UFGTime: Mining Intertwined Dependencies in Multivariate Time Series via an Efficient Pure Graph Approach

Graph Neural Networks (GNNs) have become a cornerstone in multivariate time series forecasting by addressing the challenge of modeling inter-series dependencies often overlooked by traditional temporal approaches. However, real-world temporal dependencies (inter- and intra-dependencies) are inherently intertwined, making it difficult to treat them as separate processes. Recent pure graph paradigms attempt to capture these dependencies holistically by transforming time series into fully connected graphs. While effective, these methods suffer from prohibitive computational complexity O (( NT ) 2 ), limiting their scalability for large-scale data and long-term forecasting. To address these challenges, we propose UFGTime, a novel framework that leverages spectral signals to construct a "spectral-variate graph," embedding multivariate temporal dependencies in a compact spectral representation and modeling inter- and intra-signal connections through frequency similarities. Empowered by our proposed graph framelet message-passing function, UFGTime efficiently aggregates global information, avoids over-smoothing, and achieves near-linear complexity O ( kNT ). Extensive experiments on diverse datasets demonstrate that UFG-Time consistently outperforms state-of-the-art baselines, offering a scalable, accurate, and resource-efficient pure graph solution for multivariate time series forecasting.