基于复杂网络的时间序列双变量联动波动

选择伦敦金与Au9999下午收盘价格作为样本数据研究时间序列双变量之间的联动波动规律.依据粗粒化方法,将伦敦金与Au9999价格的联动波动状态转化为由5个{P,N,M}字符组成的字符串,每个字符串代表5天的价格联动波动模态.将模态作为节点,模态之间的转化为边,构建价格联动波动复杂网络.运用复杂网络理论对时间序列双变量联动波动模态的统计、变化规律和演化机制进行分析.结果表明:时间序列双变量联动波动模态分布具有幂律性、群簇性和周期性,其联动波动模态主要通过少数几种模态进行转换与演化.本方法不仅可以研究不同类型时间序列双变量联动波动,同时可为多变量联动波动研究提供思路.     

基于复杂网络的时间序列双变量相关性波动研究

为了研究具有时间序列特征的双变量之间相关性的波动规律, 本文选取国际原油期货价格和中国大庆原油现货价格作为样本数据, 借鉴统计物理学的方法进行研究.运用粗粒化方法建立了相关性波动模态, 并利用复杂网络理论和分析方法对双变量相关性波动模态的统计、变化规律及其演化机理三个问题进行了分析.结果显示, 双变量相关性波动模态分布具有幂律性、群簇性和周期性, 相关性波动主要通过少数几种模态进行传递和演化.这些研究成果不仅可以作为双变量间相关性波动研究的方法, 也为不同变量间相关性波动一般规律的研究提供了思路.     

国际石油价格复杂网络的动力学拓扑性质

为了分析国际石油价格波动的变化特征,依据粗粒化方法,将1986年1月2日至2009年11月17日美国西得克萨斯原油现货逐日离岸价格转化为由3个表示涨落字符{R,e,D}构成的102种5字串组成的价格波动状态为网络节点(即连续5天的价格波动组合),按照时间顺序连边,构建原油价格有向加权波动网络,用复杂网络拓扑结构记录原油价格波动周涨落的信息,计算网络的度与度分布、聚类系数、最短路径长度等动力学统计量.结果表明,石油价格序列的波动网络节点度与累积度分布、节点度值与秩呈幂律分布,前32个节点(模态)的节点度值比较大,且这些石油价格波动模态中都包含表示价格变化上升趋势的字符.原油价格波动网络部分节点的中介中心性能力较强,24.5%的节点承担了网络80.97%的中介中心性功能,平均路径长度2.285,距离是2和3的情况占总数的86.8%,从网络结构拓扑性质这一新的角度验证了原油价格变化的复杂特征.这些对于我们识别具有拓扑统计重要性的节点模态,理解原油价格波动的内在规律和价格变化信息的传导有一定指导意义.     

利用复杂网络研究中国温度序列的拓扑性质

依据粗粒化方法,将中国1961—2002年逐日平均温度序列转化为由5个特征字符{R,r,e,d,D}构成的温度符号序列.以符号序列中的125种3字串组成的温度波动模态为网络的节点(即连续4d的温度波动组合),并按照时间顺序连边,构建有向加权的温度波动网络,进而将温度波动模态间的相互作用等综合信息蕴含于网络的拓扑结构之中.对随机序列和Lorenz系统的混沌序列分别构建随机和混沌波动网络.计算三种网络的度与度分布、聚类系数、最短路径长度等动 关键词： 气候变化 气候复杂网络 拓扑结构     

一种新的心率变异性度量方法

心率变异性的复杂波动反映了心脏的自主调节功能.本文提出了一种新的心率变异性度量方法——ICBN方法,该方法通过改进的自适应噪声完备集合经验模态分解方法对心率变异性信号进行分解,得到多个模态分量,计算每个模态分量的bubble熵得到熵值向量,把该向量映射成复杂网络,通过计算网络的特征参数,对心率变异性在不同时频尺度状态下的非线性特征之间的耦合关系进行度量.首先,采用时域、频域和ICBN分析方法对29名充血性心力衰竭病人和29名正常窦性心律对象的心率变异性进行分析,结果表明:时域指标三角指数HRVTi,频域指标LF/HF,网络层级加权值WB,平均点权值PW,特征路径长度CL具有统计学差异;基于网络层级加权值WB,特征路径长度CL,频域指标LF/HF和Fisher判别方法的识别模型对充血性心力衰竭病人的识别正确率达到89.66%.然后,又对43名房颤心律失常患者和43名正常窦性心律对象的心率变异性进行分析,结果表明:时域指标SDNN,pNN50,RMSSD,频域指标LF/HF,网络层级加权值WB,平均点权值PW具有统计学差异;时域指标pNN50,RMSSD,频域指标LF/HF和网络层级加权值WB,平均点权值PW作为特征向量,Fisher判别方法作为分类器,对房颤心律失常患者的识别正确率达到91.86%.综合以上实验结果可知,本文为心率变异性的度量研究提供了一种新的思路.     

基于时间序列符号化模式表征的有向加权复杂网络

时间序列复杂网络分析近些年已发展成为非线性信号分析领域的一个国际热点课题.为了能更有效地挖掘时间序列(特别是非线性时间序列)中的结构特征,同时简化时间序列分析的复杂度,提出了一种新的基于时间序列符号化结合滑窗技术模式表征的有向加权复杂网络建网方法.该方法首先按照等概率区段划分的方式将时间序列做符号化处理,结合滑窗技术确定不同时刻的符号化模式作为网络的节点;然后将待分析时间序列符号化模式的转换频次和方向作为网络连边的权重和方向,从而建立时间序列有向加权复杂网络.通过对Logistic系统不同参数设置对应的时间序列复杂网络建网测试结果表明,相比经典的可视图建网方法,本文方法的网络拓扑能更简洁、直观地展示时间序列的结构特征.进而,将本文方法应用于规则排列采集的自然风场信号分析,其网络特性指标能较准确地预测采集信号的排布规律,而可视图建网方法的网络特性指标没有任何规律性的结果.     

基于复杂网络理论的北京公交网络拓扑性质分析

为分析公交复杂网络的拓扑性质, 本文以北京市为例, 选取截止到2010年7月的北京全市(14区、2县)的1165条公交线路和9618个公交站点为样本数据, 运用复杂网络理论构建起基于邻接站点的有向加权复杂网络模型. 该方法以公交站点作为节点, 相邻站点之间的公交线路作为边, 使得网络既具有复杂网络的拓扑性质同时节点(站点)又具有明确的地理坐标. 对网络中节点度、点强度、强度分布、平均最短路径、聚类系数等性质的分析显示, 公交复杂网络的度和点强度分布极为不均, 网络中前5%和前10%节点的累计强度分布分别达到22.43%和43.02%; 点强度与排列序数、累积强度分布都服从幂律分布, 具有无标度和小世界的网络特点, 少数关键节点在网络中发挥着重要的连接作用. 为分析复杂网络中的关键节点, 本文通过承载压力分析和基于"掠夺" 的区域中心节点提取两种方法, 得到了公交复杂网络中两类不同表现的关键节点. 这些规律也为优化城市公交网络及交通规划发展提供了新的参考建议.     

基于多路可视图的健康与心梗患者心电图信号复杂网络识别

可视图(visibility graph, VG)算法已被证明是将时间序列转换为复杂网络的简单且高效的方法,其构成的复杂网络在拓扑结构中继承了原始时间序列的动力学特性.目前,单维时间序列的可视图分析已趋于成熟,但应用于复杂系统时,单变量往往无法描述系统的全局特征.本文提出一种新的多元时间序列分析方法,将心梗和健康人的12导联心电图(electrocardiograph, ECG)信号转换为多路可视图,以每个导联为一个节点,两个导联构成可视图的层间互信息为连边权重,将其映射到复杂网络.由于不同人群的全连通网络表现为完全相同的拓扑结构,无法唯一表征不同个体的动力学特征,根据层间互信息大小重构网络,提取权重度和加权聚类系数,实现对不同人群12导联ECG信号的识别.为判断序列长度对识别效果的影响,引入多尺度权重度分布熵.由于健康受试者拥有更高的平均权重度和平均加权聚类系数,其映射网络表现为更加规则的结构、更高的复杂性和连接性,可以与心梗患者进行区分,两个参数的识别准确率均达到93.3%.     

激光时空混沌模型的加权网络投影同步

提出了一种实现加权网络时空混沌投影同步的方法.通过构造合适的Lyapunov函数,确定了加权网络中连接节点之间耦合函数的结构以及网络节点状态方程中分离配置的线性项的系数矩阵的取值范围.以Bragg声光双稳系统作为局域函数,单向耦合映像格子作为空间扩展系统构成激光时空混沌模型.通过仿真模拟检验了采用激光时空混沌模型作为网络节点的加权网络的投影同步效果.结果显示,对于任意的节点之间耦合强度的权重值,加权网络的投影同步均可以实现. 关键词： 投影同步 加权网络 时空混沌 Bragg声光双稳系统     

环形加权网络的时空混沌延迟同步

研究了环形加权网络的时空混沌延迟同步问题.以随时间和空间演化均呈现混沌行为的时空混沌系统作为网络的节点,通过环形加权连接使所有节点建立关联.基于线性稳定性定理,通过确定网络的最大Lyapunov指数,得到了实现网络延迟同步的条件.在最大Lyapunov指数小于零的区域内,任取节点之间耦合强度的权重值,均可以使整个网络实现延迟同步.采用具有时空混沌行为的自催化反应扩散系统作为网络节点,仿真模拟验证了该方法的有效性. 关键词： 延迟同步 加权网络 时空混沌 Lyapunov指数     

Visibility graph network analysis of gold price time series

Mapping time series into a visibility graph network, the characteristics of the gold price time series and return temporal series, and the mechanism underlying the gold price fluctuation have been explored from the perspective of complex network theory. The network degree distribution characters, which change from power law to exponent law when the series was shuffled from original sequence, and the average path length characters, which change from L∼lnN$L\sim lnN$ into lnL∼lnN$lnL\sim lnN$ as the sequence was shuffled, demonstrate that price series and return series are both long-rang dependent fractal series. The relations of Hurst exponent to the power-law exponent of degree distribution demonstrate that the logarithmic price series is a fractal Brownian series and the logarithmic return series is a fractal Gaussian series. Power-law exponents of degree distribution in a time window changing with window moving demonstrates that a logarithmic gold price series is a multifractal series. The Power-law average clustering coefficient demonstrates that the gold price visibility graph is a hierarchy network. The hierarchy character, in light of the correspondence of graph to price fluctuation, means that gold price fluctuation is a hierarchy structure, which appears to be in agreement with Elliot’s experiential Wave Theory on stock price fluctuation, and the local-rule growth theory of a hierarchy network means that the hierarchy structure of gold price fluctuation originates from persistent, short term factors, such as short term speculation.     

A jump diffusion model for spot electricity prices and market price of risk

We construct a jump-diffusion model with seasonality, mean-reversion, time-dependent jump intensity and heteroskedastic disturbance for electricity spot prices, while keeping the analytical tractability of futures prices. We find that the jump component plays a considerably larger role than the diffusion component in the variance of spot prices. Moreover, the jump intensity is much higher during summer and winter. We also explore the seasonal market price of risk (MPR) with different maturities, from one month to five months. Our results show that the diffusion risk and the jump risk are priced quite differently.     

Spatial price dynamics: From complex network perspective

The spatial price problem means that if the supply price plus the transportation cost is less than the demand price, there exists a trade. Thus, after an amount of exchange, the demand price will decrease. This process is continuous until an equilibrium state is obtained. However, how the trade network structure affects this process has received little attention. In this paper, we give a evolving model to describe the levels of spatial price on different complex network structures. The simulation results show that the network with shorter path length is sensitive to the variation of prices.     

The Relationship between Crude Oil Futures Market and Chinese/US Stock Index Futures Market Based on Breakpoint Test

Combined with the B-P (breakpoint) test and VAR–DCC–GARCH model, the relationship between WTI crude oil futures and S&P 500 index futures or CSI 300 index futures was investigated and compared. The results show that breakpoints exist in the relationship in the mean between WTI crude oil futures market and Chinese stock index futures market or US stock index futures market. The relationship in mean between WTI crude oil futures prices and S&P 500 stock index futures, or CSI 300 stock index futures is weakening. Meanwhile, there is a decreasing dynamic conditional correlation between the WTI crude oil futures market and Chinese stock index futures market or US stock index futures market after the breakpoint in the price series. The Chinese stock index futures are less affected by short-term fluctuations in crude oil futures returns than US stock index futures.     

Market efficiency and the phase-lagging model of the price evolution

The paper presents a novel mathematical model of price evolution within the market. The model accounts for a finite time lag between the disturbance (news) and the market response to it. It follows from the model that any single disturbance brings the market out of its efficient state and the market is to come back into this state after some finite relaxation time. A quantitative measure of the market efficiency-the market efficiency coefficient-has been introduced. It has been demonstrated that a phase-lagging market is never either fully efficient or fully inefficient due to the finiteness of the frequency of disturbances (news) acting upon the market.     

Modeling stock price dynamics by continuum percolation system and relevant complex systems analysis

The continuum percolation system is developed to model a random stock price process in this work. Recent empirical research has demonstrated various statistical features of stock price changes, the financial model aiming at understanding price fluctuations needs to define a mechanism for the formation of the price, in an attempt to reproduce and explain this set of empirical facts. The continuum percolation model is usually referred to as a random coverage process or a Boolean model, the local interaction or influence among traders is constructed by the continuum percolation, and a cluster of continuum percolation is applied to define the cluster of traders sharing the same opinion about the market. We investigate and analyze the statistical behaviors of normalized returns of the price model by some analysis methods, including power-law tail distribution analysis, chaotic behavior analysis and Zipf analysis. Moreover, we consider the daily returns of Shanghai Stock Exchange Composite Index from January 1997 to July 2011, and the comparisons of return behaviors between the actual data and the simulation data are exhibited.     

Modeling of price and profit in coupled-ring networks

We study the behaviors of magnetization, price, and profit profiles in ring networks inthe presence of the external magnetic field. The Ising model is used to determine thestate of each node, which is mapped to the buy-or-sell state in a financial market, where+1 is identified as the buying state, and ?1 as the selling state. Price and profit mechanisms are modeled basedon the assumption that price should increase if demand is larger than supply, and itshould decrease otherwise. We find that the magnetization can be induced between two ringsvia coupling links, where the induced magnetization strength depends on the number of thecoupling links. Consequently, the price behaves linearly with time, where its rate ofchange depends on the magnetization. The profit grows like a quadratic polynomial withcoefficients dependent on the magnetization. If two rings have opposite direction of netspins, the price flows in the direction of the majority spins, and the network with theminority spins gets a loss in profit.     

The oscillation of stock price by majority orienting traders with investment position

We consider an interacting particle system for the stock price fluctuation. The change of the stock price with a feedback by the price considering the herding behavior (majority orienting behavior) of traders, gives the van der Pol equation as a deterministic approximation. Considering the investment position of each trader, we introduce the delayed van der Pol equation. The history of investment positions, for example sell or buy, of each trader for a stock makes a memory effect, which is modeled by using the time retardation. The delayed van der Pol equation model seems to be natural and explains typical phenomena, for example triangle pattern, volatility jumps, price jumps and price trends, known for the time series of a stock price.