Graphical Models in Heavy-Tailed Markets

Heavy-tailed statistical distributions have long been considered a more realistic statistical model for the data generating process in financial markets in comparison to their Gaussian counterpart. Nonetheless, mathematical nuisances, including nonconvexities, involved in estimating graphs in heavy-tailed settings pose a significant challenge to the practical design of algorithms for graph learning. In this work, we present graph learning estimators based on the Markov random field framework that assume a Student-t data generating process. We design scalable numerical algorithms, via the alternating direction method of multipliers, to learn both connected and k-component graphs along with their theoretical convergence guarantees. The proposed methods outperform state-of-the-art benchmarks in an extensive series of practical experiments with publicly available data from the S&P500 index, foreign exchanges, and cryptocurrencies.