Tracking the Best Imputer under Drift: Continual Competence Routing for Non-Stationary Time Series

Time-series imputation is typically deployed statically: an imputer is selected offline and retained as the stream evolves. Yet even when all imputers remain frozen, their relative competence can change with missingness structure and data regime. We formulate this problem as continual competence routing under sparse reconstruction feedback and introduce Continual Competence Routing (CCR), which tracks time-varying competence using multi-scale memories of audited reconstruction evidence while leaving the underlying imputers fixed. Our analysis identifies a fundamental distinction between coverage and freshness. Under a linear relative-competence model, arbitrarily strong all-history geometric coverage can remain stale after a change in expert ordering, whereas sufficiently informative post-change coverage controls fresh competence-estimation error and supports recovery of the current ordering. Across clinical and general time-series streams, frozen expert libraries exhibit substantial competence-oracle headroom and recurrent reversals in the best imputer. Fresh geometry is informative on ETTh1 and Weather but weaker on clinical streams. Under sparse audits, multi-scale routing improves over static deployment in several settings but does not uniformly beat the best static or fixed-memory baseline. Successful continual imputation therefore depends on evidence that is not merely abundant, but relevant to the current competence regime.