中国股市复杂网络中的分形特征

Fractal characteristic of the Chinese stock market complex network

利用阈值法构建中国股市复杂网络模型,从时间和空间两个角度对中国股市复杂网络的分形特征进行分析.首先利用分形几何学对静态网络进行分析,得到静态网络的分形维数,并发现其分形维数随着网络阈值的增大而减小.再利用R/S分析方法对中国股市复杂网络聚集系数时间序列进行分析,发现其具有长记忆性和持久性,且在长时间窗口下这一性质更值得信赖.H值大致呈现出随着时间窗口和阈值的增加而增加的规律.周期天数n呈现出随着时间窗口的增加而增长,随着阈值的增加而下降的规律.这说明在实际市场中,长时间窗口和高联系度股票产生的交易者群体行为惯性更强,长时间窗口和低联系度股票产生的交易者群体行为惯性的持续周期更长.这些研究成果表明了证券市场时间和空间两个维度的内在联系.

By using the threshold method, this paper constructs the Chinese stock market complex network and analyzes the fractal characteristics of the network from the dimensions of time and space. Firstly, the static network is analyzed with the fractal geometry theory, from which the fractal dimension of the network is obtained. The result shows that the fractal dimension decreases with the threshold. Then, based on the R/S analysis method, this paper analyzes the time series of the clustering coefficient of network. The result illustrates that the time series show the long memory and persistence. And in the long time window, this result is more trustworthy. Approximately, the Hurst index increases when the time window and the threshold increase. The cycle increases when the time window increases and the threshold decreases. It illustrates that in the real market, the trader＇s group behavior inertia is stronger in the case of long time window and high correlation stocks, and the cycle of the trader＇s group behavior inertia is longer in the case of long time window and low correlation stocks.