Time series data inform critical decisions across many real-world domains. While large language model (LLM) agents can analyze data through natural language and tools, it remains unclear whether they can conduct reliable time series analysis across multi-turn conversations. Existing benchmarks focus on single-step tasks such as forecasting and anomaly detection, overlooking practical workflows where user goals evolve, agents must build on prior analyses, and conclusions emerge from accumulated evidence. In this work, we introduce TimeSage-MT, a multi-turn benchmark for agentic time series reasoning with 240 tasks and 2,680 dialogue turns across 8 real-world domains, spanning basic exploration to decision-oriented analysis. TimeSage-MT is built through a reproducible pipeline that converts real-world time series data into multi-turn conversations with verifiable answers. It provides a unified evaluation protocol and public leaderboard for comparing time series agentic systems. To demonstrate the benchmark's utility, we evaluate frontier LLMs alongside TimeSage, a novel structured agent equipped with a comprehensive time series skill library. The results show sharp performance drops on decision-oriented tasks, driven by failures in memory, uncertainty handling, and domain-based decision making. TimeSage-MT exposes critical gaps in current agentic reasoning and provides a rigorous foundation for future development.

Time series generation (TSG) plays a fundamental role in data engineering and knowledge discovery, serving as a key enabler for data augmentation, representation learning, privacy preservation, and scenario simulation analysis in temporal data mining. By synthesizing realistic and controllable time series, TSG directly benefits downstream tasks such as forecasting, anomaly detection, and classification by data augmentation and improving model generalization. This survey presents a comprehensive and systematic review of TSG methodologies, spanning traditional non-deep learning approaches, such as rule-based, statistical, and simulation-based methods, and modern deep generative models, including variational autoencoders, generative adversarial networks, diffusion models, normalizing flows, and large language models. To organize the rapidly growing literature, we introduce a unified multi-level taxonomy to organize the technical landscape of TSG and clarify the relationships among diverse approaches. The taxonomy emphasizes underlying modeling principles rather than individual representative models. Specifically, it categorizes TSG methods according to modeling backbones, generation settings (conditional versus unconditional), sampling regularity, and modality characteristics. Building on this taxonomy, we systematically review advanced methods within each category and discuss how they address key challenges such as irregular sampling, long-sequence modeling, multivariate dependencies, and controllable generation, and how they are applied in real-world scenarios. Furthermore, we present a holistic evaluation framework encompassing five core dimensions, including fidelity, diversity, controllability, downstream performance, and privacy protection. Finally, we identify critical open challenges and outline promising research directions from data characteristics, application scenarios, and modeling paradigm perspectives. This survey aims to serve as a structured reference and roadmap for researchers and practitioners in this rapidly evolving field.

Most time series foundation models are pretrained by directly predicting future observations, which often yields weakly structured latent representations that capture surface noise rather than coherent and predictable temporal dynamics. In this work, we introduce EIDOS, a foundation model family that shifts pretraining from future value prediction to latent-space predictive learning. We train a causal Transformer to predict the evolution of latent representations, encouraging the emergence of structured and temporally coherent latent states. To ensure stable targets for latent-space learning, we design a lightweight aggregation branch to construct target representations. EIDOS is optimized via a joint objective that integrates latent-space alignment, observational grounding to anchor representations to the input signal, and direct forecasting supervision. On the GIFT-Eval benchmark, EIDOS mitigates structural fragmentation in the representation space and achieves state-of-the-art performance. These results demonstrate that constraining models to learn predictable latent dynamics is a principled step toward more robust and reliable time series foundation models.

Temporal data-including time series and spatio-temporal data- are pervasive in real-world applications. Generated in massive volumes by physical and virtual sensors, they record dynamic system behaviors and enable a wide range of downstream tasks. Effectively analyzing such data is crucial to unlocking their rich information content. Recent advances in large language models and other foundation models have accelerated their use in time series and spatio-temporal data mining. These approaches not only improve pattern recognition and reasoning across diverse domains but also support progress toward artificial general intelligence that can understand and process temporal data. In this survey, we present a comprehensive, up-to-date review of large models tailored or adapted for time series and spatio-temporal data along four dimensions: data types, model categories, model scopes, and application areas/tasks. We organize existing work into two main groups: large models for time series analysis (LM4TS) and for spatio-temporal data mining (LM4STD), and further distinguish general-purpose from domain-specific models. We also curate related resources, including datasets, model implementations, and tools, organized by major application areas. Overall, this survey consolidates recent advances and highlights foundations, applications, resources, and open research opportunities in large model-centric temporal data analysis.

Modeling long-range dependencies in time series generation poses a fundamental trade-off between representational capacity and computational efficiency. Traditional temporal diffusion models suffer from local entanglement and the 𝒪(L^2) cost of attention mechanisms. We address these limitations by introducing PaCoDi (Parallel Complex Diffusion), a spectral-native architecture that decouples generative modeling in the frequency domain. PaCoDi fundamentally alters the problem topology: the Fourier Transform acts as a diagonalizing operator, converting locally coupled temporal signals into globally decorrelated spectral components. Theoretically, we prove the Quadrature Forward Diffusion and Conditional Reverse Factorization theorem, demonstrating that the complex diffusion process can be split into independent real and imaginary branches. We bridge the gap between this decoupled theory and data reality using a Mean Field Theory (MFT) approximation reinforced by an interactive correction mechanism. Furthermore, we generalize this discrete DDPM to continuous-time Frequency SDEs, rigorously deriving the Spectral Wiener Process describe the differential spectral Brownian motion limit. Crucially, PaCoDi exploits the Hermitian Symmetry of real-valued signals to compress the sequence length by half, achieving a 50

Spatio-temporal reasoning in time series involves the explicit synthesis of temporal dynamics, spatial dependencies, and textual context. This capability is vital for high-stakes decision-making in systems such as traffic networks, power grids, and disease propagation. However, the field remains underdeveloped because most existing works prioritize predictive accuracy over reasoning. To address the gap, we introduce ST-Bench, a benchmark consisting of four core tasks, including etiological reasoning, entity identification, correlation reasoning, and in-context forecasting, developed via a network SDE-based multi-agent data synthesis pipeline. We then propose STReasoner, a model that integrates time series, graph structure, and text for explicit reasoning. To promote spatially grounded logic, we introduce S-GRPO, a reinforcement learning algorithm that rewards performance gains specifically attributable to spatial information. Experiments show that STReasoner achieves average accuracy gains between 17% and 135% at only 0.004x the cost of proprietary models and generalizes robustly to real-world data.

Recent advances in multimodal time series learning underscore a paradigm shift from analytics centered on basic patterns toward advanced time series understanding and reasoning. However, existing multimodal time series datasets mostly remain at the level of surface alignment and question answering, without reaching the depth of genuine reasoning. The absence of well-defined tasks that genuinely require time series reasoning, along with the scarcity of high-quality data, has limited progress in building practical time series reasoning models (TSRMs). To this end, we introduce Time Series Reasoning Suite (TSR-Suite), which formalizes four atomic tasks that span three fundamental capabilities for reasoning with time series: (1) perception, acquired through scenario understanding and causality discovery; (2) extrapolation, realized via event-aware forecasting; and (3) decision-making, developed through deliberation over perception and extrapolation. TSR-Suite is the first comprehensive time series reasoning suite that supports not only thorough evaluation but also the data pipeline and training of TSRMs. It contains more than 23K samples, of which 2.3K are carefully curated through a human-guided hierarchical annotation process. Building on this foundation, we introduce TimeOmni-1, the first unified reasoning model designed to address diverse real-world problems demanding time series reasoning. The model is trained in multiple stages, integrating a mixture of task scenarios, novel reward functions, and tailored optimizations. Experiments show that TimeOmni-1 delivers strong out-of-distribution generalization across all tasks and achieves a high rate of valid responses. It significantly improves causality discovery accuracy (64.0% vs. 35.9% with GPT-4.1) and raises the valid response rate by over 6% compared to GPT-4.1 on the event-aware forecasting task.

With natural gas becoming a key component of energy systems, precise demand forecasting is crucial for supporting efficient planning and resource management. However, existing methods face two key challenges: substantial noise in industrial datasets and heterogeneous consumption patterns across sectors. Data noise caused by sensor errors, irregular reporting, and logging inconsistencies obscures underlying consumption trends. Simultaneously, sector-specific variations in demand make it challenging to develop a unified forecasting model capable of capturing diverse consumption behaviors. To address these challenges, we propose a novel data forecasting framework that integrates contrastive learning with targeted noise filtering to enhance data representation and prediction robustness. The noise filtering module incorporates a denoising task that enables the model to learn to suppress noise and improve representation reliability. Meanwhile, the contrastive learning mechanism leverages sector-specific information to capture both shared patterns and sectoral usage behaviors. We further introduce a false negative removal strategy to refine sample selection, reducing representation bias and enhancing generalization. Our approach is validated on a large-scale dataset from the ENN Group, covering over 10,000 industrial, commercial, and welfare-related customers across multiple regions. Experimental results demonstrate that our model consistently outperforms a range of state-of-the-art forecasting baselines across both short-and long-term horizons, achieving notably better accuracy and robustness in real-world scenarios. This work demonstrates the potential of noise-robust and sector-aware representation learning for advancing natural gas demand forecasting in real-world applications.

Spatial-Temporal Graph (STG) forecasting on large-scale networks has garnered significant attention. However, existing models predominantly focus on short-horizon predictions and suffer from notorious computational costs and memory consumption when scaling to long-horizon predictions and large graphs. Targeting the above challenges, we present FaST, an effective and efficient framework based on heterogeneity-aware Mixture-of-Experts (MoEs) for long-horizon and large-scale STG forecasting, which unlocks one-week-ahead (672 steps at a 15-minute granularity) prediction with thousands of nodes. FaST is underpinned by two key innovations. First, an adaptive graph agent attention mechanism is proposed to alleviate the computational burden inherent in conventional graph convolution and self-attention modules when applied to large-scale graphs. Second, we propose a new parallel MoE module that replaces traditional feed-forward networks with Gated Linear Units (GLUs), enabling an efficient and scalable parallel structure. Extensive experiments on real-world datasets demonstrate that FaST not only delivers superior long-horizon predictive accuracy but also achieves remarkable computational efficiency compared to state-of-the-art baselines. Our source code is available at: https://github.com/yijizhao/FaST.

Source-free domain adaptation (SFDA) is a challenging, yet valuable task within unsupervised domain adaptation (UDA), which adapts pretrained models to diverse unlabeled target domains while safeguarding the data security of the source domain. However, existing SFDA methods primarily focus on computer vision applications, often overlooking the unique characteristics of time series, such as temporal dependencies and sequential nature. Moreover, the fine-tuning paradigm of current SFDA methods is typically limited to posterior adaptation, focusing solely on constraining the statistical properties of model outputs. We argue that this black-box paradigm lacks semantic interpretability and risks aligning with spurious contextual noise, leading to negative transfer. This necessitates a paradigm evolution from blind statistical adaptation to interpretable adaptation. To this end, we introduce model salience as a quantifiable proxy of semantic interpretability, representing the importance weights a trained model assigns to specific temporal fragments. Accordingly, we propose a novel fine-tuning paradigm for time-series SFDA, termed PrEPoA, which integrates Prior Evaluation of model salience with Posterior Adaptation. In the prior evaluation stage, a key pattern reconstruction (KPR) module based on a sensitive masking mechanism is designed to quantify the model salience, while a novel interpattern triplet loss is introduced to calibrate it. In the posterior adaptation stage, robust prototype clustering (RPC) generates trustworthy reference labels as pseudo-ground truth for adaptation. Comprehensive experiments on the wireless sensor data mining (WISDM), human activity recognition (HAR), heterogeneity HAR (HHAR), machine fault diagnosis (MFD), and sleep stage classification (SSC) datasets demonstrate the superiority of our PrEPoA framework compared to nine UDA and seven SFDA methods. Furthermore, we experimentally validate that PrEPoA serves as a plug-and-play module that effectively incorporated into other SFDA methods.

Electrocardiography (ECG) is a cornerstone of cardiac assessment, making the learning of informative ECG representations fundamental to tasks ranging from disease diagnosis to clinical report generation. However, existing methods operate almost exclusively in the observable ECG signal space. In practice, the standard twelve-lead ECG represents multiple projections of the same underlying cardiac electrical activity from different spatial orientations. Therefore, representation learning in the ECG space inevitably introduces substantial redundancy, which may lead to spurious correlations and increased risk of overfitting. To address this and motivated by the Frank vectorcardiogram (VCG) model, we propose learning a unified latent representation of cardiac electrical activity directly in the VCG space. We introduce LVCG, the first general self-supervised representation learning framework designed to operate in this physically grounded latent space. By learning view-invariant latent VCG representations rather than lead-specific artifacts, VCG minimizes redundancy and improves generalization. LVCG generally outperforms ECG-space baselines across tasks, demonstrating enhanced robustness and generalization, especially in domain shift settings. Our code has been made available at https://anonymous.4open.science/r/LVCG-A0C4

Diffusion models have been widely used in time series and spatio-temporal data, enhancing generative, inferential, and downstream capabilities. These models are applied across diverse fields such as healthcare, recommendation, climate, energy, audio, and traffic. By separating applications for time series and spatiotemporal data, we offer a structured perspective on model category, task type, data modality, and practical application domain. This study aims to provide a solid foundation for researchers and practitioners, inspiring future innovations that tackle traditional challenges and foster novel solutions in diffusion model-based data mining tasks and applications. For more detailed information, we have open-sourced a repository.1

Demand forecasting is a cornerstone of e-commerce operations, directly impacting inventory planning and fulfillment scheduling. However, existing forecasting systems often fail during high-impact periods such as flash sales, holiday campaigns, and sudden policy interventions, where demand patterns shift abruptly and unpredictably. In this paper, we introduce EventCast, a modular forecasting framework that integrates future event knowledge into time-series prediction. Unlike prior approaches that ignore future interventions or directly use large language models (LLMs) for numerical forecasting, EventCast leverages LLMs solely for event-driven reasoning. Unstructured business data, which covers campaigns, holiday schedules, and seller incentives, from existing operational databases, is processed by an LLM that converts it into interpretable textual summaries leveraging world knowledge for cultural nuances and novel event combinations. These summaries are fused with historical demand features within a dual-tower architecture, enabling accurate, explainable, and scalable forecasts. Deployed on real-world e-commerce scenarios spanning 4 countries of 160 regions over 10 months, EventCast achieves up to 86.9

Time series forecasting is vital in diverse sectors such as energy and transportation, where non-stationary dynamics are deeply intertwined with external events in other modalities such as texts. However, incorporating natural language-based external events to improve non-stationary forecasting remains largely unexplored, as most approaches still rely on a single modality, resulting in limited contextual knowledge and model underperformance. Enabling fine-grained multimodal interactions between temporal and textual data is challenged by two fundamental issues: (1) the gap in modeling interactions among discrete external events and continuous time series in a unified framework; (2) classical uniform diffusion timestep ignores event-induced non-stationary variability, leading to imbalanced denoising difficulty across diffusion stages. In this work, we propose event-aware non-stationary time series forecasting EventTSF, an autoregressive diffusion framework that integrates historical time series and textual events via step-wise diffusion. To mitigate the imbalanced denoising difficulty of uniform timestep sampling, EventTSF uses an event-aware flow-matching timestep conditioned on event semantics. Extensive experiments on 7 synthetic and real-world datasets show that EventTSF outperforms 12 non-stationary time series forecasting baselines, achieving average gains of 41.3% in probabilistic forecasting and 27.5% in deterministic forecasting across all evaluation metrics.

Earth-system analysis reconstructs changing physical processes from observations that differ in source, scale, timing, and modality. Natural hazards make this work consequential because incomplete evidence can change estimates of severity, exposure, and mechanism. We introduce EarthVerse, a benchmark that evaluates scientific agents through package-scoped investigations. Its 405 reproducible tasks are grounded in 199 documented events and 19 hazard families. Agents inspect heterogeneous event packages, choose compatible evidence, execute transparent calculations, reconcile source differences, and preserve provenance in the final answer. We provide executable ground truth that decomposes each task into fine-grained answer units, together with task-specific rubrics that assess the supporting research process while allowing multiple valid paths. We evaluate 25 model and agent systems under a controlled tool-using protocol, then use controlled studies to locate failures in evidence access, tool selection, memory, reasoning, interaction, and scientific execution. Across systems, the best mean answer-unit accuracy is 84.65

Time series research is moving beyond fixed forecasting benchmarks toward realistic tasks that combine prediction, contextual reasoning, tool use, and structured decision support. Most benchmarks are built around clean data and short evaluation loops; agents alone may miss temporal constraints, evidence checks, or review before finalizing outputs. We first formalize next-generation time series tasks as three-component tuples consisting of a task file, a workspace, and a validation interface. We then present AION, a time series harness built from six component groups: agents, skills, rules, memory, evaluation, and protocols. In this harness, we use three design principles: temporal grounding, temporal knowledge-grounded reasoning, and reliability mechanisms such as post-experiment analysis and layered review. A Kaggle Store Sales case study shows that the harness produces more detailed process traces, more artifacts, and more review steps than the same base agent operating in OpenCode direct build mode. Taken together, these results argue for a paradigm shift from fixed tasks to realistic ones under real-world constraints.

Global air quality forecasting grapples with extreme spatial heterogeneity and the poor generalization of existing transductive models to unseen regions. To tackle this, we propose OmniAir, a semantic topology learning framework tailored for global station-level prediction. By encoding invariant physical environmental attributes into generalizable station identities and dynamically constructing adaptive sparse topologies, our approach effectively captures long-range non-Euclidean correlations and physical diffusion patterns across unevenly distributed global networks. We further curate WorldAir, a massive dataset covering over 7,800 stations worldwide. Extensive experiments show that OmniAir achieves state-of-the-art performance against 18 baselines, maintaining high efficiency and scalability with speeds nearly 10 times faster than existing models, while effectively bridging the monitoring gap in data-sparse regions.

Time series foundation models (TSFMs) are revolutionizing the forecasting landscape from specific dataset modeling to generalizable task evaluation. However, we contend that existing benchmarks exhibit common limitations in four dimensions: constrained data composition dominated by reused legacy sources, compromised data integrity lacking rigorous quality assurance, misaligned task formulations detached from real-world contexts, and rigid analysis perspectives that obscure generalizable insights. To bridge these gaps, we introduce , a next-generation task-centric benchmark comprising 50 fresh datasets and 98 forecasting tasks, tailored for strict zero-shot TSFM evaluation free from data leakage. Integrating large language models and human expertise, we establish a rigorous human-in-the-loop benchmark construction pipeline to ensure high data integrity and redefine task formulation by aligning forecasting configurations with real-world operational requirements and variate predictability. Furthermore, we propose a novel pattern-level evaluation perspective that moves beyond traditional dataset-level evaluations based on static meta labels. By leveraging structural time series features to characterize intrinsic temporal properties, this approach offers generalizable insights into model capabilities across diverse patterns. We evaluate 12 representative TSFMs and establish a multi-granular leaderboard to facilitate in-depth analysis and visualized inspection.

LLM-driven Anomaly Detection (AD) helps enhance the understanding and explanatory abilities of anomalous behaviors in Time Series (TS). Existing methods face challenges of inadequate reasoning ability, deficient multi-turn dialogue capability, and narrow generalization. To this end, we 1) propose a multi-agent-based TS Evolution algorithm named TSEvol. On top of it, we 2) introduce the AD reasoning and multi-turn dialogue Dataset TSEData-20K and contribute the Chatbot family for AD, including ChatAD-Llama3-8B, Qwen2.5-7B, and Mistral-7B. Furthermore, 3) we propose the TS Kahneman-Tversky Optimization (TKTO) to enhance ChatAD's cross-task generalization capability. Lastly, 4) we propose a LLM-driven Learning-based AD Benchmark LLADBench to evaluate the performance of ChatAD and nine baselines across seven datasets and tasks. Our three ChatAD models achieve substantial gains, up to 34.50

Transformer-based and CNN-based methods demonstrate strong performance in long-term time series forecasting. However, their high computational and storage requirements can hinder large-scale deployment. To address this limitation, we propose integrating lightweight MLP with advanced architectures using knowledge distillation (KD). Our preliminary study reveals different models can capture complementary patterns, particularly multi-scale and multiperiod patterns in the temporal and frequency domains. Based on this observation, we introduce TimeDistill, a cross-architecture KD framework that transfers these patterns from teacher models (e.g., Transformers, CNNs) to MLP. Additionally, we provide a theoretical analysis, demonstrating that our KD approach can be interpreted as a specialized form of mixup data augmentation. TimeDistill improves MLP performance by up to 18.6%, surpassing teacher models on eight datasets. It also achieves up to 7x faster inference and requires 130x fewer parameters. Furthermore, we conduct extensive evaluations to highlight the versatility and effectiveness of TimeDistill. The code is available at Github Code Repo.