A Survey of Reasoning and Agentic Systems in Time Series with Large Language Models

Abstract:

Time series reasoning treats time as a first-class axis and incorporates intermediate evidence directly into the answer.
This survey defines the problem and organizes the literature by reasoning topology with three families: direct reasoning in one step, linear chain reasoning with explicit intermediates, and branch-structured reasoning that explores, revises, and aggregates.
The topology is crossed with the main objectives of the field, including traditional time series analysis, explanation and understanding, causal inference and decision making, and time series generation, while a compact tag set spans these axes and captures decomposition and verification, ensembling, tool use, knowledge access, multimodality, agent loops, and LLM alignment regimes.
Methods and systems are reviewed across domains, showing what each topology enables and where it breaks down in faithfulness or robustness, along with curated datasets, benchmarks, and resources that support study and deployment (with an accompanying repository at \url{https://anonymous.4open.science/r/Time-Series-Reasoning-Survey-TMLR/}).
Evaluation practices that keep evidence visible and temporally aligned are highlighted, and guidance is distilled on matching topology to uncertainty, grounding with observable artifacts, planning for shift and streaming, and treating cost and latency as design budgets.
We emphasize that reasoning structures must balance capacity for grounding and self-correction against computational cost and reproducibility, while future progress will likely depend on benchmarks that tie reasoning quality to utility and on closed-loop testbeds that trade off cost and risk under shift-aware, streaming, and long-horizon settings.
Taken together, these directions mark a shift from narrow accuracy toward reliability at scale, enabling systems that not only analyze but also understand, explain, and act on dynamic worlds with traceable evidence and credible outcomes.

Submission Type: Long submission (more than 12 pages of main content)

Changes Since Last Submission:

**1. Mathematical Formalization (Section 2)**
* **Added Problem Formulation (Sec 2.1):** Formally defined the Time Series Reasoning (TSR) input tuple $(X_{1:T}, C, K)$ and model $M_\theta$.
* **Added Topology Definitions (Sec 2.2):** Introduced equations distinguishing Direct, Linear Chain, and Branch-Structured topologies via probability factorization.
* **Added Objective Functions (Sec 2.3):** Defined formal loss functions for Forecasting ($L_{pred}$), Explanation ($L_{gen}$), Policy Learning ($J(\pi)$), and Generation ($D$).

**2. New Visualization (Introduction)**
* **Added Figure 1:** Introduced a new "Illustrative Reasoning Traces" figure to visualize the distinction between topologies on a concrete anomaly detection task.
* **Updated Introduction Text:** Revised the introduction to explicitly reference the new figure and the hierarchy of reasoning capabilities.

**3. Comparative Analysis & Critical Depth**
* **Added Comparative Analysis (Sec 3.5, 4.6, 5.6):** Added dedicated subsections discussing the trade-offs of each topology (e.g., Efficiency vs. Robustness, Cost vs. Exploration).
* **Clarified Linear Chain Definition (Sec 4.6):** Explicitly distinguished Linear Chain from Direct Reasoning based on the visibility of intermediate tokens to address Chain-of-Thought ambiguity.

**4. Terminology and Scope Refinements**
* **Renamed "Alignment" to "Adaptation" (Sec 2.4.4):** Changed the attribute tag "LLM Alignment Regimes" to "LLM Adaptation Regimes" to avoid confusion with safety alignment.
* **Refined Multimodal Terminology:** Updated "Multimodal Alignment" to "Cross-Modal Alignment" (Sec 7.2).
* **Clarified Scope:** Added text distinguishing Time Series Reasoning from generic text reasoning based on inductive bias mismatch (Sec 6.3) and temporal synchronization challenges (Sec 7.2).

Assigned Action Editor: ~Feng_Zhou9

Submission Number: 6363