Eur. Phys. J. B (2015) 88: 321
https://doi.org/10.1140/epjb/e2015-60282-3

Regular Article

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

¹ Nordita, Center for Quantum Materials, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
² Nanostructure Physics, KTH Royal Institute of Technology, Roslagstullsbacken 21, 10691 Stockholm, Sweden
³ The Kavli Institute for Systems Neuroscience, NTNU, 7030 Trondheim, Norway
⁴ Institute for Materials Science, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

^a Present address: Singapore-MIT Alliance for Research and Technology, 1 CREATE Way, #09-02, Create Tower, 138602 Singapore
^b e-mail: stanislav@smart.mit.edu

Received: 10 April 2015
Received in final form: 31 July 2015
Published online: 7 December 2015

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.