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Time series is a special type of sequence data, a sequence of real-valuedrandom variables collected at even intervals of time. The real-worldmultivariate time series comes with noises and contains complicated local andglobal temporal dynamics, making it difficult to forecast the future timeseries given the historical observations. This work proposes a simple andeffective framework, coined as TimeSQL, which leverages multi-scale patchingand smooth quadratic loss (SQL) to tackle the above challenges. The multi-scalepatching transforms the time series into two-dimensional patches with differentlength scales, facilitating the perception of both locality and long-termcorrelations in time series. SQL is derived from the rational quadratic kerneland can dynamically adjust the gradients to avoid overfitting to the noises andoutliers. Theoretical analysis demonstrates that, under mild conditions, theeffect of the noises on the model with SQL is always smaller than that withMSE. Based on the two modules, TimeSQL achieves new state-of-the-artperformance on the eight real-world benchmark datasets. Further ablationstudies indicate that the key modules in TimeSQL could also enhance the resultsof other models for multivariate time series forecasting, standing asplug-and-play techniques.

TimeSQL: Improving Multivariate Time Series Forecasting with Multi-Scale Patching and Smooth Quadratic Loss