分析法,对三种外汇品种的日对数收益率序列进行多重分形分析,对它们的多重分形强度进行比较。实证研究表明,三种外汇品种的日对数收益率序列均具有明显的多重分形特征,且美元兑英镑序列的多重分形强度最大。此外,研究还发现,虽然买入美元兑英镑外汇的风险较另两种外汇的风险更大,但获利的机会也更大。

大鼠初级视皮层神经元整合野调制的多重分形去趋势波动分析

初级视皮层(V1区)神经元整合野的外周调制作用是动物执行视觉图像-背景分割和目标识别的神经基础。采用多重分形去趋势波动的方法,分析了整合野调制下神经元响应的多重分形性,并分析了其与整合野抑制作用的关系。结果表明:不同模式下神经元的响应信号均具有多重分形特征,谱宽Δα能显著区分两种典型的整合野调制状态,且神经元的分形性强度与整合野的抑制指数呈正相关。该研究表明整合野的调制作用改变了神经元响应的复杂程度,提高了其携带信息的能力。

三维空气污染物系统的多元多重分形分析

运用最新提出的多元多重分形去趋势波动分析法(MV-MFDFA)研究北京和上海两地的三维空气污染物(PM_(2.5)、PM_(10)、NO_2)浓度指数系统的非线性波动特征及动态复杂性。实证结果表明,两地污染物系统及其分量序列均存在长程相关性和时变的多重分形特征,相比较而言,北京污染物系统序列的多重分形强度更大,而上海污染物系统的长程相关性更强。此外,两地污染物系统在不同时间标度下呈现出不同的多重分形特征。最后,研究了两地污染物系统序列具有多重分形性的原因,指出胖尾概率分布和长程相关性是导致序列多重分形性的共同原因,且胖尾概率分布的贡献更大。

股票收益率序列的多重分形特征分析

运用多重分形消除趋势波动分析法,研究中石油和中石化两个上市公司股票收益率的多重分形特征,并结合多重分形谱方法,比较两股票收益率序列的多重分形性的强弱及风险大小.结果表明,两个公司的股票收益率序列均具有明显的多重分形特征,且中石化收益率序列的多重分形性更强,波动复杂程度更高.总体相比,买入中石化股票获利的空间更大,但风险也较买入中石油的更高.

生理老化下心率变异性信号的研究

近些年我国人口老龄化日益加重,研究生理老化对心脏系统带来的影响具有非常重要的意义。利用去趋势波动分析方法,分别研究了健康年轻人以及老年人HRV信号的相关性。为了进一步研究,建立了多重分形去趋势波动分析法,分别分析健康年轻人以及健康老年人HRV信号的多重分形特性。

国内传统能源、新能源和国际原油市场相关性分析

随着全球经济一体化的快速发展,国内能源市场和国际能源市场之间的联系日益加深,市场间的相互关系和波动溢出效应受到监管部门和研究者的广泛关注.以中证能源指数、中证内地新能源主题指数和WTI原油日收盘价的对数收益率序列为研究对象,运用多重分形消除趋势波动分析方法研究国内传统能源市场、新能源市场和国际能源市场之间的相互关系及波动特征.实证结果表明,3个市场之间的交互关系存在多重分形性,且新能源和传统能源之间交互关系的多重分析性最强,意味着国内能源市场是一个低效市场,市场的波动受到市场外的因素影响较大.同时指明,序列的胖尾分布是造成多重分形性的主要原因.

Long memory of price-volume correlation in metal futures market based on fractal features

An empirical test on long memory between price and trading volume of China metals futures market was given with MF-DCCA method. The empirical results show that long memory feature with a certain period exists in price-volume correlation and a fittther proof was given by analyzing the source of multifractal feature. The empirical results suggest that it is of important practical significance to bring the fractal market theory and other nonlinear theory into the analysis and explanation of the behavior in metal futures market.

Multifractal Characteristics of Intermittent Turbulence in the Urban Canopy Layer

The multifractality of energy and thermal dissipation of fully developed intermittent turbulence is investigated in the urban canopy layer under unstable conditions by the singularity spectrum for the fractal dimensions of sets of singularities characterizing multifractals. In order to obtain high-order moment properties of smallscale turbulent dissipation in the inertial range, an ultrasonic anemometer with a high sampling frequency of 100 Hz was used. The authors found that the turbulent signal could be singular everywhere. Moreover, the singular exponents of energy and thermal dissipation rates are most frequently encountered at around 0.2, which is significantly smaller than the singular exponents for a wind tunnel at a moderate Reynolds number. The evidence indicates a higher intermittency of turbulence in the urban canopy layer at a high Reynolds number, which is demonstrated by the data with high temporal resolution. Furthermore, the temperature field is more intermittent than the velocity field. In addition, a large amount of samples could be used for verification of the results.

Multi-scale interactions in interpersonal coordination

Background:Interpersonal coordination is an essential aspect of daily life,and crucial to performance in cooperative and competitive team sports.While empirical research has investigated interpersonal coordination using a wide variety of analytical tools and frameworks,to date very few studies have employed multifractal techniques to study the nature of interpersonal coordination across multiple spatiotemporal scales.In the present study we address this gap.Methods:We investigated the dynamics of a simple dyadic interpersonal coordination task where each participant manually controlled a virtual object in relation to that of his or her partner.We tested whether the resulting hand-movement time series exhibits multi-scale properties and whether those properties are associated with successful performance.Results:Using the formalism of multifractals,we show that the performance on the coordination task is strongly multi-scale,and that the multi-scale properties appear to arise from interaction-dominant dynamics.Further,we find that the measure of across-scale interactions,multifractal spectrum width,predicts successful performance at the level of the dyad.Conclusion:The results are discussed with respect to the implications of multifractals and interaction-dominance for understanding control in an interpersonal context.

MULTIPLICITY-PRESERVING TRIANGULAR SET DECOMPOSITION OF TWO POLYNOMIALS

In this paper, a multiplicity-preserving triangular set decomposition algorithm is proposed for a system of two polynomials, which involves only computing the primitive polynomial remainder sequence of two polynomials once and certain GCD computations. The algorithm decomposes the unmixed variety defined by two polynomials into square free and disjoint （for non-vertical components, see Definition 4） algebraic cycles represented by triangular sets which may have negative multiplicities. Thus, the authors can count the multiplicities of the non-vertical components. In the bivariate case, the amthors give a complete algorithm to decompose tile system into zeros represented by triangular sets with multiplicities. The authors also analyze the complexity of the algorithm in the bivariate ease. The authors implement the algorithm and show the effectiveness of the method with extensive experiments.

Joint Multifractal Analysis of Scaling Relationships Between Soil Water-Retention Parameters and Soil Texture

Soil water-retention characteristics at measurement scales are generally different from those at application scales, and there is scale disparity between them and soil physical properties. The relationships between two water-retention parameters, the scaling parameter related to the inverse of the air-entry pressure （avG, cm- 1） and the curve shape factor related to soil pore-size distribution （n） of the van Genuchten water-retention equation, and soil texture （sand, silt, and clay contents） were examined at multiple scales. One hundred twenty-eight undisturbed soil samples were collected from a 640-m transect located in Fuxin, China. Soil water-retention curves were measured and the van Genuchten parameters were obtained by curve fitting. The relationships between the two parameters and soil texture at the observed scale and at multiple scales were evaluated using Pearson correlation and joint multifractal analyses, respectively. The results of Pearson correlation analysis showed that the parameter c^vG was significantly correlated with sand, silt, and clay contents at the observed scale. Joint multifractal analyses, however, indicated that the parameter ~vG was not correlated with silt and sand contents at multiple scales. The parameter n was positively correlated with clay content at multiple scales. Sand content was significantly correlated with the parameter n at the observed scale but not at multiple scales. Clay contents were strongly correlated to both water-retention parameters because clay content was relatively low in the soil studied, indicating that water retention was dominated by clay content in the field of this study at all scales. These suggested that multiple-scale analyses were necessary to fully grasp the spatial variability of soil water-retention characteristics.