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Nonlinearity in stock networks

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  • David Hartman
  • Jaroslav Hlinka

Abstract

Stock networks, constructed from stock price time series, are a well-established tool for the characterization of complex behavior in stock markets. Following Mantegna's seminal paper, the linear Pearson's correlation coefficient between pairs of stocks has been the usual way to determine network edges. Recently, possible effects of nonlinearity on the graph-theoretical properties of such networks have been demonstrated when using nonlinear measures such as mutual information instead of linear correlation. In this paper, we quantitatively characterize the nonlinearity in stock time series and the effect it has on stock network properties. This is achieved by a systematic multi-step approach that allows us to quantify the nonlinearity of coupling; correct its effects wherever it is caused by simple univariate non-Gaussianity; potentially localize in space and time any remaining strong sources of this nonlinearity; and, finally, study the effect nonlinearity has on global network properties. By applying this multi-step approach to stocks included in three prominent indices (NYSE100, FTSE100 and SP500), we establish that the apparent nonlinearity that has been observed is largely due to univariate non-Gaussianity. Furthermore, strong nonstationarity in a few specific stocks may play a role. In particular, the sharp decrease in some stocks during the global financial crisis of 2008 gives rise to apparent nonlinear dependencies among stocks.

Suggested Citation

  • David Hartman & Jaroslav Hlinka, 2018. "Nonlinearity in stock networks," Papers 1804.10264, arXiv.org, revised Jun 2018.
  • Handle: RePEc:arx:papers:1804.10264
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    Cited by:

    1. Chen, Wei & Qu, Shuai & Jiang, Manrui & Jiang, Cheng, 2021. "The construction of multilayer stock network model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    2. Francesca Mariani & Gloria Polinesi & Maria Cristina Recchioni, 2022. "A tail-revisited Markowitz mean-variance approach and a portfolio network centrality," Computational Management Science, Springer, vol. 19(3), pages 425-455, July.
    3. Ludmila Petkovová & David Hartman & Tomáš Pavelka, 2020. "Problems of Aggregation of Sustainable Development Indicators at the Regional Level," Sustainability, MDPI, vol. 12(17), pages 1-20, September.
    4. Chun-Xiao Nie & Fu-Tie Song, 2021. "Entropy of Graphs in Financial Markets," Computational Economics, Springer;Society for Computational Economics, vol. 57(4), pages 1149-1166, April.
    5. Dimitar Kitanovski & Igor Mishkovski & Viktor Stojkoski & Miroslav Mirchev, 2024. "Network-based diversification of stock and cryptocurrency portfolios," Papers 2408.11739, arXiv.org.
    6. Luigi Caputi & Anna Pidnebesna & Jaroslav Hlinka, 2024. "Integral Betti signature confirms the hyperbolic geometry of brain, climate, and financial networks," Papers 2406.15505, arXiv.org.
    7. Romain Bocher, 2022. "The Intersubjective Markets Hypothesis," Journal of Interdisciplinary Economics, , vol. 34(1), pages 35-50, January.
    8. Huang, Qi-An & Zhao, Jun-Chan & Wu, Xiao-Qun, 2022. "Financial risk propagation between Chinese and American stock markets based on multilayer networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 586(C).

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