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arXiv · 2601.06264

Graph structure learning for stable processes

Florian Brück·Sebastian Engelke·Stanislav Volgushev
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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.

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Florian Brück, Sebastian Engelke, Stanislav Volgushev. 2026-01-09. Graph structure learning for stable processes. https://arxiv.org/abs/2601.06264

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