Abstract:Modeling uncertainty in heavy-tailed time series remains a critical challenge for deep probabilistic forecasting models, which often struggle to capture abrupt, extreme events. While Lévy stable distributions offer a natural framework for modeling such non-Gaussian behaviors, the intractability of their probability density functions severely limits conventional likelihood-based inference. To address this, we introduce DeepLévy, a neural framework that learns mixtures of Lévy stable distributions by minimizing the discrepancy between empirical and parametric characteristic functions. DeepLévy incorporates a mixture mechanism that adaptively learns context-dependent weights and parameters over multiple Lévy components, enabling flexible multi-horizon uncertainty modeling. Evaluations on both real and synthetic datasets demonstrate that DeepLévy outperforms state-of-the-art deep probabilistic forecasting approaches in tail risk metrics, especially under extreme volatility.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.10364 [cs.LG] |
| (or arXiv:2605.10364v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.10364 arXiv-issued DOI via DataCite (pending registration) |
From: Yang Yang [view email]
[v1]
Mon, 11 May 2026 11:08:40 UTC (638 KB)
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