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随机矩阵在金融股票中的应用

发布时间:2018-02-20 00:43

  本文关键词: A股 B股 随机矩阵 特征向量 特征值 出处:《郑州大学》2014年硕士论文 论文类型:学位论文


【摘要】:本文运用随机矩阵理论的方法,研究经济异常波动对金融股票市场的影响.文中研究选取的时间段为2007年1月4日至2009年12月31日三年的时间,研究对象为深圳证券交易所双重上市公司A股与B股各41支股票.本文利用Pearson相关系数方法分别构造A、B股相关系数矩阵.通过研究这些矩阵的特征值、相关系数和特征向量的统计性质,动态地研究A、B股之间的异同.其动态性具体体现在三个方面:一、研究A、B股的不稳定性u(t)时,选取滑动时间窗口T=20天,每次向后滑动19天,A、B股各产生38个时间段,对比分析A、B股在这些时期不稳定性的变化情况.二、比较A、B股最大特征值λmax、平均相关系数cij及不稳定性v(t)三者之间的关系时,选取滑动时间窗口T=100天,每次向后滑动1天,A、B股各产生633个时间段,分别求出A、B股对应633个矩阵的最大特征值和平均相关系数.此时计算A、B股u(t)时,所取时间窗口为T=2天,每次向后滑动一天,共产生731个时间段,算出这731个时间段对应的u(t),即每天41支股票指数不稳定性的变化,最后把它们三者表示在同一图形中,比较三者的关系;研究特征值和平均相关系数的动态关系时,因为股票时间序列长度为732天,我们取T=183天,每次向后滑动10天,共产生了55个时间段,对应55个矩阵;分析相矩阵C的五个较大特征值对应特征向量随时间变化的稳定性时,同样动态地取时间窗口为T=232天,每次向后推移99天,因为A股与B股的长度都为732,因此产生了5个时间段且生成5个矩阵C.三、对于A、B股分别取四个有代表性的时间段,讨论在各个时间段A、B股对应最大特征值的特征向量的分布. 最后,通过分析比较得出结论:第一、A股价格相对B股稍高,这可能是A股市场机制比较完善,投资者比较多的原因.第二、深圳证券交易所双重上市公司A、B股股票与市场波动有相似的运动趋势,但B股反应更敏感.第三、最大特征值与对应最大特征值的特征向量对市场整体产生影响,且后者具有稳定性.这些结论可以增强投资者对股市的了解,合理地分配资金,争取减少风险增加收益.
[Abstract]:In this paper, we use the method of stochastic matrix theory to study the influence of abnormal economic fluctuations on the financial stock market. The time period chosen in this paper is from January 4th 2007 to December 31st 2009. The objects of this study are 41 A-shares and 41 B-shares of dual-listed companies in Shenzhen Stock Exchange. In this paper, the correlation coefficient matrices of A and B shares are constructed by using Pearson correlation coefficient method, and the eigenvalues of these matrices are studied. The statistical properties of correlation coefficient and eigenvector are dynamically studied in three aspects: first, when studying the instability of A and B strands, the sliding time window is chosen for 20 days. After 19 days of backward sliding, A and B stock each produce 38 time periods. The changes of instability of A and B shares in these periods are compared and analyzed. Secondly, when comparing the relationship among A, B shares maximum eigenvalue 位 max, average correlation coefficient cij and instability VT, In this paper, the maximum eigenvalue and average correlation coefficient of A and B shares corresponding to 633 matrices are obtained by selecting a sliding time window of 100 days, sliding backward for one day, and producing 633 times of B shares, respectively. When calculating A, B share UT, the time window is T ~ (2) day, and the time window is T ~ (2), respectively, when calculating A, B share UT), the maximum eigenvalue and average correlation coefficient of A and B shares are calculated respectively. A total of 731 time periods are generated by sliding backward for one day, and the changes of the instability of 41 stock indices in these 731 periods are calculated. Finally, they are expressed in the same graph, and the relationships among the three are compared. When studying the dynamic relationship between the eigenvalue and the average correlation coefficient, because the stock time series is 732 days, we take the time series T3 days and slide back 10 days each time, a total of 55 time periods are generated, corresponding to 55 matrices; When the stability of the eigenvector corresponding to the five larger eigenvalues of phase matrix C is analyzed, the time window is also dynamically selected as T ~ (232) days, each time going back for 99 days. Because the length of A shares and B shares are both 732, five time periods and five matrices C are generated. Thirdly, four representative time periods are taken for A and B shares, and the distribution of eigenvector corresponding to the maximum eigenvalue of A and B shares in each time period is discussed. Finally, the conclusion is drawn through the analysis and comparison: first, the price of A shares is slightly higher than that of B shares, which may be the reason why the mechanism of the A share market is relatively perfect and the investors are more. Second, There is a similar movement trend between A and B shares in Shenzhen Stock Exchange, but B shares are more sensitive to the reaction. Third, the maximum eigenvalue and the characteristic vector corresponding to the largest eigenvalue have an impact on the market as a whole. These conclusions can enhance investors' understanding of the stock market, allocate funds reasonably, and strive to reduce risk and increase returns.
【学位授予单位】:郑州大学
【学位级别】:硕士
【学位授予年份】:2014
【分类号】:F832.51;O151.21

【共引文献】

相关期刊论文 前5条

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