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U.S. stock market interaction network as learned by the Boltzmann machine

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  • Stanislav S. Borysov
  • Yasser Roudi
  • Alexander V. Balatsky

Abstract

We study historical dynamics of joint equilibrium distribution of stock returns in the U.S. stock market using the Boltzmann distribution model being parametrized by external fields and pairwise couplings. Within Boltzmann learning framework for statistical inference, we analyze historical behavior of the parameters inferred using exact and approximate learning algorithms. Since the model and inference methods require use of binary variables, effect of this mapping of continuous returns to the discrete domain is studied. The presented results show that binarization preserves the correlation structure of the market. Properties of distributions of external fields and couplings as well as the market interaction network and industry sector clustering structure are studied for different historical dates and moving window sizes. We demonstrate that the observed positive heavy tail in distribution of couplings is related to the sparse clustering structure of the market. We also show that discrepancies between the model’s parameters might be used as a precursor of financial instabilities. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Stanislav S. Borysov & Yasser Roudi & Alexander V. Balatsky, 2015. "U.S. stock market interaction network as learned by the Boltzmann machine," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 88(12), pages 1-14, December.
    • Handle: RePEc:spr:eurphb:v:88:y:2015:i:12:p:1-14:10.1140/epjb/e2015-60282-3
    DOI: 10.1140/epjb/e2015-60282-3
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    References listed on IDEAS

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    1. Dorogovtsev, S.N. & Mendes, J.F.F., 2003. "Evolution of Networks: From Biological Nets to the Internet and WWW," OUP Catalogue, Oxford University Press, number 9780198515906.
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    Cited by:

    1. Zhang, Ditian & Zhuang, Yangyang & Tang, Pan & Han, Qingying, 2022. "The evolution of foreign exchange market: A network view," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P2).
    2. Ditian Zhang & Yangyang Zhuang & Pan Tang & Hongjuan Peng & Qingying Han, 2023. "Financial price dynamics and phase transitions in the stock markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(3), pages 1-21, March.

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