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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 analysis shows that binarization preserves market correlation structure. Properties of distributions of external fields and couplings as well as industry sector clustering structure are studied for different historical dates and moving window sizes. We found that a heavy positive tail in the distribution of couplings is responsible for the sparse market clustering structure. We also show that discrepancies between the model parameters might be used as a precursor of financial instabilities.

Suggested Citation

  • Stanislav S. Borysov & Yasser Roudi & Alexander V. Balatsky, 2015. "U.S. stock market interaction network as learned by the Boltzmann Machine," Papers 1504.02280, arXiv.org, revised Sep 2015.
    • Handle: RePEc:arx:papers:1504.02280
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    Cited by:

    1. 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.
    2. 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).

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