LévyHyper: A Lévy Process-Driven Dynamic Hypergraph Framework for Stock Return Prediction with Jump-Aware Temporal Modeling

Stock return prediction for quantitative trading in U.S. equity markets has evolved from parametric econometric modeling toward data-driven deep learning systems that must jointly capture temporal dynamics, discontinuous jumps, and evolving cross-asset dependencies. Existing approaches still face three key challenges in deep learning-based stock return prediction: jump-aware temporal modeling is often missing or handled by ad hoc heuristics; higher-order stock relations are frequently encoded by static graphs/hypergraphs that do not adapt across market conditions, and temporal and relational learning are commonly implemented as sequential blocks with limited bidirectional interaction. We propose LévyHyper, an end-to-end framework that unifies jump-aware temporal encoding with regime-adaptive dynamic hypergraph learning and multi-scale hypergraph reasoning. LévyHyper integrates a neural jump-aware temporal layer motivated by Lévy jump-diffusion modeling, a regime-weighted fusion of predefined and learned hyperedges via a differentiable constructor, and a multi-scale hypergraph convolution module for hierarchical temporal aggregation. Experiments on S&P 500 data (463 stocks, 10 evaluation phases, prediction horizon τ=5 trading days) show that LévyHyper improves IC/RankIC and portfolio-level Sharpe ratio over strong baselines on average. We additionally report uncertainty estimates, significance tests, and transaction-cost sensitivity to support robust conclusions.