A Study of Dynamic Stock Relationship Modeling and S&P500 Price Forecasting Based on Differential Graph Transformer

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.