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.

翻译：普适知识表示是多元时间序列基础模型的核心问题，目前仍未得到解决。本文从第一性原理出发研究该问题，并作出四方面贡献。首先，揭示了一项新的实证发现：具有不同时间粒度（或对应频率分辨率）的时间序列在频域中展现出不同的联合分布。这暗示了学习普适知识的一个关键方面——一个被先前研究忽视的方面。其次，提出了一种新颖的傅里叶知识注意力机制，能够从时域和频域同时学习时间粒度感知的表示。第三，首次将自回归空白填充预训练框架引入时间序列分析，从而形成一种与生成任务无关的预训练策略。为此，我们开发了通用时间序列模型，这是一个统一的多元时间序列基础模型，解决了当前时间序列模型的局限性——这些模型通常需要针对下游任务适配进行标记、预训练或模型层面的定制。第四，大量实验表明，GTM在所有生成任务（包括长期预测、异常检测和插补）上均优于最先进的方法。