Financial complex network model based on textual mutual information

Abstract

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.

Information flow between stock markets: A Koopman decomposition approach

“…[9] For instance, to detect the influence stored in cross-correlations, the concept of time delay stability is designed. [10][11][12][13][14] The influence is realized by a successive physical process of sending signals from the influencer, receiving signals by the influenced one and its responses. The signals may be different completely, but the delay time from the sending to the response is determined by the intrinsic properties of the systems and keeps unchanged.…”

Theoretical analyses of stock correlations affected by subprime crisis and total assets: Network properties and corresponding physical mechanisms*

“…[1][2][3][4] In general, the complex network can be divided into small world networks, [5] self-similarity ones, [6] regular ones, [7] partly or wholly heterogeneous one. [8] It is capable of modelling real physical or engineering phenomena like traffic flow, [9][10][11][12][13][14][15] the transcription of mRNA, [16] the directional motion of active particles, [17][18][19][20][21][22][23][24][25] etc., which leads the technology networks, [26] social networks, [27] financial network, [28][29][30][31][32][33][34][35][36][37][38][39] biological networks, etc. to emerge.…”

“…Furthermore, due to the in-terrelationship among stocks, it is quite necessary to use the complex network to study the correlation among real stocks in financial market. [28][29][30][31][32][33][34][35][36][37][38][39] Owing to the academic significance and practical values of the complex network, some typical methods have been introduced into the studies like Euler diagram, [45] E-R random diagram, [46] etc. Among these analytical methods, the minimum spanning tree (MST) method is considered as an effective way to identify the risk channel of financial market.…”