一种基于文本互信息的金融复杂网络模型

复杂网络能够解决许多金融问题,能够发现金融市场的拓扑结构特征,反映不同金融主体之间的相互依赖关系.相关性度量在金融复杂网络构建中至关重要.通过将多元金融时间序列符号化,借鉴文本特征提取以及信息论的方法,定义了一种基于文本互信息的相关系数.为检验方法的有效性,分别构建了基于不同相关系数(Pearson和文本互信息)和不同网络缩减方法(阈值和最小生成树)的4个金融复杂网络模型.在阈值网络中提出了使用分位数来确定阈值的方法,将相关系数6等分,取第4部分的中点作为阈值,此时基于Pearson和文本互信息的阈值模型将会有相近的边数,有利于这两种模型的对比.数据使用了沪深两地证券市场地区指数收盘价,时间从2006年1月4日至2016年12月30日,共计2673个交易日.从网络节点相关性看,基于文本互信息的方法能够体现出大约20%的非线性相关关系;在网络整体拓扑指标上,本文计算了4种指标,结果显示能够使所保留的节点联系更为紧密,有效提高保留节点的重要性以及挖掘出更好的社区结构;最后,计算了阈值网络的动态指标,将数据按年分别构建网络,缩减方法只用了阈值方法,结果显示本文提出的方法在小世界动态和网络度中心性等指标上能够成功捕捉到样本区间内存在的两次异常波动.此外,本文构建的地区金融网络具有服从幂律分布、动态稳定性、一些经济欠发达地区在金融地区网络中占据重要地位等特性.

Financial complex network model based on textual mutual information

Complex networks are widely used in many problems of the financial field. It can be used to find the topological structure properties of the financial markets and to embody the interdependence between different financial entities. The correlation is important to create the complex networks of the financial markets. A novel approach to incorporating textual mutual information into financial complex networks as a measure of the correlation coefficient is developed in the paper. We will symbolize the multivariate financial time series firstly, and then calculate correlation coefficient with textual mutual information. Finally, we will convert it into a distance. To test the proposed method, four complex network models will be built with different correlation coefficients (Pearson's and textual mutual information's) and different network simplification methods (the threshold and minimum spanning tree). In addition, for the threshold networks, a quantile method is proposed to estimate the threshold automatically. The correlation coefficients are divided into 6 equal parts. And the midpoint of the 4th interval will be taken as the threshold according to our experience, which can make the MI methods and Pearson methods have the closest number of edges to compare the two methods. The data come from the closing prices of Chinese regional indexes including both Shanghai and Shenzhen stock market. The data range from January 4, 2006 to December 30, 2016, including 2673 trading days. In view of node correlation, the numerical results show that there are about 20% of the nonlinear relationships of the Chinese regional financial complex networks. In view of the network topology, four topological indicators for the regional financial complex network models will be calculated in the paper. For average weighted degree, the novel method can make the reserved nodes closely compared with Pearson's correlation coefficient. For network betweenness centralization, it can improve the betweenness importance of reserved nodes effectively. From the perspective of modularity, the novel method can detect better community structures. Finally, in dynamic network topology features, the data of regional indexes will be equally divided yearly for constructing complex network separately. The simplification method used in the section is the threshold method. The numerical results show that the proposed methods can successfully capture the two-abnormal fluctuation in the sample interval with the dynamics of the small-world and the network degree centralization. In addition, we find that the proposed regional financial network models follow the power-law distribution and are dynamically stable. Some developing regions are more important than the developed ones in the regional financial networks.