When Do Heavy Tails Help? Identifiability Limits and Predictive Uncertainty in Lévy-Driven Neural SDEs for Electricity Markets

Electricity markets shaped by renewable generation exhibit heavy-tailed price shocks that standard forecasting models neither capture nor bound. We introduce LévySDE-Net, a neural stochastic differential equation with drift and diffusion parameterized by neural networks and driven by $\alpha$-stable Lévy motion, paired with phase-space reconstruction and maximal Lyapunov exponent estimation to characterize a market's intrinsic predictability horizon. Evaluated on Nord Pool electricity price areas, LévySDE-Net and a Gaussian-forced counterpart both substantially outperform econometric and recurrent baselines at short horizons, but heavy-tailed forcing confers no consistent point-forecast advantage over Gaussian forcing – a result we trace, via a synthetic identifiability analysis, to a genuine confound between the Lévy stability parameter and the diffusion scale under discretely observed data. Instead, Lévy forcing's distinguishing effect is on predictive uncertainty: it systematically widens ensemble spread and interval width relative to Gaussian forcing, and in the wind-driven price area this divergence emerges at a rollout horizon consistent with the area's independently estimated Lyapunov time. Our results indicate that heavy-tailed stochastic forcing's principal value lies not in point accuracy but in producing forecast uncertainty calibrated to a market's underlying dynamical instability.