Large language models (LLMs) are increasingly used as natural-language interfaces to structured data, yet they remain brittle when reasoning over time series. Visual patterns can be misleading, numerical claims can be hallucinated, and textual context can override evidence from the signal. We study zero-shot time-series reasoning as a multimodal evidence arbitration problem for LLM agents. We propose TS-Debate, an inference-time multi-agent protocol that requires no task-specific fine-tuning. TS-Debate first elicits relevant domain knowledge, then assigns modality-specialized agents to textual context, visual patterns, and numerical signals, and coordinates their interaction through a verification-conflict-calibration procedure. Reviewer agents check decision-critical claims with lightweight code execution and numerical lookup, resolve cross-modal disagreement, and calibrate the final answer. Unlike generic multi-agent debate or unconstrained tool use, TS-Debate specifies how evidence is exposed, which claims are checkable, and how verification outcomes shape synthesis. Across 20 tasks from three public benchmarks, TS-Debate improves classification and question answering performance over strong baselines, while revealing that debate is most useful for global-structure and cross-view reasoning rather than local value reconstruction.

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