本文运用上证A股市场2001年1月1日至2016年12月31日的503支股票的时间序列数据进行实证分析,主要运用随机矩阵理论和复杂网络的研究方法,分析中国股票市场中股票收益率之间相关系数矩阵特征值及特征向量的统计性质,计算市场股票收益率的整体趋势从而消除市场模式,提出股票排序具有从整体上去除市场趋势的作用,并对去除市场模式后的时间序列构建股票关联网络并分析其拓扑结构的演化过程。 首先,对所选取的数据进行清洗和计算,得到研究时间区间内上市公司的收益率数据,并计算股票间收益率的相关系数矩阵。运用随机矩阵理论分析矩阵的特征根和特征向量的统计性质,发现实证数据的最大特征根是随机矩阵预测上限的114.75倍,并且其对应的特征向量对研究的所有股票均有正向影响,这就意味着真实股票市场并不是完全随机的,股票之间的互相关性存在一些重要的市场信息。因此运用该向量计算出代表市场趋势的参数,并且用资本资产定价模型去除该市场趋势,得到反应股票自身波动情况的收益率数据并计算其相关系数矩阵。提出股票的排序观具有消除市场效应的作用,运用股票排序后的时间序列计算相关系数矩阵,并与随机矩阵理论和资产资本定价模型去除市场趋势后的相关系数矩阵进行配对资料样本吻合度检验,得到在95%的显著性水平下两个矩阵并无显著差异。 其次,运用阈值法分别对两种去除市场趋势后的时间序列数据构建股票关联网络,发现这种网络的拓扑结构与随机网络的拓扑结构截然不同,说明了中国股票市场存在区别于随机网络的内部信息和结构。本文计算得出股票关联网络的一些拓扑结构参数,如度和度分布、集聚系数、平均最短路径、最大连通集团节点数等,比较两个去趋势股票关联网络在拓扑结构上的异同,从复杂网络的角度进一步验证股票排序去除市场趋势的效果,验证两个股票关联网络结构的相似性。通过比较股票关联网络和随机网络的拓扑结构参数在不同阈值条件下的差别,确定构建股票关联网络的最优阈值为0.19。通过对网络进行模拟攻击,发现在此基础上构建的股票关联网络,更加依赖于那些度较大的股票,即在股票关联网络中与其他股票相关性更强的股票,并且此时网络的度分布为幂律分布,且幂指数为1.71。 最后,运用上述确定最优网络阈值的方法计算出2001年至2016年各年度的最优阈值,分别构建各年度的股票关联网络并计算其网络拓扑结构参数,结果表明,中国股票市场的网络结构随着市场表现的变化而变化,特别是在金融动荡期间,如2008年全球金融危机和2015年中国股灾,股票关联网络的拓扑结构参数明显高于其他年份,其中最大连通集团节点数2008年和2015年分别高于其他年份的2.45倍和3.22倍。这一发现对风险管理起到一定的作用,因为从整体的角度看股票市场的相互关联关系是非常重要的。随后,又对两个代表性动荡时期的股票关联网络的结构参数进行比较,分别从集聚系数、最大连通集团节点数和网络度三个方面比较两个网络的异同。

In this paper, we do the empirical analysis of 503 stocks in Shanghai A-share market from January 1st, 2001 to December 31th, 2016. Based on random matrix theory (RMT) and complex network methods, we analyze the statistical properties of the eigenvalues and eigenvectors of the correlation coefficient matrix for the time series of stock returns. And putting forward the sorting data of stocks has the effect of removing market trend, and we analyze the evolution of the topology structure of the stock correlation network after removing market trend. Firstly, the selected data is preprocessed and calculated to obtain the time series of stock return in the studied time interval, and the correlation coefficient matrix of the stock returns can be calculated using the data. Based on random matrix theory (RMT), the eigenvalues and eigenvectors of the correlation coefficient matrix for stock returns are calculated. It is found that the largest eigenvalue of the correlation coefficient matrix for stock returns is 114.75 times the upper limit of the random matrix prediction. Besides, the eigenvector of the largest eigenvalue has positive influence for all stocks, that is to say, the stock market is not completely random and there are some important market information in the cross-correlation coefficient matrix between stocks. Therefore, the eigenvector is used to calculate the parameters which can represent the trend of the stock market index, and the market index, also means the market mode, is removed based on the capital asset pricing model (CAPM). The resulting returns represent the fluctuation of the stocks.Putting forward the sorting data of stocks has the effect of removing market trend, and the correlation coefficient matrix is calculated by using the sorting data of stocks. The coincidence test of paired data samples was performed with the correlation coefficient matrix after removing the market trend from the random matrix theory and the asset capital pricing model. There was no significant difference between the two matrices at the 95% level of significance. Secondly, using the time series of stock returns after removing the market trend, the stock correlation network is constructed based on threshold method. We find the stock correlation network topology is quite different from random network, indicating a specific internal structure of Chinese stock market. By comparing the difference of the topological statistical properties for the stock correlation network and its corresponding random network, such as the clustering coefficient, the average shortest path and the size of first giant component, the optimal threshold of stock correlation network is determined which is 0.19. Then, through simulated attack on the network, it is found that the stock correlation network based on the optimal threshold is more dependent on stocks whose degree are larger than other stocks. These stocks are more relevant to other stocks in the stock correlation network, and then the distribution is a power-law with the exponent of 1.71. Finally, to investigate the evolution of topological structure of Chinese stock network, as with the previous approaches, we build the stock correlation network of each calendar year in the time period from 2001 till 2016. We find that the topological statistical properties of stock correlation network vary according to market condition. Particularly during the 2008 financial crisis and 2015 Chinese stock market turbulence, the value of the average degree, the clustering coefficient and the size of first giant component are significantly bigger than the other years. The size of the first giant component in 2008 and 2015 are 2.45 and 3.22 times higher than those in other years. The result show that the internal network structure of financial market vary as the financial market performance changes, and may shed light on risk management that the overall structure of stock market should be taken into consideration. Then, the topological statistical properties of the stock correlation networks in two representative turbulent periods are compared. The similarities and differences of the two networks are compared from the three aspects of the clustering coefficient, the size of the first giant component and the average degree.