基于递归图的系统复杂性分析
发布时间：2018-08-17 19:18
【摘要】：重现是一个动态系统最基本的性质,它可以用来描述系统行为在相空间中的特性,研究这些特性的可视化及其分析最有力的工具就是递归图。由于递归图包含了系统所有行为的相关信息,因此本文采用基于递归图的方法来研究复杂性动态系统内部之间的转化以及动态系统之间的相关关系,并将该方运用到股票市场。本文首先通过基于递归图和加权递归图的香农熵方法对模拟数据进行研究,香农熵是一种评价动态系统复杂性的标准方法,并且可以用来识别不同动态行为之间的变化,我们结合该方法与模拟数据来研究递归图与时间序列复杂性的关系,得出加权递归图的香农熵方法可以很好的反映时间序列复杂性,即周期到混沌的转化或者混沌到混沌的转化,并且将该方法运用到股票市场来探索股票指数的复杂性变化。其次,为了更加充分验证递归图对于时间序列复杂性的分析性能,我们采用递归定量分析(RQA)方法进一步说明递归图研究动态系统复杂性变化的有效性及可靠性,递归定量分析能够从更深一层角度分析系统内部复杂性的变化。再次,我们提出研究不同阈值对递归定量分析方法的影响,我们发现阈值的增加会造成系统复杂性和稳定性的提高。最后我们利用联合递归图(JRP)研究动态系统之间的相关性,联合递归图不仅可以反映两个序列之间的关系而且能够反映它们之间相互影响的程度,我们结合中国市场三大代表指数(SSE,SZSE,CYBZ)分析它们之间的相关性,得出SSE和CYBZ之间的相关性高于其他两者之间。
[Abstract]:Reproduction is the most basic property of a dynamic system. It can be used to describe the behavior of the system in the phase space. The most powerful tool to study the visualization and analysis of these properties is the recursive graph. Because the recursive graph contains the information about all the behaviors of the system, this paper uses the recursive graph method to study the transformation between the complex dynamic systems and the correlation between the dynamic systems, and applies this method to the stock market. Firstly, the Shannon entropy method based on recursive graph and weighted recursive graph is used to study the simulation data. Shannon entropy is a standard method to evaluate the complexity of dynamic system, and it can be used to identify the changes between different dynamic behaviors. We study the relationship between the recursive graph and the complexity of time series by combining this method with the simulated data. It is concluded that the Shannon entropy method of weighted recursive graph can well reflect the complexity of time series. That is, the transformation from cycle to chaos or from chaos to chaos, and the method is applied to the stock market to explore the complexity of the stock index. Secondly, in order to fully verify the performance of recursive graph in analyzing the complexity of time series, we use the recursive quantitative analysis (RQA) method to further illustrate the effectiveness and reliability of recursive graph in studying the complexity change of dynamic system. Recursive quantitative analysis can analyze the complexity of the system from a deeper perspective. Thirdly, we propose to study the influence of different thresholds on the recursive quantitative analysis. We find that the increase of threshold will increase the complexity and stability of the system. Finally, we use joint recursive graph (JRP) to study the correlation between dynamic systems. Joint recursive graph can not only reflect the relationship between two sequences, but also reflect the degree of interaction between them. The correlation between SSE and CYBZ is higher than that between the other two.
【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
本文编号：2188632
[Abstract]:Reproduction is the most basic property of a dynamic system. It can be used to describe the behavior of the system in the phase space. The most powerful tool to study the visualization and analysis of these properties is the recursive graph. Because the recursive graph contains the information about all the behaviors of the system, this paper uses the recursive graph method to study the transformation between the complex dynamic systems and the correlation between the dynamic systems, and applies this method to the stock market. Firstly, the Shannon entropy method based on recursive graph and weighted recursive graph is used to study the simulation data. Shannon entropy is a standard method to evaluate the complexity of dynamic system, and it can be used to identify the changes between different dynamic behaviors. We study the relationship between the recursive graph and the complexity of time series by combining this method with the simulated data. It is concluded that the Shannon entropy method of weighted recursive graph can well reflect the complexity of time series. That is, the transformation from cycle to chaos or from chaos to chaos, and the method is applied to the stock market to explore the complexity of the stock index. Secondly, in order to fully verify the performance of recursive graph in analyzing the complexity of time series, we use the recursive quantitative analysis (RQA) method to further illustrate the effectiveness and reliability of recursive graph in studying the complexity change of dynamic system. Recursive quantitative analysis can analyze the complexity of the system from a deeper perspective. Thirdly, we propose to study the influence of different thresholds on the recursive quantitative analysis. We find that the increase of threshold will increase the complexity and stability of the system. Finally, we use joint recursive graph (JRP) to study the correlation between dynamic systems. Joint recursive graph can not only reflect the relationship between two sequences, but also reflect the degree of interaction between them. The correlation between SSE and CYBZ is higher than that between the other two.
【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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