用动态图结构增强Transformer，提升美股股价预测精度。
A Study of Dynamic Stock Relationship Modeling and S&P500 Price Forecasting Based on Differential Graph Transformer
- 引入微分图机制捕捉股票间关系的动态变化。
- 在10年美股数据上，误差比传统模型低72%（RMSE 0.24 vs 0.87）。
- 适合量化投资、金融建模人员参考，尤其关注波动率策略。
股价预测对投资决策和风险管理至关重要，但受市场非线性动态和股票间相关性时变影响，仍具挑战。传统静态相关模型难以捕捉动态关系。为此，提出差分图变压器（DGT）框架，通过微分图机制将序列图结构变化融入多头自注意力，自适应保留高价值连接并抑制噪声；因果时间注意力捕获价格序列的全局/局部依赖。评估皮尔逊、互信息、斯皮尔曼、肯德尔τ等相关度量在全局/局部/双重范围的表现，作为空间注意力先验。基于10年标普500收盘价（z-score归一化，64天滑动窗口），结合空间先验的DGT优于GRU基线（均方根误差：0.24 vs 0.87）。肯德尔τ全局矩阵表现最佳（平均绝对误差：0.11）。聚类分析揭示‘高波动成长’与‘防御型蓝筹’两类股票，后者相关性稳定，误差更低（RMSE: 0.13）。在波动率行业，肯德尔τ与互信息表现更优。研究创新性融合微分图结构与Transformer，验证动态关系建模有效性，并识别最优相关度量与作用范围，聚类结果支持定制化量化策略。该框架通过动态建模与跨资产交互分析，推动金融时序预测发展。
原文摘要 · Abstract (English)
Stock price prediction is vital for investment decisions and risk management, yet remains challenging due to markets' nonlinear dynamics and time-varying inter-stock correlations. Traditional static-correlation models fail to capture evolving stock relationships. To address this, we propose a Differential Graph Transformer (DGT) framework for dynamic relationship modeling and price prediction. Our DGT integrates sequential graph structure changes into multi-head self-attention via a differential graph mechanism, adaptively preserving high-value connections while suppressing noise. Causal temporal attention captures global/local dependencies in price sequences. We further evaluate correlation metrics (Pearson, Mutual Information, Spearman, Kendall's Tau) across global/local/dual scopes as spatial-attention priors. Using 10 years of S&P 500 closing prices (z-score normalized; 64-day sliding windows), DGT with spatial priors outperformed GRU baselines (RMSE: 0.24 vs. 0.87). Kendall's Tau global matrices yielded optimal results (MAE: 0.11). K-means clustering revealed "high-volatility growth" and "defensive blue-chip" stocks, with the latter showing lower errors (RMSE: 0.13) due to stable correlations. Kendall's Tau and Mutual Information excelled in volatile sectors. This study innovatively combines differential graph structures with Transformers, validating dynamic relationship modeling and identifying optimal correlation metrics/scopes. Clustering analysis supports tailored quantitative strategies. Our framework advances financial time-series prediction through dynamic modeling and cross-asset interaction analysis.
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