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

Multivariate time series are usually sequences of real-valued variables recorded at regular intervals. Forecasting them poses significant challenges due to their inherent noise and complex temporal dynamics. To effectively address these challenges, we introduce TimeSQL, a novel approach specifically designed for multivariate time series. TimeSQL employs multi-scale patching and a smooth quadratic loss (SQL) function. This enables it to adeptly capture both local and long-term patterns in complex, noisy data environments. The multi-scale patching approach provides a comprehensive view of temporal correlations, while the SQL, rooted in the rational quadratic kernel, strategically adjusts gradients to avoid overfitting. Through both theoretical and empirical analysis, we have demonstrated that TimeSQL exhibits superior noise resilience compared with models based on Mean Squared Error (MSE). Evaluated across eight diverse benchmark datasets, TimeSQL consistently delivers exceptional performance in multivariate time series forecasting. Furthermore, ablation studies underscore the adaptability of TimeSQL's components, enhancing the performance of various other forecasting models and proving their utility as plug-and-play modules.