Multi-likelihood methods for developing relationship networks using stock market data

The development of stock relationship networks is an important topic to explore the potential connections between different stocks. The methods based on the threshold and correlation relationship have been designed in recent years to construct networks by selecting the highly correlated links. However, if a single threshold value is used, one of the major challenges in these methods is the balance between the degree of stocks and the connectivity of the generated network. To address this issue, we propose a new method to make proper selections of links and maintain the connectivity of established networks. Instead of using a single threshold value for the whole network, our proposed approach selects a threshold value for each stock using the maximum likelihood estimation. The innovation of our method is to apply different distribution functions to the weak and strong correlations separately. Using the dataset from the Chinese Shanghai security market, we develop the stock correlation networks and analyze the topological properties of established networks, including the degree distribution, clustering coefficient and clique. Our results suggest that the proposed method is able to provide better insights into the characteristics of the stock market.