Dispersion complexity-entropy curves: an effective method to detect the structures of complex systems

Abstract Complexity-entropy curves(CEC) is a useful tool to detect the structure of time series. It’s widely applied in many research areas since it can distinguish the chaotic system and the stochastic process well. However, the original permutation complexity-entropy curves(PCEC) based on permutation entropy(PE) has a defect for it can not take means and amplitudes of time series into consideration, which may lead to some errors when distinguishing the systems. In this paper, we propose dispersion complexity-entropy curves(DCEC) to overcome the defects of PCEC. In addition, we expand the curves from two-dimension to threedimension. We first compare DCEC with PCEC by simulated data. The result shows that DCEC are not only more distinguishable but also more robust with the change of parameters when detecting periodic series. Then, we apply our method to real-world data to illustrate its practicability. We propose a creative feature extraction method based on DCEC and combine it with MSVM to diagnose the different types of bearing fault, which obtains perfect results for the accuracy achieves 100%. We also apply DCEC to stock indices in different countries and different periods to analyze the complexity degree of financial markets. The results successfully detect American financial crisis in 2008 and the rapid development of the economy in China during 2014-2018. These demonstrate that DCEC can serve as an effective method to analyze complex systems.