复杂系统时间序列的复杂性及相关性研究

发布时间：2019-06-02 16:02

【摘要】：在现实世界中复杂系统随处可见,分析来自这些复杂系统的时间序列是研究其内在机理与运行机制的重要手段之一.本文主要对时间序列的复杂性与相关性展开研究,在前人的基础上提出几种新的统计模型,并将其应用到金融时间序列与交通时间序列的分析中.首先,我们研究基于熵值的时间序列复杂性问题.我们提出改进的广义样本熵与替代数据分析以及基于双指数形式的广义排列熵分析这两种新的模型.改进的广义样本熵与替代数据分析利用豪斯多夫距离替代原始方法中的距离定义,不仅能够有效地克服原始方法在时间序列长度与模式向量长度之间的苛刻关系、数值退化等方面的局限性,并且在估计精确度、数据敏感性、数据抗噪性和数据量化分析等方面具有更强的优势.基于双指数形式的广义排列熵分析则将排列熵推广到带有两种指数参数的形式,可以有效放大排列熵在序列连续时的一些细微变化和整体的变化趋势,同时广义排列熵与指数之间也存在着幂律关系.其次,我们研究基于去趋势波动分析的时间序列相关性问题.我们提出基于经验模式分解与总体经验模式分解的交叉相关性分析以及多重分形去趋势波动分析与替代数据分析这两种方法.在基于经验模式分解与总体经验模式分解的交叉相关性分析中,我们运用经验模式分解、总体经验模式分解、DCCA交叉相关系数等多种方法,从一个新的角度对不同股票市场间的长期交叉相关性展开研究.而多重分形去趋势波动分析与替代数据分析则是受到广义样本熵与替代数据分析的启发,结合多重分形去趋势波动分析,对北京的交通时间序列展开研究.交通时间序列与人造的二项多重分形序列具有很高的相似度,它们具有相似的多重分形与相关性方面的特点.最后,我们研究基于顺序递归图的时间序列的多标度行为.我们提出基于顺序递归图的多标度递归定量分析方法.相比于传统的递归定量分析,多标度递归定量分析结合多标度技术,可以挖掘与辨识不同的系统在不同时间尺度上的潜在性质.研究结果表明,系统大时间尺度的重现特性与传统单一时间尺度的重现特性是不同的,一些系统在大的时间尺度上表现出更加准确的结果.多标度递归定量分析在复杂系统识别方面具有很强的优势.
[Abstract]:In the real world, complex systems are everywhere. Analyzing the time series from these complex systems is one of the important means to study their internal mechanism and operation mechanism. In this paper, the complexity and correlation of time series are studied, and several new statistical models are proposed and applied to the analysis of financial time series and traffic time series. First of all, we study the complexity of time series based on entropy. We propose two new models: improved generalized sample entropy and alternative data analysis and generalized permutation entropy analysis based on double exponential form. The improved generalized sample entropy and substitution data analysis use Hausdorf distance to replace the definition of distance in the original method, which can not only effectively overcome the harsh relationship between the length of time series and the length of pattern vector. The limitations of numerical degradation and so on, and have stronger advantages in estimation accuracy, data sensitivity, data anti-noise and data quantitative analysis. The generalized arrangement entropy analysis based on double exponential form extends the arrangement entropy to the form with two kinds of exponential parameters, which can effectively amplify some subtle changes and the overall change trend of the arrangement entropy when the sequence is continuous. At the same time, there is also a power-law relationship between the generalized permutation entropy and the index. Secondly, we study the correlation of time series based on de-trend fluctuation analysis. We propose two methods based on empirical pattern decomposition and overall empirical pattern decomposition, as well as multifractal de-trend fluctuation analysis and alternative data analysis. In the cross-correlation analysis based on empirical pattern decomposition and overall empirical pattern decomposition, we use empirical pattern decomposition, overall empirical mode decomposition, DCCA cross-correlation coefficient and so on. This paper studies the long-term cross-correlation between different stock markets from a new perspective. The multifractal de-trend fluctuation analysis and alternative data analysis are inspired by the generalized sample entropy and alternative data analysis, combined with the multifractal de-trend fluctuation analysis, the traffic time series in Beijing is studied. Traffic time series has high similarity with artificial binomial multifractal series, and they have similar characteristics of multifractal and correlation. Finally, we study the multi-scale behavior of time series based on sequential recurrent graphs. We propose a multi-scale recurrent quantitative analysis method based on sequential recurrent graphs. Compared with the traditional recurrent quantitative analysis, multi-scale recurrent quantitative analysis combined with multi-scale technology can mine and identify the potential properties of different systems on different time scales. The results show that the reproduction characteristics of the large time scale are different from those of the traditional single time scale, and some systems show more accurate results on the large time scale. Multi-scale recurrent quantitative analysis has strong advantages in complex system recognition.
【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224

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