Nie Chun-Xiao, Song Fu-Tie
Department of Finance, School of Business, East China University of Science and Technology, Shanghai 200237, China.
Entropy (Basel). 2018 Mar 7;20(3):177. doi: 10.3390/e20030177.
We analyze the dimension of a financial correlation-based network and apply our analysis to characterize the complexity of the network. First, we generalize the volume-based dimension and find that it is well defined by the correlation-based network. Second, we establish the relationship between the Rényi index and the volume-based dimension. Third, we analyze the meaning of the dimensions sequence, which characterizes the level of departure from the comparison benchmark based on the randomized time series. Finally, we use real stock market data from three countries for empirical analysis. In some cases, our proposed analysis method can more accurately capture the structural differences of networks than the power law index commonly used in previous studies.
我们分析了基于金融相关性的网络的维度，并应用我们的分析来刻画该网络的复杂性。首先，我们推广了基于成交量的维度，发现它在基于相关性的网络中定义良好。其次，我们建立了雷尼指数与基于成交量的维度之间的关系。第三，我们分析了维度序列的含义，它刻画了基于随机时间序列偏离比较基准的程度。最后，我们使用来自三个国家的真实股票市场数据进行实证分析。在某些情况下，我们提出的分析方法比先前研究中常用的幂律指数能够更准确地捕捉网络的结构差异。
