TSComp: Cross-scale Compositional Pre-training for Time Series Foundation Models

Time series foundation models (TSFMs) aim to learn transferable temporal representations across diverse downstream tasks. However, time series are inherently multi-scale: the observed signal is jointly composed of distinct temporal structures at different scales, each capturing different temporal dynamics. This poses two challenges for transferable pre-training: scale-specific structures should be explicitly distinguished and their cross-scale correspondence must also be preserved because their roles depend on how they interact across scales. Conventional time-domain masked reconstruction does not explicitly enforce either property, leaving both scale-specific structures and cross-scale correspondence implicitly supervised. To address these limitations, we propose TSComp, a cross-scale compositional pre-training framework for TSFMs. TSComp uses scale-balanced tokenization to construct aligned scale-specific representations, scale coefficient attention to model interactions among corresponding structures across scales, and multi-scale directional masking to infer missing components from complementary cross-scale context. Its pre-training objectives jointly supervise scale energy distribution calibration, signal recomposition, and coefficient reconstruction, making scale-specific recovery and cross-scale composition explicit learning targets. The resulting scale-specific representations are adapted to downstream tasks through a scale-aware adaptation method. Experiments across forecasting, imputation, classification, and anomaly detection demonstrate effective transfer across diverse downstream settings and competitive performance against both multi-task foundation models and task-specific architectures. Our code is available at https://anonymous.4open.science/r/TSComp-66B0.