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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2601.06264 |
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| _version_ | 1866914244692279296 |
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| author | Brück, Florian Engelke, Sebastian Volgushev, Stanislav |
| author_facet | Brück, Florian Engelke, Sebastian Volgushev, Stanislav |
| contents | We introduce Ising-Hüsler-Reiss processes, a new class of multivariate Lévy 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 Lévy 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 Lévy processes. The methodology is illustrated in simulations and a real data application to modeling dependence of stock returns. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06264 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Graph structure learning for stable processes Brück, Florian Engelke, Sebastian Volgushev, Stanislav Methodology We introduce Ising-Hüsler-Reiss processes, a new class of multivariate Lévy 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 Lévy 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 Lévy processes. The methodology is illustrated in simulations and a real data application to modeling dependence of stock returns. |
| title | Graph structure learning for stable processes |
| topic | Methodology |
| url | https://arxiv.org/abs/2601.06264 |