In the domain of financial markets, deep learning techniques have emerged as a significant tool for the development of investment strategies. The present study investigates the potential of time series forecasting (TSF) in financial application scenarios, aiming to predict future spreads and inform investment decisions more effectively. However, the inherent nonlinearity and high volatility of financial time series pose significant challenges for accurate forecasting. To address these issues, this paper proposes the IGWO-MALSTM model, a hybrid framework that integrates Improved Grey Wolf Optimization (IGWO) for hyperparameter tuning and a multi-head attention (MA) mechanism to enhance long-term sequence modeling within the long short-term memory (LSTM) architecture. The IGWO algorithm improves population diversity during initialization using the Mersenne Twister, thereby enhancing the convergence speed and search capability of the optimizer. Simultaneously, the MA mechanism mitigates gradient vanishing and explosion problems, enabling the model to better capture long-range dependencies in financial sequences. Experimental results on real futures market data demonstrate that the proposed model reduces Mean Square Error (MSE) by up to 61.45% and Mean Absolute Error (MAE) by 44.53%, and increases the R² score by 0.83% compared to existing benchmark models. These findings confirm that IGWO-MALSTM offers improved predictive accuracy and stability for financial time series forecasting tasks.

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.

Self-distillation has been widely applied in the field of deep learning. However, the lack of interaction between the multiple shallow branches in the self-distillation framework reduces the effectiveness of self-distillation methods. To address this issue, a feature map fusion self-distillation scheme is proposed. According to the depth of the teacher model, multiple shallow branches as student models are constructed to build a self-distillation framework. Then, the feature map fusion module fuses the intermediate feature maps of each branch to enhance the interaction between the branches. Specifically, this fusion module employs a spatial enhancement module to generate attention masks for multiple feature maps, which are averaged and applied to create intermediate maps. The mean of these intermediate maps results in the final fusion feature map. The experimental findings on the CIFAR10 and CIFAR100 datasets illustrate that our proposed technique has clear advantages in increasing the classification accuracy of the deep learning models. On average, 0.7% and 2.5% accuracy boosts are observed on the CIFAR10 and CIFAR100.