energy load forecasters

Abstract: Time Series Foundation Models (TSFMs) provide general-purpose forecasting capabilities, yet their forecasts can remain misaligned with the temporal characteristics of a target domain. This motivates lightweight forecast correction even when only black-box access to the TSFM is available. Our key observation is that two forms of historical information provide complementary correction signals: historical analogues reveal how similar contexts evolved, while past forecast errors reveal a TSFM's characteristic deviations in the target domain. Based on this observation, we propose ECHO, a black-box forecast correction framework that learns from both sources. ECHO uses AnalogE to assess retrieved historical analogues together with the current context and base forecast, learning transferable corrections through cross-domain pretraining. In parallel, RecentE learns target-specific residual corrections from past forecast errors and refines them as causally available feedback accumulates. ECHO dynamically combines the two corrections according to their observed forecasting performance. Across 5 representative TSFMs and 9 real-world datasets, ECHO reduces MSE in all 45 backbone--dataset settings, yielding an average relative reduction of 9.26\% in macro-average MSE. Its gains also extend to long-horizon forecasting.

Abstract: Retrieval-augmented time-series forecasting uses the continuations of historical segments similar to the current context as references for a forecaster. Most existing methods build the retrieval memory once from the training segment, leaving observations revealed after deployment unavailable as references, and generally do not calibrate how much the retrieved information should influence a frozen forecaster. We identify two key determinants of retrieval utility for a frozen forecaster: whether the history still reflects the current state, and whether the correction it induces aligns with the forecaster's residual errors, an alignment that can shift between validation and deployment when the memory becomes stale. We propose FreshCast, a plug-in retrieval framework that keeps the forecaster frozen, continuously updates a non-parametric memory with new observations, forms a memory forecast through relational kernel regression, and calibrates its weight in closed form on the validation segment. Under a simplified generative model, we characterize the optimal combination gain through the second-order relation between forecaster error and memory correction, and show that a sufficiently long look-back can make periodic memory information redundant. Across seven benchmarks and ten forecasting architectures, FreshCast reduces average MSE for every evaluated forecaster and input length, by 14.6% and 5.6% at input lengths 96 and 720, and achieves lower MSE than the evaluated retrieval-augmented and online baselines in their comparison settings. Ablations show that freezing the memory at the end of training removes most of the gain, identifying post-training observations as a primary source of improvement. For a frozen forecaster, useful historical references must remain timely and provide information that helps correct its remaining errors.