TS-MTM: Temporal-Spectral Masked Time-Series Modeling for Forecasting

Time series forecasting is a cornerstone of numerous real-world applications, where prediction accuracy relies on capturing intricate periodic patterns and evolving spectral dynamics. While Masked Time-series Modeling (MTM) has emerged as a powerful self-supervised paradigm, its conventional one-dimensional (1D) formulation often fails to resolve the underlying structural dependencies essential for long-term forecasting explicitly. To address this limitation, we propose TS-MTM, a Temporal-Spectral Masked Time-series Modeling framework that formalizes pretraining within a joint representation space. By leveraging autocorrelation-based periodicity, TS-MTM transforms 1D sequences into period-aware 2D temporal-spectral representations, a transition grounded in stochastic-process theory. Within this augmented space, we introduce two synergistic mechanisms: Axial-Period Cross Masking (APCM) to capture temporal dependencies across phases, and Structure-aware Spectral Magnitude Masking (SSMM) to reconstruct global frequency-domain signatures. To ensure representation consistency, a Dual-domain Contextual Contrastive objective is employed to align these complementary views on the signal manifold, yielding unified embeddings that preserve temporal-spectral coherence. Extensive evaluations across nine benchmark datasets demonstrate that TS-MTM consistently achieves state-of-the-art performance under both in-domain and cross-domain settings, underscoring its robustness and generalization for complex temporal dynamics. Code is available at https://github.com/zpc2002zpc/TS-MTM.