The Research Of Denoising Based On Random Matrix Theory In Financial Networks

Financial market is a highly complex dynamics of complex systems. It helps to understand the nature of the correlation base on complex networks. Random matrix theory has a wide range of applications in nuclear physics, multivariate statistics and wireless communications. Recently random matrix theory applies to study the correlation of financial correlation coefficient matrix in the financial field. Correlation coefficient matrix is the key factor in constructing network. In this paper we combine random matrix theory and network construction.This paper studies to denoising financial networks based on random matrix.(1) We select stock data of Shanghai stock market, and divide the data into four stages. We discuss the statistical properties of eigenvalues and eigenvectors of financial correlation coefficient matrix and random matrix based on random matrix theory, and improve the existing denoising method to construct the correlation coefficient matrix which is more appropriate to build financial networks. And then we build the financial network model.(2) We analyze and compare the original financial network, the denoising financial network and the noise financial network based on random matrix theory and the key node of networks. We find that the key important information is still in the original network and noise information corresponds to information which the nodes of small degree in the original network respect. Then we analyze the topological structure of the financial networks from the point of minimum spanning tree, motif and community structure.(3) We apply the denoising method which is based on random matrix theory to study financial network of Shanghai stock exchange150index. We analyze the topological properties of the network, such as scale-free, clustering coefficient and nodes centralities, which explains inherent law and development trend of Shanghai denoising financial network. Then we attack the network by random and deliberate methods to analyze the robustness of the denoising network, which further prove the improved denoising method is significant to study financial networks.This paper puts forward the improved denoising method in financial networks based on random matrix theory. We find the topological properties of the improved financial networks are more obvious and the topological structure is more tightness.