Abstract
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.
Highlights
Complex network analysis in recent years has become a powerful tool to investigate challenging problems in a wide range of research areas
We have studied the stock relationship network using the data of 280 stocks from the Shanghai Stocks Exchange based on the Pearson correlation coefficient and mutual information
We have compared the stock price patterns for stock pairs that have similar or different value ranks based on mutual information and the correlation coefficient
Summary
Complex network analysis in recent years has become a powerful tool to investigate challenging problems in a wide range of research areas. A complex network is defined as a system with a large number of nodes and relationships between these nodes [1]. A variety of methods have been applied to study complex networks in biology, social sciences, finance and engineering. The stock network is an important financial system [2]. Each node in a stock network stands for a stock, and the edge connecting a pair of stocks represents the correlation between the prices of these two stocks. The stock networks have been used to observe and analyze the dynamics of the stock market as well as make predictions of future prices [3]
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