LagLLM: LLM-empowered lead–lag dependency learning for spatial-temporal time series forecasting

Spatial-temporal time series forecasting is challenging due to complex lead-lag dependencies, which are often ignored or inadequately modeled by existing methods. Thus, we propose LagLLM, the first LLM-empowered framework that explicitly models lead–lag dependencies by unifying data-driven dynamics modeling and knowledge-driven semantic reasoning. Specifically, LagLLM constructs a lead-lag graph by integrating learnable embeddings, spatial proximity, and prompt-guided reasoning from a frozen LLM, which can capture lead-lag dependencies informed by the underlying data structure and semantic knowledge. In addition, LagLLM introduces structural token sorting based on the graph, which can make a fine-tuned LLM explicitly perceive directional and delayed interactions. Experiments on eight real-world datasets show that LagLLM achieves the state-of-the-art performance with improved accuracy, robustness, and interpretability. The code is available at https://github.com/w2obin/LagLLM-2026.