Learning Agentic Time Series Forecasting via Trajectory Distillation and Memory-Based Reinforcement Learning

Time series forecasting is a fundamental task in temporal data analytics, and large language model (LLM)-based agents offer a promising paradigm through autonomous tool interaction and evidence-grounded reasoning. However, two fundamental challenges remain: how to acquire forecast-relevant evidence through adaptive tool interactions, and how to translate such evidence into accurate numerical predictions. To address these challenges, we propose CastFlow, a role-specialized agentic forecasting framework that bridges general-purpose tool reasoning and specialized temporal forecasting. Specifically, CastFlow introduces an Experience Memory that distills successful tool-use trajectories from training data, guiding a frozen LLM to orchestrate a multi-view toolkit for evidence acquisition. A lightweight specialized LLM then performs evidence-grounded temporal reasoning to refine an ensemble forecasting prior. To enhance this capability, we develop a two-stage training strategy combining supervised fine-tuning and reinforcement learning with verifiable rewards, where final forecasting outcomes of the overall workflow guide the optimization of the specialized model. Extensive experiments on ten real-world benchmarks demonstrate that CastFlow outperforms competitive baselines on nine datasets. Our findings highlight the importance of bridging autonomous evidence acquisition and specialized temporal reasoning for accurate and adaptive agentic forecasting. The source code is available at https://github.com/Forever-Pan/CastFlow.

Cross-domain multimodal time series forecasting is a challenging task, requiring models to integrate precise numerical comprehension, cross-domain semantic understanding, and effective multimodal fusion. Existing approaches either build Time Series Foundation Models (TSFMs) from scratch or leverage pretrained Large Language Models (LLMs). However, TSFMs often overlook semantic understanding and lack the ability to perform future-oriented semantic reasoning, and LLMs struggle with numerical comprehension and accurate quantitative forecasting. To overcome these limitations, we propose KairosAgent, a novel agentic framework for multimodal time series forecasting, including an LLM-based reasoner and a TSFM-based forecaster. KairosAgent unifies textual reasoning and numerical forecasting by dynamically invoking analytical tools to enhance the numerical understanding and semantic reasoning capabilities of LLMs. The reasoning results are subsequently fused into the TSFM pipeline, enabling more accurate and reliable future predictions. To further improve the reasoning, we curate a large-scale corpus of high-quality trajectories, alongside a reinforcement learning from forecasting paradigm with multi-turn refinement and turn-level credit assignment. Experiments demonstrate that KairosAgent achieves superior zero-shot forecasting performance while maximizing the utility of pretrained LLMs and TSFMs, presenting a promising direction for efficient and interpretable time series agents. The project page is at https://foundation-model-research.github.io/KairosAgent .

Time series forecasting is fundamental to decision-making in complex systems, where future dynamics are influenced not only by historical observations but also by evolving contextual features. Recent advances in large language models (LLMs) have extended forecasting beyond numerical extrapolation toward context-aware reasoning. However, existing approaches often lack explicit mechanisms to identify relevant contexts, reason about their impacts, and validate forecasts against temporal and domain constraints. In this work, we propose CastFSR, an agentic framework that formulates context-aware forecasting as a Fast--Slow--Reflect workflow. In fast thinking, CastFSR profiles observations and selects lightweight forecasters to construct a data-driven forecast prior. In slow deliberation, it retrieves contextual evidence, adaptively determines informative look-back windows, and reasons about how contexts reshape future dynamics. In reflection, it iteratively refines forecasts to ensure temporal, contextual, and domain consistency. CastFSR supports both training-free inference with off-the-shelf LLMs and efficient deployment through a two-stage SFT and reinforcement learning strategy that transfers its orchestration capability to compact LLMs. Extensive experiments on public datasets demonstrate that CastFSR consistently outperforms representative baselines. Our code is available at https://github.com/Xiaoyu-Tao/CastFSR.