Yan Yan, Wu Boyao, Tian Tianhai, Zhang Hu
School of Mathematics and Physics, Wuhan Institute of Technology, Wuhan 430205, China.
School of Mathematics, Monash University, Melbourne, VIC 3800, Australia.
Entropy (Basel). 2020 Jul 15;22(7):773. doi: 10.3390/e22070773.
Complex network is a powerful tool to discover important information from various types of big data. Although substantial studies have been conducted for the development of stock relation networks, correlation coefficient is dominantly used to measure the relationship between stock pairs. Information theory is much less discussed for this important topic, though mutual information is able to measure nonlinear pairwise relationship. In this work we propose to use part mutual information for developing stock networks. The path-consistency algorithm is used to filter out redundant relationships. Using the Australian stock market data, we develop four stock relation networks using different orders of part mutual information. Compared with the widely used planar maximally filtered graph (PMFG), we can generate networks with cliques of large size. In addition, the large cliques show consistency with the structure of industrial sectors. We also analyze the connectivity and degree distributions of the generated networks. Analysis results suggest that the proposed method is an effective approach to develop stock relation networks using information theory.
复杂网络是从各类大数据中发现重要信息的有力工具。尽管针对股票关系网络的发展已经开展了大量研究，但相关系数主要用于衡量股票对之间的关系。对于这个重要主题，信息论的讨论要少得多，尽管互信息能够衡量非线性成对关系。在这项工作中，我们建议使用部分互信息来构建股票网络。路径一致性算法用于滤除冗余关系。利用澳大利亚股票市场数据，我们使用不同阶数的部分互信息构建了四个股票关系网络。与广泛使用的平面最大过滤图（PMFG）相比，我们能够生成具有大尺寸团块的网络。此外，大团块与产业部门的结构一致。我们还分析了生成网络的连通性和度分布。分析结果表明，所提出的方法是一种利用信息论构建股票关系网络的有效方法。
