Development of stock correlation networks using mutual information and financial big data

Stock correlation networks use stock price data to explore the relationship between different stocks listed in the stock market. Currently this relationship is dominantly measured by the Pearson correlation coefficient. However, financial data suggest that nonlinear relationships may exist in the stock prices of different shares. To address this issue, this work uses mutual information to characterize the nonlinear relationship between stocks. Using 280 stocks traded at the Shanghai Stocks Exchange in China during the period of 2014-2016, we first compare the effectiveness of the correlation coefficient and mutual information for measuring stock relationships. Based on these two measures, we then develop two stock networks using the Minimum Spanning Tree method and study the topological properties of these networks, including degree, path length and the power-law distribution. The relationship network based on mutual information has a better distribution of the degree and larger value of the power-law distribution than those using the correlation coefficient. Numerical results show that mutual information is a more effective approach than the correlation coefficient to measure the stock relationship in a stock market that may undergo large fluctuations of stock prices.