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Universal and nonuniversal allometric scaling behaviors in the visibility graphs of world stock market indices

Author

Listed:
  • Meng-Cen Qian

    (Fudan)

  • Zhi-Qiang Jiang

    (ECUST)

  • Wei-Xing Zhou

    (ECUST)

Abstract

The investigations of financial markets from a complex network perspective have unveiled many phenomenological properties, in which the majority of these studies map the financial markets into one complex network. In this work, we investigate 30 world stock market indices through their visibility graphs by adopting the visibility algorithm to convert each single stock index into one visibility graph. A universal allometric scaling law is uncovered in the minimal spanning trees, whose scaling exponent is independent of the stock market and the length of the stock index. In contrast, the maximal spanning trees and the random spanning trees do not exhibit universal allometric scaling behaviors. There are marked discrepancies in the allometric scaling behaviors between the stock indices and the Brownian motions. Using surrogate time series, we find that these discrepancies are caused by the fat-tailedness of the return distribution, the nonlinear long-term correlation, and a coupling effect between these two influence factors.

Suggested Citation

  • Meng-Cen Qian & Zhi-Qiang Jiang & Wei-Xing Zhou, 2009. "Universal and nonuniversal allometric scaling behaviors in the visibility graphs of world stock market indices," Papers 0910.2524, arXiv.org.
    • Handle: RePEc:arx:papers:0910.2524
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    File URL: http://arxiv.org/pdf/0910.2524
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    Cited by:

    1. Chuang Liu & Wei-Xing Zhou, 2009. "Superfamily classification of nonstationary time series based on DFA scaling exponents," Papers 0912.2016, arXiv.org.
    2. An, Haizhong & Gao, Xiangyun & Fang, Wei & Huang, Xuan & Ding, Yinghui, 2014. "The role of fluctuating modes of autocorrelation in crude oil prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 382-390.
    3. Zhao, Xiaojun & Zhang, Pengyuan, 2020. "Multiscale horizontal visibility entropy: Measuring the temporal complexity of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    4. Xi, Xian & An, Haizhong, 2018. "Research on energy stock market associated network structure based on financial indicators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1309-1323.
    5. An, Sufang & Gao, Xiangyun & Jiang, Meihui & Sun, Xiaoqi, 2018. "Multivariate financial time series in the light of complex network analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 1241-1255.

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