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.

Many spatial–temporal systems, such as traffic and energy networks, exhibit lead–lag dependencies, where changes in one location can influence another minutes or even hours later. Existing methods often overlook or inadequately model these dependencies, resulting in less accurate predictions. To address this problem, we propose LagLLM, an LLM-empowered framework that combines data-driven dynamics modeling with knowledge-driven semantic reasoning. LagLLM constructs a lead–lag graph to identify delayed influences between regions. It also organizes input data according to the learned graph, helping the LLM better perceive directional and delayed interactions. Experiments on eight real-world datasets show that LagLLM achieves accurate and robust forecasts.