Time series is a special type of sequence data, a sequence of real-valued random variables collected at even intervals of time. The real-world multivariate time series comes with noises and contains complicated local and global temporal dynamics, making it difficult to forecast the future time series given the historical observations. This work proposes a simple and effective framework, coined as TimeSQL, which leverages multi-scale patching and smooth quadratic loss (SQL) to tackle the above challenges. The multi-scale patching transforms the time series into two-dimensional patches with different length scales, facilitating the perception of both locality and long-term correlations in time series. SQL is derived from the rational quadratic kernel and can dynamically adjust the gradients to avoid overfitting to the noises and outliers. Theoretical analysis demonstrates that, under mild conditions, the effect of the noises on the model with SQL is always smaller than that with MSE. Based on the two modules, TimeSQL achieves new state-of-the-art performance on the eight real-world benchmark datasets. Further ablation studies indicate that the key modules in TimeSQL could also enhance the results of other models for multivariate time series forecasting, standing as plug-and-play techniques.

这项研究提出了名为TimeSQL的简单而有效的框架，它利用多尺度拼接和平滑二次损失来解决时间序列的预测问题，其模块能够提供新的最先进性能，并增强其他多元时间序列预测模型的结果。

TimeSQL: 多尺度修补和平滑二次损失提升多变量时间序列预测