Robust temporal alignment for multivariate time series forecasting

Temporal alignment of time series is crucial in the task of multivariate time series forecasting, as temporal misalignment can introduce randomness into the learned quantitative relationships between the target and related factor time series, resulting in unreliable forecasting outcomes. Nevertheless, anomalous information gain (AIG) and data outliers present significant challenges to the temporal alignment of time series. To address the issues of AIG and data outliers in this study, a time-delay-related ellipsoid is utilized to construct the alignment deviation metric, an information gain-based regularization term is designed to reinforce this metric by penalizing the occurrence of AIG, and an equiprobable ellipsoid-based outlier filtering process is introduced. Finally, a time-delay estimation (TDE) method robust to AIG and data outliers is proposed, upon which the time series alignment is performed. The robustness of the proposed method against AIG and data outliers is validated through simulation and real-data experiments. The wind speed forecast errors of the forecasting models are significantly reduced after aligning the related time series using our method; for instance, the mean squared error (MSE) achieved by traditional machine learning models and deep learning models is reduced to at least 74% and 95 %, respectively.