GLARE: Global and Local Reconstruction for Time Series Forecasting with Exogenous Variables

Exogenous variables can improve time series forecasting through their relationships with the endogenous variable. However, relationships estimated over the full training period may differ from those fitted to recent observations. We propose GLARE, a lightweight forecasting framework that reconstructs the endogenous variable from exogenous variables through global and local relationships. An MLP captures global relationships through a pointwise mapping learned over the full training period. Ridge regression captures local relationships by fitting coefficients to the lookback window of each instance. The global and local reconstructions are blended into a single exogenous reconstruction, and a residual forecaster predicts the remaining residual. On the 12 TSF-X datasets, GLARE achieves state-of-the-art forecasting performance with a single linear residual forecaster and only hundreds to a few thousand additional parameters. Our code is available at: https://anonymous.4open.science/r/GLARE-6350.