Study of cross-correlation in a self-affine time series of taxi accidents

We study in this paper the cross-correlation between self-affine time series of real variables recorded simultaneously in cases of taxi accidents. For this purpose, we apply the DCCA method and show that the cross-correlation can be divided into three distinct groups, if we look for the detrended covariance function, i.e., long-range cross-correlations, short-range cross-correlations and no cross-correlations. Finally, it will be seen that the detrended covariance function is robust, if compared with other methods, in identifying these types of cross-correlations.     

离散时间序列的网络模体分析

时间序列可以被转换成网络的形式,复杂网络理论也因此可以用于刻画时间序列的时域和相空间特性.本文针对可视图算法和相空间重构算法这两种时间序列的转换算法,研究了它们的伴生网络在倍周期分岔和混沌等各种类型时间序列的模体分布特征,分析了这两种算法各自的优点.     

一种基于误差补偿的多元混沌时间序列混合预测模型

针对多元混沌时间序列的预测问题, 考虑到单纯改进储备池算法无法明显地提高预测精度, 提出一种基于误差补偿的时间序列混合预测模型. 实际观测的数据既包含线性特征又包含非线性特征. 首先利用自回归移动平均模型预测线性特征, 使得残差数据仅含非线性特征; 然后, 建立正则化回声状态网络模型预测; 最后, 将非线性部分的预测值与线性部分的预测值相加, 以实现高精度的多元混沌时间序列预测. 基于Lorenz和太阳黑子-黄河径流量时间序列的仿真实验验证了本文所提模型的有效性. 关键词： 回声状态网络 混沌 多元时间序列预测 误差补偿     

面向级联失效的相依网络鲁棒性研究

针对相依网络耦合强度、子网络边以及耦合边对网络鲁棒性影响的问题,基于三种典型网络模型,建立对称相依网络和不对称相依网络模型.针对六种不同的相依网络模型,计算其网络临界成本,比较耦合边权值和子网络边权值对相依网络成本的贡献程度,发现耦合边对网络的贡献更大.采用仿真和理论证明的方法,获得使网络具有最小网络成本时的子网络负载参数α值和耦合强度参数β值,并证明了网络成本变化趋势与该参数对有关.以网络成本作为鲁棒性测度的变量,通过对六种相依网络模型进行级联失效仿真,给出了网络具有最强鲁棒性时参数对的取值,以及网络鲁棒性与耦合强度之间的关系,发现网络鲁棒性并不是随着耦合强度单调地增加或减少.     

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.     

负荷作用下相依网络中的级联故障

研究负荷作用下相依网络中的级联故障具有重要的现实意义, 可为提高相依网络的鲁棒性提供参考. 构建了双层相依网络级联故障模型, 主要研究了外部度和内部度对负荷贡献比、耦合因素、层内度-度相关性对相依网络级联故障的影响. 研究表明, 当外部度和内部度对负荷贡献比达到一定值时, 相依网络抵抗级联故障的鲁棒性最强. 而耦合因素的影响是多方面的, 为了达到较高鲁棒性, 建议采用异配耦合方式和尽可能大的平均外部度, 并尽量使外部度保持均匀分布. 另外, 与不考虑负荷作用时相反, 当表征层内度-度相关性的相关系数越大时, 其抵抗级联故障的能力越强.     

基于混沌算子网络的时间序列多步预测研究

结合相空间重构理论和时间序列分析理论,提出一种用于时间序列多步预测的网络模型.网络采用多个混沌算子加权求和的形式构成.网络各层单元采用固定权值连接,混沌算子的控制参数利用混沌优化算法进行训练调节,从而控制预测网络的动力学行为.利用已知时间序列数据构造出训练样本,训练样本在网络训练过程中仅使用一次,促使网络的动力学特性随时间的推移而变化,并逐渐逼近被预测系统的动力学特性,最终完成对未来时刻数据的预测.在对理论数据进行预测分析时,通过计算预测序列的Lyapunov指数验证了预测网络的有效性.在对实际时间序列的预测过程中,该网络表现出了良好的预测性能.仿真结果表明,该预测网络可对多种时间序列在一定的预测步长范围内实现有效的预测.     

DCCA cross-correlation coefficient: Quantifying level of cross-correlation

In this paper, a new coefficient is proposed with the objective of quantifying the level of cross-correlation between nonstationary time series. This cross-correlation coefficient is defined in terms of the DFA method and the DCCA method. The implementation of this cross-correlation coefficient will be illustrated with selected time series.     

基于混合神经网络和注意力机制的混沌时间序列预测

为提高混沌时间序列的预测精度,提出一种基于混合神经网络和注意力机制的预测模型(Att-CNNLSTM),首先对混沌时间序列进行相空间重构和数据归一化,然后利用卷积神经网络(CNN)对时间序列的重构相空间进行空间特征提取,再将CNN提取的特征和原时间序列组合,用长短期记忆网络(LSTM)根据空间特征提取时间特征,最后通过注意力机制捕获时间序列的关键时空特征,给出最终预测结果.将该模型对Logistic,Lorenz和太阳黑子混沌时间序列进行预测实验,并与未引入注意力机制的CNN-LSTM模型、单一的CNN和LSTM网络模型、以及传统的机器学习算法最小二乘支持向量机(LSSVM)的预测性能进行比较.实验结果显示本文提出的预测模型预测误差低于其他模型,预测精度更高.     

基于视神经网络的混沌时间序列奇异信号实时检测算法

提出了一种基于视神经网络的实时检测混沌时间序列中的奇异点算法,设计了视神经网络奇异点检测器(RNNND);然后设计了基于反向传播(BP)神经网络和径向基函数(RBF)神经网络的混沌时间序列奇异点检测器.利用Lorenz理论模型产生的时间序列和实测输油管道压力时间序列分别检验了这3个奇异点检测器在抗干扰能力、检测微弱信号能力和运算速度等方面的性能.仿真和分析表明,RNNND具有良好的检测精度和较快检测速度.最后详细分析了3种奇异点检测器优缺点并给出了适用场合.     

Cross and joint ordinal partition transition networks for multivariate time series analysis

We propose the construction of cross and joint ordinal pattern transition networks from multivariate time series for two coupled systems, where synchronizations are often present. In particular, we focus on phase synchronization, which is a prototypical scenario in dynamical systems. We systematically show that cross and joint ordinal pattern transition networks are sensitive to phase synchronization. Furthermore, we find that some particular missing ordinal patterns play crucial roles in forming the detailed structures in the parameter space, whereas the calculations of permutation entropy measures often do not. We conclude that cross and joint ordinal partition transition network approaches provide complementary insights into the traditional symbolic analysis of synchronization transitions.     

Characterizing pseudoperiodic time series through the complex network approach

Recently a new framework has been proposed to explore the dynamics of pseudoperiodic time series by constructing a complex network [J. Zhang, M. Small, Phys. Rev. Lett. 96 (2006) 238701]. Essentially, this is a transformation from the time domain to the network domain, which allows for the dynamics of the time series to be studied via organization of the network. In this paper, we focus on the deterministic chaotic Rössler time series and stochastic noisy periodic data that yield substantially different structures of networks. In particular, we test an extensive range of network topology statistics, which have not been discussed in previous work, but which are capable of providing a comprehensive statistical characterization of the dynamics from different angles. Our goal is to find out how they reflect and quantify different aspects of specific dynamics, and how they can be used to distinguish different dynamical regimes. For example, we find that the joint degree distribution appears to fundamentally characterize spatial organizations of cycles in phase space, and this is quantified via an assortativity coefficient. We applied network statistics to electrocardiograms of a healthy individual and an arrythmia patient. Such time series are typically pseudoperiodic, but are noisy and nonstationary and degrade traditional phase-space based methods. These time series are, however, better differentiated by our network-based statistics.     

基于多元局部多项式方法的混沌时间序列预测

根据Takens定理，把混沌时间序列构造为一组序列对，然后用多元局部多项式方法来预测其序列.这种核估计方法可以结合局域法与全局法的优点，使得预测的精度更高.仿真结果表明，该方法非常有效.     

Markov transition probability-based network from time series for characterizing experimental two-phase flow

We generate a directed weighted complex network by a method based on Markov transition probability to represent an experimental two-phase flow. We first systematically carry out gas-liquid two-phase flow experiments for measuring the time series of flow signals. Then we construct directed weighted complex networks from various time series in terms of a network generation method based on Markov transition probability. We find that the generated network inherits the main features of the time series in the network structure. In particular, the networks from time series with different dynamics exhibit distinct topological properties. Finally, we construct two-phase flow directed weighted networks from experimental signals and associate the dynamic behavior of gas-liquid two-phase flow with the topological statistics of the generated networks. The results suggest that the topological statistics of two-phase flow networks allow quantitative characterization of the dynamic flow behavior in the transitions among different gas-liquid flow patterns.     

Determining the input dimension of a neural network for nonlinear time series prediction

Determining the input dimension of a feed-forward neural network for nonlinear time series prediction plays an important role in the modelling.The paper first summarizes the current methods for determining the input dimension of the neural network.Then inspired by the fact that the correlation dimension of a nonlinear dynamic system is the most important feature of it ,the paper pressents a new idea that the input dimension of the neural network for nonlinear time series prediction can be taken as an integer just greater than or equal to the correlation dimension.Fimally,some validation examples and results are given.     

Detecting positive feedback in multivariate time series: The case of metal prices and US inflation

The objective of this paper is to examine causality and feedback relationships between primary commodity prices and US inflation. To this end, the bivariate noisy Mackey–Glass process recently developed by Kyrtsou and Labys [Evidence for chaotic dependence between US inflation and commodity prices, J. Macroecon. 28(1) (2006) 256–266] has been applied to assess this relationship. Results obtained support evidence in favour of causality, which can help to identify the influences of speculative price behaviour on inflation.     

基于度的正/负相关相依网络模型及其鲁棒性研究

利用典型的Barabási-Albert无标度网络构建了基于度的正/负相关相依网络模型, 该模型考虑子网络间的相依方式及相依程度, 主要定义了两个参数F和K, F表示相依节点比例, K表示相依冗余度. 在随机攻击及基于度的蓄意攻击模式下, 针对网络的级联失效问题, 研究了不同的F值和K值对该相依网络模型鲁棒性的影响, 与随机相依网络模型进行了对比研究. 仿真结果表明:无论是随机相依或是基于度的正/负相关相依网络, 其鲁棒性都是随着F的增大而减弱, 随着K的增大而增强; 在随机攻击下, 全相依模式(F=1)时, 基于度正相关相依网络模型鲁棒性最优, 部分相依模式 (F =0.2, 0.5, 0.8)时, 基于度的负相关相依网络模型则表现出更好的鲁棒性. 而在基于度的蓄意攻击下, 无论F为何值, 基于度的正相关相依网络模型表现出弱鲁棒性.     

A coherence-based approach for the pattern recognition of time series

A pattern recognition approach based on the frequency domain measure of squared coherence is a useful approach to identify linearly related groupings of time series over different periods of time. It is considered in an application to identify similar patterns of the yearly rates of change in the Gross Domestic Product (GDP) of twenty two highly developed countries in an econophysics context. The approach is also tested in simulation studies using linearly related time series, and it is shown to have a very good success rate of correct pattern matching.     

储备池状态空间重构与混沌时间序列预测

分析了现有的基于回声状态网络(ESN)的迭代预测方法，指出了该方法在理论上存在的问题以及应用中存在的障碍.提出了一种基于储备池的直接预测方法，该方法利用预测原点和预测时域之间的关系直接构建预测器，因此可以预先对预测器的稳定性施加约束，从而避免了在迭代预测方法中由于网络回路闭合而产生的稳定性问题.在仿真中，首先以Lorenz时间序列为例分析了迭代预测方法在闭合回路前后储备池的变化情况，然后通过Mackey-Glass标杆问题的测试验证了直接预测方法的可行性.     

Improving the prediction of chaotic time series

One of the features of deterministic chaos is sensitive to initial conditions. This feature limits the prediction horizons of many chaotic systems. In this paper, we propose a new prediction technique for chaotic time series. In our method, some neighbouring points of the predicted point, for which the corresponding local Lyapunov exponent is particularly large, would be discarded during estimating the local dynamics, and thus the error accumulated by the prediction algorithm is reduced. The model is tested for the convection amplitude of Lorenz systems. The simulation results indicate that the prediction technique can improve the prediction of chaotic time series.