Nonlinear Dynamics

, Volume 96, Issue 4, pp 2449–2462 | Cite as

Multivariate multiscale complexity-entropy causality plane analysis for complex time series

  • Xuegeng MaoEmail author
  • Pengjian Shang
  • Qinglei Li
Original Paper


The multivariate multiscale complexity-entropy causality plane (MMCECP) is introduced for evaluating the dynamical complexity and long-range correlations of multivariate nonlinear systems. Numerical simulations from different classes of systems are applied to confirm the effectiveness of the proposed measure. We observe that the MMCECP not only can characterize the deterministic properties of the systems, but also can distinguish Gaussian and non-Gaussian processes. Moreover, it is immune to varying degrees of noises at large scales. Then we apply it to financial time series analysis, mainly investigating the classification of stock market dynamics. Empirical results illustrate that the MMCECP is robust and valid to detect the physical structures of stock markets.


Complexity-entropy causality plane Multivariate Multiscale Permutation entropy Nonlinear time series 



The financial supports from the funds of the Fundamental Research Funds for the Central Universities (2019YJS205, 2018JBZ104), the China National Science (61771035) and the Beijing National Science (4162047) are gratefully acknowledged.

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest concerning the publication of this manuscript. Name: Xuegeng Mao


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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
  2. 2.Lab for Climate and Ocean-Atmosphere Studies, Department of Atmospheric and Oceanic Sciences, School of PhysicsPeking UniversityBeijingPeople’s Republic of China

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