Universal knowledge representation is a central problem for multivariate time series(MTS) foundation models and yet remains open. This paper investigates this problem from the first principle and it makes four folds of contributions. First, a new empirical finding is revealed: time series with different time granularities (or corresponding frequency resolutions) exhibit distinct joint distributions in the frequency domain. This implies a crucial aspect of learning universal knowledge, one that has been overlooked by previous studies. Second, a novel Fourier knowledge attention mechanism is proposed to enable learning time granularity-aware representations from both the temporal and frequency domains. Third, an autoregressive blank infilling pre-training framework is incorporated to time series analysis for the first time, leading to a generative tasks agnostic pre-training strategy. To this end, we develop the General Time-series Model (GTM), a unified MTS foundation model that addresses the limitation of contemporary time series models, which often require token, pre-training, or model-level customizations for downstream tasks adaption. Fourth, extensive experiments show that GTM outperforms state-of-the-art (SOTA) methods across all generative tasks, including long-term forecasting, anomaly detection, and imputation.

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