TVTS: Learning Time-Varying Dynamics and Directed Cross-Variable Dependencies for Multivariate Time Series Forecasting

Multivariate Time Series Forecasting (MTSF) requires jointly modeling both temporally heterogeneous patterns and cross-variable dependencies. However, many recent designs rely on time-invariant temporal filters and symmetric similarity for variable interactions, which limits the faithful representation of position-dependent temporal dynamics and directional information propagation. To address these challenges, we propose the Time-Varying Directed Geometry framework for Multivariate Time Series Forecasting (TVTS). For temporal modeling, we introduce a Time-Varying Convolutional Filter that learns distinct spectral responses across relative temporal positions through a structured basis expansion, thereby relaxing the shift-invariance assumption of conventional filters. For cross-variable modeling, we propose Directed Geometric Clustering, which constructs a sparse anisotropic topology to represent non-reciprocal predictive dependencies beyond symmetric similarity. Extensive experiments on diverse and challenging real-world benchmarks demonstrate that TVTS consistently achieves state-of-the-art forecasting performance with high computational efficiency across forecasting horizons.