时间序列的多尺度不可逆性和复杂度研究

发布时间：2018-04-27 07:09

本文选题：时间序列分析 + 多尺度分析　；参考：《北京交通大学》2017年博士论文

【摘要】：真实世界复杂系统是由多数量、大规模的内在成分构成的,这些内在成分在时间和空间尺度上互相影响,表现出多层次结构、突现性和自组织性等特点,这使得我们在刻画复杂系统内在结构时变得非常困难.本文主要利用时间序列的不可逆性分析和复杂度分析这两种重要手段来探索复杂系统内在结构和动态演化.由于复杂系统的输出序列具有非平稳性和非线性,基于平稳性和线性假设构建的传统理论方法已不再适用.在本文中,我们从两方面研究复杂系统输出的序列:一方面是基于概率分布理论,探讨非平稳时间序列的多尺度不可逆性;另一方面是基于信息论中的熵分析,研究时间序列的多尺度复杂度.本文总共分为六章,组织结构如下:第一章为引言部分,介绍本文的研究背景、研究对象、研究意义和主要工作.第二章探讨了时间不可逆性在多尺度上的波动变化.我们不仅研究了不可逆指数和可视图系列模型的不可逆度量方法,还进一步探索了时间序列在多重时间尺度上的不可逆性.由此,我们提出基于PG指数平面的多尺度不可逆度量和基于有向水平可视图的多尺度不可逆分析方法,并分别对六种生成序列:白噪声、1/f噪声、均匀分布U[0,1]、Henon映射、逻辑映射和一维随机游走过程进行数值模拟,对比验证模型的有效性.此外,我们还分析了不同程度的噪音对序列不可逆性的影响,对比验证两种模型的鲁棒性.对金融时间序列的实证分析中,我们发现其不可逆性具有多尺度特征,且相近地域内的股指序列具有相似的复杂结构.这一发现让我们可以更好地了解时间序列的内在结构及其复杂程度,并通过在多重尺度上的不同呈现,达到对序列进行分类的目的.第三章提出了基于序列分割的时间不可逆性分析方法.该方法利用Jensen-Shannon散度对时间序列进行分割,并在分割思想的基础上,首次提出交叉对比分割,以此识别序列及其子序列具有相同边界的片段(即共同片段),并度量它们的不可逆程度.我们将这种方法应用到石油价格序列,通过研究分割后序列片段的结构特征,发现这些共同片段与某些特殊事件相关联,且其不可逆程度较低.同时,通过对比分析每日价格和每周价格序列在不同分割片段上的不可逆性,我们研究了时间尺度对序列局部结构的影响.第四章研究了非平稳时间序列的多尺度复杂度并构建了两种模型.第一个模型是基于交叉样本熵(CSE),提出了多尺度交叉样本熵(MCSE),用于度量时间序列间交互作用的复杂度,同时反映序列间的内在相似程度.我们将这个模型应用到金融序列上,通过实证分析,发现交叉样本熵能有效反映两个序列间的相似程度及其同步状况.此外,考虑到序列自身复杂度会影响多序列间同步性,我们对该模型进行了改进,提出相对交叉样本熵ACSE,进一步分析多序列间的动态复杂度.第二个模型从研究序列内在排列结构来刻画时间序列的复杂度这一角度出发,提出了多尺度加权置换熵(MSWPE).通过二项重分形时间序列数值模拟,我们发现MSWPE能分析尖峰数据并给出稳定可靠的结果,同时,通过将该模型应用到交通拥堵指数(TCI),量化和区分了 TCI序列在工作日与周末的复杂程度和模式.第五章研究了非平稳时间序列的相关性.首先,针对复杂系统输出时间序列的非平稳性,我们提出多尺度去趋势波动分析方法.该方法通过计算序列的局部标度指数,度量了不同标度范围下序列的相关性,从而刻画序列的动态复杂性.不同于传统的去趋势波动分析法(DFA),局部标度指数克服了 DFA方法单一标度的局限性.然后,我们将多尺度去趋势波动分析法用于研究不同生理时间序列的相关性.通过分析不同生理状态下的心跳间隔序列,我们发现健康个体的心跳间隔序列在不同标度范围都具有较高的局部标度指数,这表明健康的生理系统具有高度复杂性;相反,病理个体的局部标度指数会随标度范围变化而明显波动.为了进一步验证多尺度去趋势波动分析法在刻画多尺度信息时的优越性,我们研究了异常值、数据长度和性别等因素对模型结果的影响,研究结果表明,我们提出的多尺度去趋势波动分析方法能够展现传统DFA方法无法刻画的多尺度信息.第六章是对本文的总结.归纳主要研究成果,同时展望下一步的工作计划.
[Abstract]:Complex systems in the real world are composed of many and large internal components. These internal components affect each other on time and space scales, showing the characteristics of multilevel structure, occurrence and self-organization. This makes it very difficult for us to describe the internal structure of complex systems. This paper mainly uses the time series. Two important means of reversibility analysis and complexity analysis are used to explore the internal structure and dynamic evolution of complex systems. Since the output sequences of complex systems are non-stationary and nonlinear, the traditional theoretical methods based on stability and linear assumptions are no longer applicable. In this paper, we study the output of complex systems from two aspects. Sequence: on the one hand, it is based on the probability distribution theory to discuss the multiscale irreversibility of the nonstationary time series; on the other hand, it is based on entropy analysis in the information theory to study the multiscale complexity of the time series. This paper is divided into six chapters. The first chapter is the introduction to the research background, the research object and the research. The second chapter discusses the fluctuation of time irreversibility on multiscale. We not only study irreversible measures of irreversible and view series models, but also explore the irreversibility of time series on multiple time scales. Thus, we propose a multiscale based on the PG exponent plane. Irreversible measurement and multiscale irreversible analysis based on directed horizontal view, and numerical simulation of six generation sequences, white noise, 1/f noise, uniform distribution U[0,1], Henon mapping, logical mapping and one dimensional random walk, are numerically simulated to verify the validity of the model. In addition, we also analyze the noise pairs of different degrees. In the empirical analysis of the financial time series, we found that the irreversibility of the two models has multi-scale characteristics, and the stock index sequence in the similar region has a similar complex structure. This discovery allows us to better understand the internal structure of the time series and the complexity of the time series. In the third chapter, a time irreversibility analysis method based on sequence segmentation is proposed. This method uses Jensen-Shannon divergence to divide the time series, and on the basis of the segmentation idea, it first proposes cross contrast segmentation to identify the sequence. We apply this method to the oil price sequence and find that the common fragments are associated with some special events and their irreversibility is low. The irreversibility of the daily price and the weekly price sequence on different segments is analyzed. We study the effect of time scale on the local structure of the sequence. In the fourth chapter, we study the multiscale complexity of the nonstationary time series and construct two models. The first model is based on the cross sample entropy (CSE), and proposes a multi scale cross sample entropy (M CSE), which is used to measure the complexity of interaction between time series, and reflects the intrinsic similarity between sequences. We apply this model to the financial sequence. Through empirical analysis, we find that the entropy of cross sample can effectively reflect the similarity and synchronization between the two sequences. In addition, the complexity of the sequence itself will affect much more. In sequence synchronization, we improved the model, proposed the relative cross sample entropy ACSE, and further analyzed the dynamic complexity between multiple sequences. The second model proposed a multi scale weighted permutation entropy (MSWPE) from the perspective of the inner permutation of the sequence to describe the complexity of the time series. Through the two terms of the re fractal time. In sequence numerical simulation, we find that MSWPE can analyze peak data and give stable and reliable results. At the same time, by applying the model to traffic congestion index (TCI), we quantify and distinguish the complexity and pattern of TCI sequences at work days and weekends. The fifth chapter studies the correlation of non stable time series. First, for complex systems. The non stationarity of the output time series, we propose a multiscale detrending wave analysis method. By calculating the local scaling exponent of the sequence, we measure the correlation of the sequence under the range of scale, thus characterizing the dynamic complexity of the sequence. It is different from the traditional detrending wave dynamic analysis (DFA), and the local scaling exponent overcomes the DFA By analyzing the correlation between different physiological time series, we find that the heart interval sequence of the healthy individuals has a higher local scale index at different scales, which is Ming Jian. On the contrary, the local scale index of the pathological individual fluctuates with the scale range. In order to further verify the superiority of the multiscale detrending wave analysis in characterizing the multi-scale information, we study the effect of the abnormal value, the length of the data and the sex on the model results. The results show that the multi scale trend fluctuation analysis method proposed by us can unfold the multi-scale information that the traditional DFA method can't depict. The sixth chapter is the summary of this paper. The main research results are summarized, and the next step of the work plan is also prospected.

【学位授予单位】：北京交通大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：F224

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