非线性Potts金融系统动态及金融时间序列统计分析

发布时间：2018-06-29 12:10

本文选题：加权分数阶排列熵 + 分数阶样本熵　；参考：《北京交通大学》2017年硕士论文

【摘要】：在本篇论文中,为了探究复杂系统中分数阶信息熵的统计特性,我们通过把分数阶信息熵用于排列熵和样本熵算法,从而将其推广为具有分数阶形式的加权分数阶排列熵和分数阶样本熵。文中通过不同的模拟数据和真实数据对加权分数阶排列熵和分数阶样本熵进行了有效性分析。实证结果表明调整分数阶数可以更灵敏和准确的刻画不同时间序列的动态变化,这有利于描绘复杂系统的的动态行为。并且本文通过数值模拟对比研究了 Potts金融模型和真实股市收益率序列的非线性复杂度行为,实证表明表明了该模型的合理性。通过结合样本熵和复杂度不变量距离,本文提出了一种新的同步性度量方法复合复杂度同步性来刻画两个具有相同长度的时间序列之间的同步程度。文中通过将多尺度复合复杂度同步性分析和多尺度交互样本熵分析运用于七只具有代表性的股票市场指数对比分析了不同指数对数收益率序列之间的配对行为。并且通过选取文中股票指数在相同时段内不同采样频率的数据来分析数据采样频率对于多尺度复合复杂度同步性的影响。并且我们通过集成经验模态分解方法将股票指数对数收益率序列分解为本征模函数序列并且研究分解后的序列多大程度上保留了原始序列的配对行为。实证结果证实了复合复杂度同步性的有效性并且该方法在区分时间序列之间细微的同步行为方面的优越性。
[Abstract]:In this paper, in order to explore the statistical characteristics of fractional information entropy in complex systems, we apply fractional order information entropy to permutation entropy and sample entropy algorithm. It is generalized to weighted fractional order permutation entropy and fractional order sample entropy. In this paper, the validity of weighted fractional permutation entropy and fractional order sample entropy are analyzed by different simulation data and real data. The empirical results show that adjusting fractional order can more sensitively and accurately describe the dynamic changes of different time series, which is helpful to describe the dynamic behavior of complex systems. The nonlinear complexity behavior of Potts financial model and real stock market return series is studied by numerical simulation, and the rationality of the model is demonstrated. By combining sample entropy and complexity invariant distance, a new measure of synchronicity is proposed in this paper to describe the degree of synchronization between two time series of the same length. In this paper, multi-scale complex complexity synchronism analysis and multi-scale interactive sample entropy analysis are applied to seven representative stock market indices to compare and analyze the pairing behavior between different exponential logarithmic rate of return series. The influence of data sampling frequency on the synchronization of multi-scale composite complexity is analyzed by selecting the data of stock index in the same period of time and different sampling frequency. Furthermore, we decompose the stock exponent logarithmic return series into eigenmode function sequences by integrating empirical mode decomposition method and study the extent to which the decomposed sequences retain the pairing behavior of the original sequences. The empirical results demonstrate the effectiveness of the synchronization of complex complexity and the superiority of the proposed method in distinguishing subtle synchronization behaviors between time series.
【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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