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

TL;DR

This paper models the joint distribution of U.S. stock returns using a Boltzmann distribution, analyzing how market correlations and clustering evolve over time and can signal financial instability.

Contribution

It introduces a Boltzmann machine approach to capture market interactions, studying the effects of binarization and identifying parameters as early indicators of instability.

Findings

Binarization preserves market correlation structure.

Heavy positive tail in couplings causes sparse clustering.

Parameter discrepancies may predict financial instability.

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.