Required-Level Risk Control for Time Series Forecasting

Reliable time series forecasting requires risk control at the temporal scale of deployment, yet long-run average coverage can mask frequent window-level failures. We propose Required-Level Risk Control (ReqRC), which replaces outcome-based updates with feedback on the least conservative level that would have satisfied each completed window's target. We uniquely decompose window shortfall into predictor shortfall and selection shortfall, identifying the latter as the component addressed by level adjustment. We establish an exact worst-case lower bound on the window success rate and derive reliability bounds for delayed order statistics, adjusted for distribution shift and infeasibility. ReqRC uses these statistics to raise the level of any causal base method without training or tuning. Across eight real-world datasets, ReqRC achieves the lowest mean shortfall and highest window success rate against ten alternatives, with improvements across all 40 predictor–method pairs. On the test set, alternatives matched to ReqRC's validation cost are less reliable, whereas those matching its success rate incur higher costs. By turning retrospective feasibility into feedback for future decisions, ReqRC provides a principled approach to cost-efficient window-level risk control.