Wang Yuanyuan, Shang Pengjian
Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, People's Republic of China.
Chaos. 2018 Oct;28(10):103107. doi: 10.1063/1.5023031.
In this paper, we propose a Shannon-Fisher information plane based on the information entropy to analyze financial stock markets. In order to evaluate the effectiveness of this method, we apply this method to two types of artificial time series: Autoregressive Fractionally Integrated Moving Average models and Chebyshev map model. The results show that with the embedding dimension and the number of possible states of the system increasing, the normalized Shannon entropy increases, and the Fisher information measure (FIM) decreases. When the parameter is not so big, the embedding dimension plays a leading role in determining the FIM. In addition, compared with the classical Shannon-Fisher information through permutation entropy, we conclude that the proposed approach can give us more accurate information on the classification of financial stock markets.
在本文中，我们提出了一种基于信息熵的香农-费希尔信息平面来分析金融股票市场。为了评估该方法的有效性，我们将此方法应用于两种类型的人工时间序列：自回归分数整合移动平均模型和切比雪夫映射模型。结果表明，随着嵌入维数和系统可能状态数的增加，归一化香农熵增加，而费希尔信息量（FIM）减小。当参数不是很大时，嵌入维数在确定FIM方面起主导作用。此外，与通过排列熵得到的经典香农-费希尔信息相比，我们得出结论，所提出的方法可以为我们提供关于金融股票市场分类的更准确信息。
