Unified Cross-Variable Correlation Learning for Long-Term Multivariate Time Series Forecasting

The complex evolution of multivariate time series is jointly shaped by the temporal variability, heterogeneity, and selectivity of cross-variable correlations. However, existing forecasting methods typically focus on only one or a subset of these properties, potentially propagating temporally misaligned, polarity-conflicting, or irrelevant information across variables and thereby limiting forecasting performance. To address this issue, we propose TimeCorr, a unified correlation learning framework for multivariate time series forecasting that jointly models dynamic correlation, heterogeneous correlation, and selective correlation. Specifically, we first propose a Dynamic Correlation Module that estimates signed cross-variable correlation weights at different temporal positions to characterize temporal variations in dependency strength. On this basis, we design a Heterogeneous Correlation Module that independently calibrates the positive and negative components of dynamic correlation weights to capture polarity-specific interaction effects. Furthermore, we construct a Selective Correlation Module that learns sparse relation masks to filter the calibrated correlation weights, retaining informative variable pairs while suppressing irrelevant interactions. Finally, the sparsified correlation weights are used to aggregate local contextual information across variables for forecasting. Extensive evaluations on eight benchmark datasets demonstrate the consistently superior forecasting performance of TimeCorr, which achieves the lowest errors in 55 evaluation cases. Relative to the second-best results in the corresponding settings, TimeCorr reduces MSE and MAE by up to 6.12% and 4.57%, respectively.