{"ID":2874443,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.03852","arxiv_id":"2509.03852","title":"MillGNN: Learning Multi-Scale Lead-Lag Dependencies for Multi-Variate Time Series Forecasting","abstract":"Multi-variate time series (MTS) forecasting is crucial for various applications. Existing methods have shown promising results owing to their strong ability to capture intra- and inter-variate dependencies. However, these methods often overlook lead-lag dependencies at multiple grouping scales, failing to capture hierarchical lead-lag effects in complex systems. To this end, we propose MillGNN, a novel \\underline{g}raph \\underline{n}eural \\underline{n}etwork-based method that learns \\underline{m}ult\\underline{i}ple grouping scale \\underline{l}ead-\\underline{l}ag dependencies for MTS forecasting, which can comprehensively capture lead-lag effects considering variate-wise and group-wise dynamics and decays. Specifically, MillGNN introduces two key innovations: (1) a scale-specific lead-lag graph learning module that integrates cross-correlation coefficients and dynamic decaying features derived from real-time inputs and time lags to learn lead-lag dependencies for each scale, which can model evolving lead-lag dependencies with statistical interpretability and data-driven flexibility; (2) a hierarchical lead-lag message passing module that passes lead-lag messages at multiple grouping scales in a structured way to simultaneously propagate intra- and inter-scale lead-lag effects, which can capture multi-scale lead-lag effects with a balance of comprehensiveness and efficiency. Experimental results on 11 datasets demonstrate the superiority of MillGNN for long-term and short-term MTS forecasting, compared with 16 state-of-the-art methods.","short_abstract":"Multi-variate time series (MTS) forecasting is crucial for various applications. Existing methods have shown promising results owing to their strong ability to capture intra- and inter-variate dependencies. However, these methods often overlook lead-lag dependencies at multiple grouping scales, failing to capture hiera...","url_abs":"https://arxiv.org/abs/2509.03852","url_pdf":"https://arxiv.org/pdf/2509.03852v1","authors":"[\"Binqing Wu\",\"Zongjiang Shang\",\"Jianlong Huang\",\"Ling Chen\"]","published":"2025-09-04T03:28:42Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\"]","methods":"[\"Graph Neural Network\"]","has_code":false}