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Analysis of complex time series based on EMD energy entropy plane

  • Jing GaoEmail author
  • Pengjian Shang
Original Paper
  • 15 Downloads

Abstract

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.

Keywords

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

Notes

Acknowledgements

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.

References

  1. 1.
    Machado, J.A.T.: Entropy analysis of integer and fractional dynamical systems. Nonlinear Dyn. 62(1–2), 371–378 (2010)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Machado, J.A.T., Duarte, F.B., Duarte, G.M.: Analysis of financial data series using fractional Fourier transform and multidimensional scaling. Nonlinear Dyn. 65(3), 235–245 (2011)CrossRefGoogle Scholar
  3. 3.
    Arqub, O.A., Al-Smadi, M.: Atangana-Baleanu fractional approach to the solutions of Bagley-Torvik and Painlevé equations in Hilbert space. Chaos, Solitons Fractals 117, 161–167 (2018)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Arqub, O.A.: Solutions of time-fractional Tricomi and Keldysh equations of Dirichlet functions types in Hilbert space. Numer. Methods Partial Differ. Equ. 34(5), 1759–1780 (2018)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Nagao, K., Yanagisawa, D., Nishinari, K.: Estimation of crowd density applying wavelet transform and machine learning. Phys. A 510, 145–163 (2018)CrossRefGoogle Scholar
  6. 6.
    Harris, F.J.: On the use of windows for harmonic analysis with the discrete Fourier transform. Proc. IEEE 66(1), 51–83 (1978)CrossRefGoogle Scholar
  7. 7.
    Lin, J., Qu, L.: Feature extraction based on morlet wavelet and its application for mechanical fault diagnosis. J. Sound Vib. 234(1), 135–148 (2000)CrossRefGoogle Scholar
  8. 8.
    Li, Y.F., Chen, K.F.: Eiminating the picket fence effect of the fast fourier transform. Comput. Phys. Commun. 78(7), 486–490 (2008)CrossRefzbMATHGoogle Scholar
  9. 9.
    Zedda, M., Singh, R.: Gas turbine engine and sensor fault diagnosis using optimization techniques. J. Propuls. Power. 18(5), 1019–1025 (2002)CrossRefGoogle Scholar
  10. 10.
    Tewfiki, A.H.: On the optimal choice of a wavelet for signal representation. IEEE Trans. Inf. Theory. 38(2), 747–765 (1992)CrossRefGoogle Scholar
  11. 11.
    Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q., Yen, N.C., Tung, C.C., Liu, H.H.: The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis. Proc. R. Soc. Math. Phys. Eng. Sci. 454, 903–995 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Malik, H., Pandya, Y., Parashar, A., Sharma, R.: Feature extraction using EMD and classifier through artificial neural networks for gearbox fault diagnosis. In: Applications of Artificial Intelligence Techniques in Engineering. pp. 309–317 (2019)Google Scholar
  13. 13.
    Shaikh, M.H.N., Farooq, O., Chandel, G.: EMD analysis of EEG signals for seizure detection. In: Advanced System Optimizer Control. pp. 189–196 (2018)Google Scholar
  14. 14.
    Zhu, B., Yuan, L., Ye, S.: Examining the multi-timescales of European carbon market with grey relational analysis and empirical mode decomposition. Phys. A 517, 392–399 (2019)CrossRefGoogle Scholar
  15. 15.
    Zhang, Y., Li, M.: Analysis and dynamic forecast on supply and demand of China’s energy based on EMD. Geogr. Geogr. Inf. Sci. 3, 67–70 (2008)Google Scholar
  16. 16.
    Guhathakurta, K., Mukherjee, I., Chowdhury, A.R.: Empirical mode decomposition analysis of two different financial time series and their comparison. Chaos Solitons Fractals 37, 1214–1227 (2008)CrossRefGoogle Scholar
  17. 17.
    Hong, L.: Decomposition and forecast for financial time series with high-frequency based on empirical mode decomposition. Energy Procedia 5, 1333–1340 (2011)CrossRefGoogle Scholar
  18. 18.
    Wang, J., Shang, P., Xia, J., Shi, W.: EMD based refined composite multiscale entropy analysis of complex signals. Phys. A 421, 583–593 (2015)CrossRefGoogle Scholar
  19. 19.
    Yin, Y., Shang, P.: Multiscale detrended cross-correlation analysis of traffic time series based on empirical mode decomposition. Fluct. Noise Lett. 14(3), 1550023 (2015)CrossRefGoogle Scholar
  20. 20.
    Yang, Y., Yu, D., Cheng, J.: A roller bearing fault diagnosis method based on EMD energy entropy and ANN. J. Sound Vib. 294, 269–277 (2006)CrossRefGoogle Scholar
  21. 21.
    Xiao, Y.H., Chen, L.W., Feng, C., Zhang, M.Y.: Gas turbine blades fault diagnosis method with EMD energy entropy and related vector machine. J. Inf. Hiding Multimed. Signal Process. 6(4), 806–814 (2015)Google Scholar
  22. 22.
    Huang, Y., Wang, K., Zhou, Q., Fang, J., Zhou, Z.: Feature extraction for gas metal arc welding based on EMD and time-frequency entropy. Int. J. Adv. Manuf. Technol. 92(1–4), 1439–1448 (2017)CrossRefGoogle Scholar
  23. 23.
    Wei, Y., Meng, Q., Zhang, Q., Wang, D.: Detecting ventricular fibrillation and ventricular tachycardia for small samples based on EMD and symbol entropy. In: International Conference Intelligent Computing. ICIC 2016: Intelligent Computing Theories and Application. pp. 18–27 (2016)Google Scholar
  24. 24.
    Zunino, L., Zanin, M., Tabak, B.M., Pérez, D.G., Rosso, O.A.: Complexity-entropy causality plane: A useful approach to quantify the stock market inefficiency. Phys. A 389, 1891–1901 (2010)CrossRefGoogle Scholar
  25. 25.
    Lamberti, P.W., Martin, M.T., Plastino, A., Rosso, O.A.: Intensive entropic non-triviality measure. Phys. A 334, 119–131 (2004)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Arqub, O.A., Maayah, B.: Numerical solutions of integrodifferential equations of Fredholm operator type in the sense of the Atangana–Baleanu fractional operator. Chaos, Solitons Fractals 117, 117–124 (2018)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Arqub, O.A., Al-Smadi, M.: Numerical algorithm for solving time-fractional partial integrodifferential equations subject to initial and Dirichlet boundary conditions. Numer. Methods Partial Differ. Equ. 34(5), 1577–1597 (2018)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Wikipedia: Logistic map. https://en.wikipedia.org/wiki/Logistic_map. Accessed 27 Oct 2018
  29. 29.
    Hénon, M., Pomeau, Y.: Two strange attractors with a simple structure. Lect. Notes Math. 565, 29–68 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Lozi, R.: Un attracteur étrange du type attracteur de Hénon. J. Phys. 39, 9–10 (1978)Google Scholar
  31. 31.
    Granger, C.W.J., Joyeux, R.: Introduction to long-memory time series models and fractional differencing. J. Time Ser. Anal. 1(1), 15 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Hosking, J.R.M.: Fractional differencing. Biometrika 68(1), 165–176 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Geweke, J., Porter-Hudak, S.: The estimation and application of long memory time series model. J. Time Ser. Anal. 4(4), 221–238 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Hosking, J.R.M.: Modeling persistence in hydrological time series using fractional differencing. Water Resour. Res. 20(12), 1898–1908 (1984)CrossRefGoogle Scholar
  35. 35.
    Podobnik, B., Horvatic, D., Ng, A.L., Stanley, H.E., Ivanov, P.C.: Modeling long-range cross-correlations in two-component ARFIMA and FIARCH processes. Phys. A 387, 3954–3959 (2008)MathSciNetCrossRefGoogle Scholar
  36. 36.
    Mcleod, A.I., Hipel, K.W.: Preservation of the rescaled adjusted range: 1. A reassessment of the hurst phenomenon. Water Resour. Res 14(3), 491–508 (1978)CrossRefGoogle Scholar
  37. 37.
    Botella-Soler, V., Castelo, J.M., Oteo, J.A., Ros, J.: Bifurcations in the Lozi map. Phys. A Math. Theor. 44(30), 305101 (2011)MathSciNetCrossRefzbMATHGoogle Scholar

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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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