Graph structure learning for stable processes
Abstract
We introduce Ising-H\"usler-Reiss processes, a new class of multivariate L\'evy processes that allows for sparse modeling of the path-wise conditional independence structure between marginal stable processes with different stability indices. The underlying conditional independence graph is encoded as zeroes in a suitable precision matrix. An Ising-type parametrization of the weights for each orthant of the L\'evy measure allows for data-driven modeling of asymmetry of the jumps while retaining an arbitrary sparse graph. We develop consistent estimators for the graphical structure and asymmetry parameters, relying on a new uniform small-time approximation for L\'evy processes. The methodology is illustrated in simulations and a real data application to modeling dependence of stock returns.
Cite
@article{arxiv.2601.06264,
title = {Graph structure learning for stable processes},
author = {Florian Brück and Sebastian Engelke and Stanislav Volgushev},
journal= {arXiv preprint arXiv:2601.06264},
year = {2026}
}