CastFSR: A Fast–Slow–Reflect Agentic Reasoning Framework for Context-Aware Time Series Forecasting

Time series forecasting often requires combining historical observations with contextual information about future conditions. Numerical forecasters capture temporal patterns, while large language models (LLMs) can interpret contextual evidence and coordinate forecasting tools. Integrating these capabilities requires deciding when context should modify a forecast and checking whether the resulting revisions are consistent with temporal and domain constraints. We introduce CastFSR, an agentic framework organized as a Fast–Slow–Reflect workflow. Fast-thinking Forecasting profiles historical observations and selects a specialized forecaster to construct a numerical forecast prior. Slow Deliberative Reasoning retrieves relevant contextual evidence using context-specific look-back windows and refines the prior through contextual reasoning. Reflective Evaluation checks temporal, contextual, and domain consistency and revises the candidate forecast when violations are detected. CastFSR supports training-free orchestration with off-the-shelf LLM coordinators and a compact policy post-trained through supervised fine-tuning and multi-turn reinforcement learning. Experiments on ten energy forecasting benchmarks show that CastFSR achieves the best or second-best results on most reported metrics against representative baselines. Module and training-stage ablations support the complementary roles of numerical priors, contextual reasoning, reflection, and post-training within the evaluated settings. Our code is available at https://anonymous.4open.science/r/CastFSR-TS/.