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

Here, 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.
 [1] ;  [2] ;  [3]
  1. KTH Royal Institute of Technology and Stockholm Univ., Stockholm (Sweden)
  2. KTH Royal Institute of Technology and Stockholm Univ., Stockholm (Sweden); The Kavli Institute for Systems Neuroscience (Trondheim)
  3. KTH Royal Institute of Technology and Stockholm Univ., Stockholm (Sweden); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 1434-6028; PII: 1814
Grant/Contract Number:
Accepted Manuscript
Journal Name:
European Physical Journal. B, Condensed Matter and Complex Systems
Additional Journal Information:
Journal Volume: 88; Journal Issue: 12; Journal ID: ISSN 1434-6028
Research Org:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org:
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING Boltzman machine; stock correlations; statistical and nonlinear physics