Inverse sample entropy analysis for stock markets

Entropy has been an important tool for the complexity analysis of time series from various fields. Based on studying all the template mismatches, a modified sample entropy (SE) method, named as inverse sample entropy (ISE), for investigating the complexity of financial time series is proposed in this paper. Different from SE, ISE considers the far neighbors of templates; it also provides more comprehensive information combined with SE. Stock markets usually fluctuate with the economy policies; ISE allows us to detect the financial crisis by the change of complexity. By experiments on both simulated data and real-world stock data, ISE shows that the threshold r is more flexible compared with that of SE, which allows ISE to be applied not only to limited type of data. Besides, it is more robust to high dimension m, so ISE can be extended to the application of high dimension analysis. For studying the impact of embedding dimension m under multiple scales on both artificial and real-world data, we made a comparison on the use of SE and ISE. Both SE and ISE are able to distinguish time series with different features and characteristics. While SE is sensitive to high dimension analysis, ISE shows robustness.