CVENet: A Complementary View and Expert Network for Time Series Forecasting with Exogenous Variables

Time series forecasting is essential in many domains. Beyond endogenous variables (i.e., target variables), exogenous variables (i.e., covariates) provide additional predictive information over the history, and often over the forecast horizon as well. However, existing methods for time series forecasting with exogenous variables (TSF-X) mainly focus on how endogenous and exogenous variables interact, and fix in advance how the series are processed before and during this interaction, leading to two shortcomings: 1) they handle non-stationarity with a single treatment, either removing the window statistics or keeping them, although the preferable one may shift along the forecast horizon, and 2) they apply the same functional form to every token, as even mixture-of-experts forecasters mostly route tokens among architecturally identical experts. To address these shortcomings, we propose CVENet, a Complementary View and Expert Network for time series forecasting with exogenous variables. Specifically, Complementary View Construction first builds two multi-scale views of the history, with and without the window statistics removed, each carried by its own stack of encoder layers with dual-correlation attention. In every encoder layer, Token-Wise Complementary Experts then route each token within a frequency-domain and a time-domain expert family and mix the two with a token-dependent gate. Finally, Horizon-Wise View Reconciliation combines the two view forecasts with a weight learned for each forecast step. Extensive experiments on twelve real-world datasets and a tokamak dataset demonstrate that CVENet outperforms state-of-the-art methods.