时间序列的相关性与相似性分析

发布时间：2019-02-28 16:26

【摘要】：近些年来,时间序列的相关性与相似性研究受到越来越多的关注,并广泛应用于经济学、生物医学、社会学等众多领域。本文主要提出并研究几种新的时间序列的相关性和相似性度量方法,将其应用于金融时间序列中。本文首先研究了q阶交叉相关系数的方法,它不仅可以用于量化序列间的交叉相关性,而且可以应用于分析两个序列间的去趋势波动幅度变化；此外,我们根据q阶交叉相关系数的定义推导出它与标度之间的幂律关系指数,并验证了该指数可以有效地判断交叉相关标度指数与自相关标度指数之间的关系。通过两组不同的模拟序列：ARFIM A序列和多重分形二项序列的结果,分析出了不同标度下的序列间的交叉相关性的程度以及波动幅度；而且,同一区域下的标普500和道琼斯指数序列展现出了较强的交叉相关性,而不同区域下的上证综合指数和道琼斯指数序列则表现出较弱的交叉相关性。对于这三种不同的序列,交叉相关标度指数与自相关标度指数关系在不同的参数下则呈现不同的特性。其次,本文还提出并研究一种新的相似性度量方法---基于相空间重构的信息聚类方法,它是在信息聚类方法的基础上对符号化过程进行了改进,采用了重构相空间的方式。之前的01符号化序列仅仅只是考虑到序列的相邻值,而相空间重构方法充分考虑到分割片段的整体性质,能够更加清晰的分析序列间的相似性。通过ARFIMA序列验证了这种新方法的有效性,以及不同参数对于结果的影响;对于不同区域和不同时间段的金融时间序列,能够给出序列间相似性的变化和区别。最后,在相似性和相关性度量的基础上,构建多组序列间的距离矩阵,根据该距离矩阵,对序列进行聚类分析,再通过系统树图清晰地展现出序列的聚类过程。研究结果表明金融时间序列的聚类分析结果可以为金融市场的投资组合决策提供有效的参考。
[Abstract]:In recent years, more and more attention has been paid to the research on the relativity and similarity of time series, and it has been widely used in many fields such as economics, biomedicine, sociology and so on. In this paper, we propose and study several new methods for measuring the correlation and similarity of time series, and apply them to financial time series. In this paper, we first study the method of Q-order cross-correlation coefficient, which not only can be used to quantify the cross-correlation between sequences, but also can be used to analyze the variation of de-trending fluctuation amplitude between two sequences. In addition, according to the definition of Q-order cross-correlation coefficient, we derive the power-law relation index between it and scale, and verify that the index can effectively judge the relationship between cross-correlation scaling index and autocorrelation scaling index. Through the results of: ARFIM A sequence and multifractal binomial sequence of two different simulated sequences, the degree of cross-correlation and the amplitude of fluctuation among the sequences under different scales are analyzed. Moreover, the S & P 500 and Dow Jones index series in the same region show strong cross-correlation, while the Shanghai Composite Index and Dow Jones index series in different regions show weak cross-correlation. For these three different sequences, the relationship between cross-correlation scaling index and autocorrelation scaling index shows different characteristics under different parameters. Secondly, this paper also proposes and studies a new similarity measurement method-information clustering method based on phase space reconstruction. Based on the information clustering method, the symbolization process is improved and the phase space reconstruction method is adopted. The previous 01 symbolic sequences only take into account the adjacent values of the sequences, while the phase space reconstruction method takes full account of the global properties of the segmented segments, so that the similarity between sequences can be analyzed more clearly. The validity of the new method and the influence of different parameters on the results are verified by ARFIMA sequence. For the financial time series of different regions and different time periods, the variation and difference of similarity between the sequences can be given. Finally, on the basis of similarity and correlation measurement, the distance matrix between multiple sequences is constructed. According to the distance matrix, the clustering process of the sequences is analyzed, and then the clustering process of the sequences is clearly demonstrated by the systematic tree graph. The results show that the cluster analysis results of financial time series can provide an effective reference for portfolio decision-making in financial markets.
【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：F224

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