Learning Predictive Uncertainty for Frozen Time-Series Forecasters

Combining time-series point forecasts does not by itself provide reliable uncertainty estimates for the resulting ensemble. Error prediction has its own learning targets and may require different expert weights from point forecasting. We propose GETUP (Gated Ensemble for Time-Series Uncertainty Prediction), a simple approach that learns these weights separately. Its zero-shot implementation uses two independent gates based on the input spectrum: one combines point forecasts, while the other combines error estimates learned after freezing the point branch. Separating error magnitude from residual shape supports both Gaussian and non-Gaussian predictive distributions. We evaluate GETUP on the TFB and expanded ProbTS benchmark grids, each covering 36 dataset–horizon combinations, alongside in-domain experiments on six datasets and four forecast horizons. Benchmark comparisons show improvements over established forecasting baselines, while controlled experiments examine the contributions of predictor-specific error learning, input-dependent scales, and residual shape. The construction supports zero-shot forecasting, uncertainty estimation for frozen pretrained models, and training on target history. Across these settings, explicitly learning forecast errors provides a simple way to improve predictive uncertainty while preserving the point forecasts.