Local Risk Structure for Adaptive Retraining in Streaming Time Series

Predictors for streaming time series must decide how much new data to collect before updating, even though the future benefit of an update is unknown. We propose RETICLE (Risk Evaluation Through Interval Comparisons of Local Errors), a data-only audit of accumulated-data quality for selecting an update size without retraining the downstream predictor at each candidate size. RETICLE fits causal local affine probes in a frozen representation and assesses their risk across bandwidths. We show that approximate quasiconvexity of the risk profile on a finite bandwidth grid is necessary for finite-sample local-learning regularity; monotone profiles are included as special cases. Using this necessary consequence as a data-quality criterion, RETICLE certifies the risk-shape condition with simultaneous confidence bounds and selects the first adequately supported checkpoint that passes. Under causal auditing assumptions, we control the probability of false shape certification simultaneously over the declared checkpoints and representations, including the selected checkpoint, without requiring independent observations. Experiments examine checkpoint selection for six downstream learners on synthetic and real time series, as well as continuous fine-tuning on three forecasting datasets with two drift detectors. RETICLE achieves the lowest test error in 12 of 18 online settings, ties for the lowest in two more, and attains an overall mean rank of 1.28 among the compared baselines.