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.