Analysis of Shannon-Fisher information plane in time series based on information entropy

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.