We study historical dynamics of joint equilibrium distribution of stock returns in the US stock market using the Boltzmann distribution model which is 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 to a low-dimensional system is studied.
Properties of distributions of external fields and couplings as well as sector-related market clustering structure are studied for different moving window sizes. Considering the parameters as external and internal biases, discrepancy between them might be used as a precursor of financial instabilities.