DeepLévy: Learning Heavy-Tailed Uncertainty in Highly Volatile Time Series

• URL: http://arxiv.org/abs/2605.10364v3
• Date: Thu, 14 May 2026 09:33:07 GMT
• Title: DeepLévy: Learning Heavy-Tailed Uncertainty in Highly Volatile Time Series
• Abstract summary: DeepLévy is a neural framework that learns mixtures of Lévy stable distributions.<n>DeepLévy incorporates a mixture mechanism that adaptively learns context-dependent weights and parameters over multiple Lévy components.
• Score: 6.2509441706443
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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