CausalExoFormer: End-to-End Lag-Aware Causal Structure Learning for Exogenous Time-Series Forecasting

Exogenous time-series forecasting requires identifying relevant external variables, capturing their delayed effects, and modeling interactions among them. These dependencies are often learned implicitly, leaving the structure of external information use difficult to inspect and control. We propose CausalExoFormer, an end-to-end Transformer that jointly learns variable relevance, temporal allocation, and directed cross-channel structure for forecasting. A factorized source–lag gate selects historical observations, a directed graph learned with acyclicity regularization models interactions among external variables, and causal-gated cross-attention integrates the resulting representations with the target history. The learned structure directly controls information flow: closing a source gate removes both its direct and graph-mediated contributions. For multivariate forecasting, a shared graph supports target-specific predictions through exact self-exclusion, preserving the separation between each target’s own history and its external inputs. Experiments on six standard benchmarks and six lake dissolved-oxygen forecasting tasks demonstrate the effectiveness of this approach. CausalExoFormer achieves the lowest horizon-averaged MAE on all six standard benchmarks and the lowest horizon-averaged MSE on four, among the evaluated methods, while consistently improving over TimeXer on the six lake tasks. Ablation studies establish the contribution of learned source–lag allocation, and environmental case studies reveal the variables and historical offsets used for prediction. Code is available at https://anonymous.4open.science/r/CausalExoFormer-C42C.