Complexity of time series is an important feature of dynamical systems such as financial systems. In order to bring out the complete non-linear behavior of financial time series, non-linear tools of complexity measurement like entropy measures are indispensable. Sample entropy (SampEn) and distribution entropy (DistEn) are popular methods of assessing the complexity in various fields. However, both sample entropy and distribution entropy show some limitations in detecting the complexity of stock markets. Therefore, we use two entropies as binary indices to analyze the complexity of time series and structure the entropy plane. In order to further improve the accuracy of the research results, we take the embedding dimension $m$ as the variable, expand the entropy point into the entropy curve for further research. Furthermore, considering the shortcomings of sample entropy and distribution entropy in practical application, we generalize them by (i) replacing sample entropy and distribution entropy with multi-scale sample entropy and multi-scale distribution entropy; (ii) generalizing Shannon entropy as Tsallis entropy. Also, scale factor $\tau$ and entropic index $q$ are taken respectively as variables to get the entropy curves. By using the artificial data, we confirm the rationality of using entropy points and entropy curves to study the complexity of time series. Finally, we apply this method to measure the complexity of real world financial time series, the results show that the entropy curves plotted by the financial time series obtained from different areas have significant differences.

时间序列的复杂性是动态系统（例如金融系统）的重要特征。为了展现金融时间序列的完全非线性行为，诸如熵度量之类的复杂性度量的非线性工具是必不可少的。样本熵（SampEn）和分布熵（DistEn）是评估各个领域复杂性的常用方法。但是，样本熵和分布熵在检测股票市场的复杂性方面都显示出一些局限性。因此，我们使用两个熵作为二元索引来分析时间序列的复杂性并构造熵平面。为了进一步提高研究结果的准确性，我们采用了嵌入维度$米$作为变量，将熵点扩展为熵曲线以进一步研究。此外，考虑到实际应用中样本熵和分布熵的不足，我们将其概括为：（i）用多尺度样本熵和多尺度分布熵代替样本熵和分布熵；（ii）将Shannon熵推广为Tsallis熵。还有比例因子$\tau$ 和熵指数 $q$分别作为变量获得熵曲线。通过使用人工数据，我们确认了使用熵点和熵曲线来研究时间序列的复杂性的合理性。最后，我们用这种方法来衡量现实世界中金融时间序列的复杂性，结果表明，从不同地区获得的金融时间序列绘制的熵曲线存在显着差异。