Research on Co-movement Effect in Stock Market by Complex Network Community Structure Analysis

金融复杂网络社团结构分析算法研究股票市场板块联动效应
王 雄1 （1. 上海交通大学数学系 上海 200240）

摘 要：近几年来，复杂网络的研究正处于蓬勃发展的阶段，其思想已经深入到科学和社会的方方面面，是描述和分析复杂系统的有力工具。金融市场是典型的复杂系统，是由以高度非线性方式相互影响的许多代理者所构成的系统。金融市场积累了海量的高频数据，为复杂网络理论研究和实证分析提供了数据支持。社团结构是许多实际复杂网络的一个重要特征。寻找和分析社团结构对于了解网络结构与分析网络特性具有极为重要的意义。联动效应是证券市场上一种典型的价格现象，它是指一些不同证券的收益波动之间往往存在着显著的关联性。本文尝试用复杂网络中的社团结构分析算法来研究金融市场中证券收益的联动效应和板块效应。
本文将市场上的股票视为结点。首先用移动平均线作出股票的趋势图，利用两支股票趋势图的斜率乘积在时段上求和得到联动相关性系数，用以度量股票间的联动效应。通过选取一定的阙值，认为联动相关性系数超过一定阙值的股票间建立连边，得到表征股票联动效应的金融复杂网络。进而利用复杂网络社团结构分析算法，得到的社团内部的联动性明显高于社团与外部的联动性，即联动性明显的板块。最后根据实证研究结果,对投资者提出有一定参考意义的投资操作建议。
关键词：金融复杂网络，社团结构分析，证券市场，板块联动效应，联动相关性系数

Research on Co-movement Effect in Stock Market by Complex Network Community Structure Analysis
Abstract: At present, researches on complex network are developing rapidly. The basic thought of complex networks, a powerful tool to depict and analyze complex system, has been penetrated and utilized in various fields of science and society. Finance market is a typical complex system, characterized by the highly nonlinear effect among different investors. Finance market contains numerous high frequency data, thus provide data resource for research and empirical study on complex network theory. Since community structure is one of the most important features of real complex network, it is of great importance to look for and analyze the community structure to get a better understanding of the network structure and its properties. Co-movement effect is a typical price phenomenon; it refers to patterns of positive correlations of returns among different traded stocks. In this article, community structure analysis algorithm in complex network is used to study the co-movement effect and board linkage of stock returns in finance market.
(1) Every stock in the stock market is denoted by a node; (2) we use moving average method to get the general trend of the stock price.; (3) calculate the summary (Sij) of the product of the slopes of stock i and stock j; (4) compare the Sij with a certain threshold value; (5) if Sij is larger than the threshold value then we build a linkage between node i and node j. After the five steps listed above, we have modeled a finance complex network which depicts the co-movement effect among various stocks. And then, complex network community structure analysis algorithm is employed to find out the community structure of stock market. It is important to note that those stock inside the same community has close correlation, that is to say, the co-movement effect inside the community is much more prominent than the co-movement effect among stocks from different communities. Finally, based on our study result, we provide useful suggestion for investors.
Key word: Finance complex network, community structure analysis, stock market, board linkage effect, board linkage effect index