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Multivariate generalized information entropy of financial time series

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  • Zhang, Yongping
  • Shang, Pengjian
  • Xiong, Hui

Abstract

In order to explore the complexity of multivariate time series, we propose a novel method: multiscale multivariate weighted fractional entropy (MMWFE). The research results show that MMWFE is able to measure the complexity of multivariate data correctly and reflect more information contained in the time series. In this paper, the reliability of the proposed method is supported by simulations on generated and empirical data. We analyze simulated pink noise and white noise to test the validity of this method, and the result is consistent with the fact that pink noise is more complex than white noise. Meanwhile, MMWFE shows a better robustness. MMWFE is then employed to bivariate stock return and volume to explore the complexity of stock markets. It successfully distinguishes Asia, Europe and Americas markets. Finally, dynamic MMWFE is applied to explore the evolution of complexity for mining more information containing in nonlinear time series.

Suggested Citation

  • Zhang, Yongping & Shang, Pengjian & Xiong, Hui, 2019. "Multivariate generalized information entropy of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1212-1223.
    • Handle: RePEc:eee:phsmap:v:525:y:2019:i:c:p:1212-1223
    DOI: 10.1016/j.physa.2019.04.029
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    References listed on IDEAS

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    1. Zunino, Luciano & Zanin, Massimiliano & Tabak, Benjamin M. & Pérez, Darío G. & Rosso, Osvaldo A., 2009. "Forbidden patterns, permutation entropy and stock market inefficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2854-2864.
    2. Mathai, A.M. & Haubold, H.J., 2007. "Pathway model, superstatistics, Tsallis statistics, and a generalized measure of entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 110-122.
    3. Xia, Jianan & Shang, Pengjian & Wang, Jing & Shi, Wenbin, 2014. "Classifying of financial time series based on multiscale entropy and multiscale time irreversibility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 400(C), pages 151-158.
    4. Matilla-García, Mariano & Marín, Manuel Ruiz & Dore, Mohammed I., 2014. "A permutation entropy based test for causality: The volume–stock price relation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 280-288.
    5. Zhang, Yongping & Shang, Pengjian, 2018. "Refined composite multiscale weighted-permutation entropy of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 189-199.
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    Cited by:

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    2. Zavala-Díaz, J.C. & Pérez-Ortega, J. & Hernández-Aguilar, J.A. & Almanza-Ortega, N.N. & Martínez-Rebollar, A., 2020. "Short-term prediction of the closing price of financial series using a ϵ-machine model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    3. Ugarte, Juan P. & Tenreiro Machado, J.A. & Tobón, Catalina, 2022. "Fractional generalization of entropy improves the characterization of rotors in simulated atrial fibrillation," Applied Mathematics and Computation, Elsevier, vol. 425(C).

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