MSGformer: A Hybrid Multi-Scale Graph–Transformer Architecture for Unified Short- and Long-Term Financial Time Series Forecasting

Forecasting financial time series is challenging due to their intrinsic nonlinearity, high volatility, and complex dependencies across temporal scales. This study introduces MSGformer, a novel hybrid architecture that integrates multi-scale graph neural networks (MSGNet) with Transformer encoders to capture both local temporal fluctuations and long-term global trends in high-frequency financial data. The MSGNet module constructs multi-scale representations using adaptive graph convolutions and intra-sequence attention, while the Transformer component enhances long-range dependency modeling via multi-head self-attention. We evaluate MSGformer on minute-level stock index data from the Chinese A-share market, including CSI 300, SSE 50, CSI 500, and SSE Composite indices. Extensive experiments demonstrate that MSGformer significantly outperforms state-of-the-art baselines (e.g., Transformer, PatchTST, Autoformer) in terms of MAE, RMSE, MAPE, and R2. The results confirm that the proposed hybrid model achieves superior prediction accuracy, robustness, and generalization across various forecasting horizons, providing an effective solution for real-world financial decision-making and risk assessment.