Time Series Reasoning via Process-Verifiable Thinking Data Synthesis and Scheduling for Tailored LLM Reasoning

Time series is a pervasive data type across various application domains, rendering the reasonable solving of diverse time series tasks a long-standing goal. Recent advances in large language models (LLMs), especially their reasoning abilities unlocked through reinforcement learning (RL), have opened new opportunities for tackling tasks with long Chain-of-Thought (CoT) reasoning. However, leveraging LLM reasoning for time series remains infancy, hindered by the absence of carefully curated time series CoT data for training, limited data efficiency caused by underexplored data scheduling, and the lack of RL algorithms tailored for exploiting such time series CoT data. In this paper, we introduce VeriTime, a framework that tailors LLMs for time series reasoning through data synthesis, data scheduling, and RL training. First, we propose a data synthesis pipeline that constructs a time series–text multimodal dataset with process-verifiable annotations. Second, we design a data scheduling mechanism that arranges training samples according to a principled hierarchy of difficulty and task taxonomy. Third, we develop a two-stage reinforcement finetuning featuring fine-grained, multi-objective rewards that leverages verifiable process-level CoT data. Extensive experiments show that VeriTime substantially boosts LLM performance across diverse time series reasoning tasks. Notably, it enables compact 3B–4B models to achieve reasoning capabilities on par with or exceeding those of larger proprietary LLMs.

Time series data are sequences of measurements recorded over time, such as sensor readings in a factory, stock prices, or patient vital signs. Yet getting large language models to truly reason about such data remains a major challenge. Current large language models often produce answers without explaining how they got there. If the reasoning process is flawed, even a correct answer may be unreliable, and errors in intermediate steps are difficult to identify or correct. This is especially problematic for time series data, where complex temporal patterns require careful, step-by-step analysis. We develop VeriTime, a framework that teaches large language models to reason over time series like a human expert. We first build an automated pipeline that generates richly annotated reasoning examples, where every intermediate step can be checked for correctness. We then train models through supervised fine-tuning on correct reasoning trajectories, followed by reinforcement learning that rewards sound intermediate reasoning, not just correct final answers. This enables compact large language models to match or surpass much larger proprietary models, making reliable time series reasoning more practical across diverse scenarios.