Training-Free Continual Learning for Multimodal Forecasting via Prompt Evolution

Adapting a forecasting system to a changing world classically means retraining. We ask whether the task of continuously learning regimes for time series forecasting can be represented by a piece of text: a guidance block, evolved by outcome-driven reflection and used in a frozen LLM forecaster's prompt. On a refreshed multimodal benchmark (weekly search indices, daily currencies, daily commodities, each window paired with web-retrieved news), we run GEPA-style prompt evolution under strict contamination control to prevent any data leakage commonly found in time series benchmark: the forecaster's knowledge cutoff predates every evaluated window. A $\sim$900-word evolved guidance carried by Llama-3.3-70B beats Time-Series Foundation Models (TSFMs) on held-out data (GM MASE 0.776 vs.\ 0.898 for TabPFN-TS-3), transfers across more recent models without measurable loss, and costs dollars rather than GPU-days to update. We provide a study of the continual learning prompt evolution: out-of-loop gains concentrate in the first reflection; in-loop improvements overstate out-of-loop gains $2$--$3\times$ unless an untouched monitor arbitrates; and error-only objectives silently suppress the text modality. We provide two extensions: compiling the guidance into executable code with a TSFM as a callable tool, which recovers most of the gain deterministically; and ablations showing the advantage widens at short horizons while removing the news text entirely does not hurt the guided forecaster, consistent with the text's value being distilled into policy during learning. We argue that continual prompt evolution is a practical, training-free alternative to retraining for multimodal forecasting.