Analysis of complex time series based on EMD energy entropy plane

  • Jing GaoEmail author
  • Pengjian Shang
Original Paper


Empirical mode decomposition (EMD) is a self-adaptive signal processing method that can be applied to nonlinear and non-stationary processes perfectly. In view of this good ability of EMD, in this paper, we propose a new method—EMD energy entropy plane—which combines two different tools—EMD energy entropy and complexity-entropy causality plane—to analyze time series. Firstly, we apply EMD energy entropy plane to synthetic data, such as logistic map, Hénon map, ARFIMA model and so on, finding that the EMD energy entropy plane presents different trends and distributions when the map is in periodic cycles and chaos. Then we demonstrate the application of EMD energy entropy plane in stock markets. Results show that it is an effective tool of distinguishing two kinds of financial markets. In addition, the introduction of multi-scale reveals the variation law of EMD energy entropy plane at different scales.


EMD energy entropy plane Financial time series Logistic map Hénon map ARFIMA model 



The financial supports from the funds of the Fundamental Research Funds for the Central Universities (2018JBZ104), the China National Science (61771035) and the Beijing National Science (4162047) are gratefully acknowledged.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this paper.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Mathematics, School of ScienceBeijing Jiaotong UniversityBeijingPeople’s Republic of China

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