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.

Financial Time Series Forecasting (TSF) remains a critical challenge in Artificial Intelligence (AI) due to the inherent complexity of financial data, characterized by strong non-linearity, dynamic non-stationarity, and multi-factor coupling. To address the performance limitations of Spiking Neural Networks (SNNs) caused by hyperparameter sensitivity, this study proposes an SNN model optimized by an Improved Cuckoo Search (ICS) algorithm (termed ICS-SNN). The ICS algorithm enhances global search capability through piecewise-mapping-based population initialization and introduces a dynamic discovery probability mechanism that adaptively increases with iteration rounds, thereby balancing exploration and exploitation. Applied to futures market price difference prediction, experimental results demonstrate that ICS-SNN achieves reductions of 13.82% in MAE, 21.27% in MSE, and 15.21% in MAPE, while improving the coefficient of determination (R²) from 0.9790 to 0.9822, compared to the baseline SNN. Furthermore, ICS-SNN significantly outperforms mainstream models such as Long Short-Term Memory (LSTM) and Backpropagation (BP) networks, reducing prediction errors by 10.8% (MAE) and 34.9% (MSE), respectively, without compromising computational efficiency. This work highlights that ICS-SNN provides a biologically plausible and computationally efficient framework for complex financial TSF, bridging the gap between neuromorphic principles and real-world financial analytics. The proposed method not only reduces manual intervention in hyperparameter tuning but also offers a scalable solution for high-frequency trading and multi-modal data fusion in future research.