TimeRelay: Relation-Aware Recurrent Variable Modeling for Multivariate Time Series Forecasting

Multivariate time series forecasting requires effective modeling of temporal dynamics within individual variables and predictive dependencies across variables. A representative class of cross-variable modeling approaches explicitly constructs variable-to-variable interactions, resulting in a candidate interaction space that grows quadratically with the number of variables. At the same time, the predictive relevance of different variable pairs can be highly non-uniform. Motivated by these observations, we propose TimeRelay, a relation-aware recurrent framework that models cross-variable dependencies from the perspective of predictive information propagation rather than explicitly materializing dense pairwise interactions. TimeRelay first constructs variable-wise temporal representations from historical observations and then applies Relation-Aware State Propagation (RASP). For each variable, RASP constructs a compact multivariate context and uses the variable–context relation to adaptively control recurrent state updates. RASP therefore propagates predictive information across variables through evolving recurrent states without explicitly constructing a dense variable-to-variable interaction matrix. Its affine recurrent form enables work-efficient parallel evaluation with linear arithmetic work in the number of variables and logarithmic dependency depth. Extensive experiments on diverse multivariate benchmarks demonstrate the effectiveness, efficiency, and scalability of TimeRelay.