CvLoss: A Cross-Variable Loss for Multivariate Time Series Forecasting

A recent study published on arXiv (2608.05742) presents Cross-Variable Loss (CvLoss), a structural regularizer aimed at enhancing multivariate time series forecasting. The researchers contend that current forecasting models, which generally adhere to the Direct Forecasting (DF) approach, produce multi-step forecasts with point-wise objectives that do not adequately address cross-variable structures. This oversight leads to an objective gap when both cross-variable and lagged dependencies exist. CvLoss mitigates this issue by penalizing discrepancies in edge-wise residuals across forecast patches, promoting consistency within the cross-variable graph. The paper illustrates the inadequacy of the DF objective in these contexts and offers CvLoss as a remedy. This research holds significance for machine learning and time series analysis, with various potential applications. The paper is accessible on arXiv, categorized under 'cross'.