Stabilizing Recursive Retrieval in Irregular Time-Series Forecasting

Retrieval-augmented forecasting extends parametric predictors with historical trajectories retrieved from external temporal memory, yet existing methods largely adopt static memory, where retrieved evidence remains independent of the model's own predictions. This limitation can fail in continual forecasting, where previous forecasts are stored and later reused, creating a recursive feedback loop among memory, retrieval, and prediction. We present ECHO (Evolving Closed-loop Historical Observations), a framework for studying and controlling recursive retrieval-augmented forecasting with evolving temporal memory. ECHO combines predictive temporal retrieval with a fixed base forecaster and models memory evolution as a dynamical process. We identify a self-confirming retrieval loop, in which retrieval errors bias predictions, biased predictions contaminate memory, and the resulting memory reinforces future forecasting errors. We analyze when such perturbations decay or amplify, introduce grounding to anchor memory evolution to observed outcomes, and develop a reliability-aware adaptive memory update. Extensive experiments on four public benchmark datasets demonstrate that ECHO achieves competitive performance compared with a wide range of state-of-the-art methods.