TCGformer: a temporal causal graph enhanced transformer model for multivariate financial time series forecasting

State-of-the-art time series forecasting models, particularly Transformers, often fail to capture the time-varying causal structures that govern interactions among financial institutions, limiting their predictive accuracy in complex environments. This article introduces the Temporal Causal Graph-Enhanced Transformer (TCGformer), a novel causal knowledge-based intelligent system that integrates causal inference into deep learning for time series prediction. Our framework employs a three-stage pipeline: we first utilize Functional Data Analysis for robust preprocessing of noisy and irregular financial data; we then construct temporal causal graph using Variable-lag Granger Causality, a state-of-the-art causal inference method for observational causal discovery in time series, to model the evolving network of inter-institutional influence; finally, we seamlessly inject this externally grounded causal knowledge into a hierarchical Transformer architecture via our proposed Graph Neural Network (GNN)—empowered hybrid routing mechanism. We conduct extensive experiments on a real-world dataset. The results demonstrate that TCGformer consistently outperforms strong baselines, including Crossformer and Transformer, across multiple evaluation metrics. Ablation and robustness analysis reveals a key insight into the model’s operational strengths: its performance advantage is particularly pronounced in the medium-to-long-term forecasting horizons. This suggests that our knowledge-driven approach is effective at capturing the fundamental, structural market dynamics that are crucial for longer-range prediction. Furthermore, the more explainable temporal causal graphs provide valuable and interpretable insights into the shifting patterns of systemic risk. TCGformer represents a novel framework that synergistically fuses temporal causal knowledge into a Transformer-based forecasting architecture, bridging the gap between causal discovery and deep learning for intelligent decision-making in finance.