Forecasting is critical in areas such as finance, biology, and healthcare. Despite the progress in the field, making accurate forecasts remains challenging because real-world time series contain both global trends, local fine-grained structure, and features on multiple scales in between. Here, we present a new forecasting method, PRISM (Partitioned Representation for Iterative Sequence Modeling), that addresses this challenge through a learnable tree-based partitioning of the signal. At the root of the tree, a global representation captures coarse trends in the signal, while recursive splits reveal increasingly localized views of the signal. At each level of the tree, data are projected onto a time-frequency basis (e.g., wavelets or exponential moving averages) to extract scale-specific features, which are then aggregated across the hierarchy. This design allows the model to jointly capture global structure and local dynamics of the signal, enabling accurate forecasting. Experiments across benchmark datasets show that our method outperforms state-of-the-art methods for forecasting. Overall, these results demonstrate that our hierarchical approach provides a lightweight and flexible framework for forecasting multivariate time series. The code is available at https://github.com/nerdslab/prism.

翻译：预测在金融、生物学和医疗健康等领域至关重要。尽管该领域已取得进展，但由于现实世界的时间序列同时包含全局趋势、局部细粒度结构以及介于两者之间的多尺度特征，实现精确预测仍具挑战性。本文提出一种新的预测方法PRISM（用于迭代序列建模的分区表示），该方法通过可学习的树状信号分区应对这一挑战。在树的根节点，全局表示捕获信号的宏观趋势，而递归分割则逐步揭示信号的局部视图。在树的每一层级，数据被投影到时频基（如小波或指数移动平均）上以提取尺度特异性特征，随后在层次结构中聚合。此设计使模型能够同时捕获信号的全局结构和局部动态，从而实现精确预测。在多个基准数据集上的实验表明，本方法在预测性能上优于现有先进方法。总体而言，这些结果证明我们的分层方法为多元时间序列预测提供了一个轻量且灵活的框架。代码可在 https://github.com/nerdslab/prism 获取。