Title: U-Cast: Learning Hierarchical Structures for High-Dimensional Time Series Forecasting
Primary area: learning on time series and dynamical systems
Keywords: Time Series Forecasting, Multivariate Time Series Forecasting

Abstract: Time series forecasting (TSF) is a central problem in time series analysis. However, as the number of channels in time series datasets scales to the thousands or more, a scenario we define as **High-Dimensional Time Series Forecasting (HDTSF)**, it introduces significant new modeling challenges that are often not the primary focus of traditional TSF research. HDTSF is challenging because the channel correlation often forms complex and hierarchical patterns. Existing TSF models either ignore these interactions or fail to scale as dimensionality grows.  To address this issue, we propose **U-Cast**, a channel-dependent forecasting architecture that learns latent hierarchical channel structures with an innovative query-based attention. To disentangle highly correlated channel representations, U-Cast adds a full-rank regularization during training.  We also release **Time-HD**, the first benchmark of large, diverse, high-dimensional datasets. Our theory shows that exploiting cross-channel information lowers forecasting risk, and experiments on Time-HD demonstrate that U-Cast surpasses strong baselines in both accuracy and efficiency. Together, U-Cast and Time-HD provide a solid basis for future HDTSF research.  Our [code](https://anonymous.4open.science/r/Time-HD-Lib-1A71) and [benchmark](https://huggingface.co/datasets/Time-HD-Anonymous/High_Dimensional_Time_Series) are available to ensure reproducibility.