Research
DeepLevy: Learning Heavy-Tailed Uncertainty in Highly Volatile Time Series
arXiv:2605.10364v1 Announce Type: new Abstract: Modeling uncertainty in heavy-tailed time series remains a critical challenge for deep probabilistic forecasting models, which often struggle to capture
arXiv:2605.10364v1 Announce Type: new 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 Levy 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 DeepLevy, a neural framework that learns mixtures of Levy stable distributions by minimizing the discrepancy between empirical and parametric characteristic functions. DeepLevy incorporates a mixture mechanism that adaptively learns context-dependent weights and parameters over multiple Levy components, enabling flexible multi-horizon uncertainty modeling. Evaluations on both real and synthetic datasets demonstrate that DeepLevy outperforms state-of-the-art deep probabilistic forecasting approaches in tail risk metrics, especially under extreme volatility.
Source: arXiv cs.LG | 2026-05-12