AltTS: Decoupling Autoregression and Cross-Variable Dependency via Alternating Optimization for Multivariate Time Series Forecasting

Multivariate time series forecasting requires learning both within-variable temporal dependencies and cross-variable interactions. When these components are optimized jointly, their predictions enter a shared residual, coupling their learning signals. We introduce ALTTS, a dual-path forecasting framework that explicitly separates temporal and cross-variable modeling and coordinates their adaptation through staged alternating optimization. The framework combines a linear temporal predictor with a masked cross-variable attention module. Its training procedure first establishes a temporal predictor, fits a cross-variable residual correction, and then alternates between the branches with block relaxation. Our analysis characterizes residual-induced gradient coupling, and local learning-signal diagnostics illustrate how this interaction can affect temporal updates. Experiments on seven forecasting benchmarks demonstrate competitive accuracy using standard architectural components. These results highlight branch coordination as an effective design dimension for multivariate forecasting. Code available at: anonymous github.