Permutation entropy analysis based on Gini-Simpson index for financial time series

In this paper, a new coefficient is proposed with the objective of quantifying the level of complexity for financial time series. For researching complexity measures from the view of entropy, we propose a new permutation entropy based on Gini-Simpson index (GPE). Logistic map is applied to simulate time series to show the accuracy of the GPE method, and expound the extreme robustness of our GPE by the results of simulated time series. Meanwhile, we compare the effect of the different order of GPE. And then we employ it to US and European and Chinese stock markets in order to reveal the inner mechanism hidden in the original financial time series. After comparison of these results of stock indexes, it can be concluded that the relevance of different stock markets are obvious. To study the complexity features and properties of financial time series, it can provide valuable information for understanding the inner mechanism of financial markets.