复杂时间序列的若干问题研究

发布时间：2018-01-05 02:33

本文关键词：复杂时间序列的若干问题研究　出处：《北京交通大学》2017年硕士论文　论文类型：学位论文

【摘要】：复杂系统在我们日常生活中普遍存在,其中金融系统与我们的关系非常密切,这些复杂系统经常会因为一些人为或自然因素导致极端事件的发生,所以由复杂系统生成的时间序列往往是非平稳的.本文主要对非平稳时间序列的复杂性与相关性以及时间不可逆性进行研究,在过去的研究基础上提出几种新的统计模型,并应用到实际的金融市场时间序列中.本文首先研究基于去趋势波动分析(DFA)的时间序列相关性,提出改进的广义多尺度去趋势波动分析(MNDFA)方法.在传统的DFA方法中,我们获得了序列的分割系数s对波动函数的影响,但未考虑时间序列的长度变量N.这就启示我们提出一种新的基于序列长度变量的分析方法,并且讨论时间序列的长度变量对序列自相关性波动函数的影响.在传统DFA方法的波动函数中加入关于序列长度的变量A(N),并研究A(N)和N之间的幂率关系,同时也讨论了标度指数α关于序列长度变量的变化趋势.这样具有两个独立变量信息的波动函数能够更加全面和准确地展现时间序列的相关性质.其次,我们研究基于时间序列熵值的复杂非线性动力系统的有关性质.在传统的置换熵(PE)方法基础上,我们提出时间序列的最大置换熵(PMAE)方法.和传统的评估序列间大小关系的PE方法相比,PMAE方法可以进一步揭示非平稳时间序列的复杂性以及潜在的相关性.改进了经典置换熵运用香农熵计算的方法,进而运用熵模型来计算置换熵值,能够更加清晰方便地反映时间序列的复杂程度.另外,我们提出多标度最大置换熵(MPMAE)方法和改进的复合多标度最大置换熵(RMPMAE)方法,并且对两种多标度方法进行了比较分析.为了研究反映动态系统复杂程度的不同指标之间的关系,我们对时间序列的DFA函数值和PMAE值进行了比较,发现两个指标在某些部分的变化趋势具有相似性,这说明虽然研究角度不同,但它们都能很好地反映非平稳序列的内在性质.最后,我们研究基于时间序列局部不可逆性度量的复杂时间序列的性质,提出几个新的度量时间序列不可逆性的变量.在传统的时间序列整体不可逆性度量的基础上,提出序列的局部时间不可逆性度量,这些变量能够更加清晰直接地表达出时间序列的不可逆性.通过对不同的度量的变化进行比较,分析其变化趋势的相同点和差异性.另外,对序列进行多标度粗粒化处理,探讨序列的不可逆性度量和序列的标度因子的关系.这些研究结果为以后复杂时间序列的研究奠定了良好的基础.
[Abstract]:Complex systems are common in our daily life, in which the financial system and our relationship is very close, these complex systems often cause extreme events because of some man-made or natural factors. Therefore, the time series generated by complex systems are often non-stationary. In this paper, the complexity and correlation of non-stationary time series and the irreversibility of time are studied. Based on the previous studies, several new statistical models are proposed and applied to the actual time series of financial markets. Firstly, this paper studies the correlation of time series based on the detrend volatility analysis (DFA). An improved generalized multi-scale de-trend volatility analysis (MNDFAA) method is proposed. In the traditional DFA method, we obtain the influence of the partition coefficient s of the sequence on the volatility function. But the length variable N of time series is not taken into account. This suggests that we propose a new analysis method based on sequence length variables. The influence of the length variable of the time series on the autocorrelation volatility function of the sequence is discussed. The variable Ahn about the length of the sequence is added to the volatility function of the traditional DFA method. The power ratio relationship between Agnon (N) and N is also studied. At the same time, we also discuss the variation trend of the scale exponent 伪 about the sequence length variable, so that the fluctuation function with the information of two independent variables can show the correlation properties of the time series more comprehensively and accurately. Secondly. We study the properties of complex nonlinear dynamical systems based on the entropy value of time series, based on the traditional permutation entropy method. We propose the maximum permutation entropy (PMAE) method for time series, which is compared with the traditional PE method for evaluating the relationship between sequences. PMAE method can further reveal the complexity and potential correlation of non-stationary time series, and improve the classical permutation entropy using Shannon entropy calculation method, and then use the entropy model to calculate the permutation entropy value. It can reflect the complexity of time series more clearly and conveniently. In addition, we propose the multi-scale maximum permutation entropy (MPMAE) method and the improved compound multi-scale maximum permutation entropy (RMPMAE) method. In order to study the relationship between different indexes which reflect the complexity of dynamic system, we compare the DFA function value and PMAE value of time series. It is found that the variation trends of the two indexes in some parts are similar, which shows that although the research angle is different, they can well reflect the intrinsic properties of the non-stationary sequence. Finally. We study the properties of complex time series based on local irreversibility metric of time series, and propose several new variables to measure irreversibility of time series, based on the traditional global irreversibility metric of time series. The local time irreversibility measures of sequences are proposed, which can express the irreversibility of time series more clearly and directly. In addition, the multi-scale coarse granulation of the sequence was carried out. The relationship between irreversibility metric of sequence and scaling factor of sequence is discussed. These results lay a good foundation for the study of complex time series in the future.
【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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