WaveFM: Wavelet Decomposition Masked Reconstruction for Multi-Scale Time-series Foundation Model

Encoder-only Time-Series Foundation Models (TSFMs) learn to understand time series through time-domain masked reconstruction. This objective captures transferable temporal dynamics, making them a strong universal backbone across domains and tasks. However, simple time-domain masked reconstruction does not fully capture the underlying temporal dynamics. In particular, it does not explicitly reflect the multi-scale nature of real-world time series and can bias learning toward low-frequency trends, reducing sensitivity to fine-grained temporal changes. To address this, we propose WaveFM, which decomposes each time series into scale-separated components and is trained to model within-scale temporal structure and cross-scale composition back to the original time series signal. Therefore, WaveFM explicitly emphasize key features for understanding time series, demonstrating how coarse trends and fine-scale deviations jointly explain the time series. Experiments on long-horizon forecasting and imputation show consistent improvements over encoder-only TSFM baselines, supporting the importance of explicitly decomposing multi-scale components for understanding time series.