time series analysis

Addressing challenges in multivariate time series visualization—including difficulty identifying dynamic patterns, integrating heterogeneous analytical tools, and interpreting temporal component effects—this paper systematically reviews existing approaches and proposes design principles that unify dynamic evolutionary modeling with multidimensional visual encoding. Leveraging theories from information visualization, temporal data analysis, and human–computer interaction, we develop an interpretable visual analytics framework supporting overview–drilldown–validation workflows. Our contributions are threefold: (1) We expose structural limitations of mainstream tools in representing time-varying features; (2) We establish a dual-driven visualization design paradigm grounded in perceptual mechanisms and analytical tasks; and (3) We distill a reusable theoretical framework and practical guidelines, while explicitly identifying three open research directions for next-generation intelligent time-series visualization systems.

This work addresses the limited time-series modeling capability of large language models (LLMs) stemming from their text-only pretraining. We propose a systematic cross-modal alignment framework specifically designed for time-series analysis. Our approach innovatively introduces a four-category taxonomy of time-series-oriented textual data, systematically synthesizes cross-modal alignment, feature fusion, and joint encoding strategies, and validates effectiveness through prompt engineering and multi-domain benchmarking on forecasting and anomaly detection tasks. Results demonstrate substantial improvements in LLMs’ understanding and generalization over time-series data; uncover principled mappings between textual data types and optimal modeling strategies; and identify key research directions—including scalable architectures and domain-adaptive learning. This study provides both theoretical foundations and practical methodologies for empowering LLMs with robust time-series analytics capabilities.

This work proposes an interactive visual analytics approach to address the challenges of visual clutter and redundancy in large-scale time series visualization, which often obscure critical trends. By integrating M4 sampling, dynamic time warping (DTW) similarity computation, and a greedy selection strategy, the method automatically identifies a representative subset of time series that preserves essential patterns while minimizing redundancy. A coordinated multi-view visualization framework further enables users to efficiently explore and interpret the data. The proposed technique significantly enhances visual clarity, interpretability, and analytical efficiency without sacrificing the core temporal characteristics of the original dataset.

Evaluating interpretability in time series classification (TSC) remains challenging due to the lack of principled metrics for assessing simplification-based explanations. Method: We propose a novel complexity–fidelity dual-dimensional metric—formally defining and quantifying the trade-off between simplification fidelity and interpretability—and conduct systematic benchmarking across mainstream TSC models (ROCKET, TSF, InceptionTime) and heterogeneous UCR/UEA datasets using piecewise linear and symbolic simplification techniques. Contribution/Results: Our analysis identifies seasonality, non-stationarity, and low entropy as key determinants of simplification efficacy. Empirical results demonstrate that simplified sequences substantially enhance interpretability utility, achieving up to 23.6% improvement in classification fidelity on sequences exhibiting these characteristics. This work establishes the first reproducible, model-agnostic, and dataset-agnostic evaluation paradigm for TSC interpretability.

Traditional time-series models suffer from poor generalization and strong task specificity, hindering unified support for diverse tasks such as forecasting, classification, and anomaly detection. To address this, we propose the Time-Series Pattern Machine (TSPM), a novel universal architecture featuring Multi-Resolution Time Imaging (MRTI) and a dual-domain (time–frequency) hybrid design. TSPM integrates multi-scale time imaging, bi-axial attention decomposition, and cross-scale/resolution mixing to enable task-adaptive deep pattern extraction. For the first time, a single model achieves state-of-the-art (SOTA) performance across eight canonical time-series tasks—surpassing both general-purpose and task-specific baselines with substantial average metric gains. This work breaks down task-specific barriers in time-series modeling and empirically validates the effectiveness and scalability of universal pattern learning as a paradigm.

Dynamic Time Warping (DTW) is commonly reduced to a scalar distance, discarding rich geometric and structural information embedded in the alignment path. Method: We propose Warp Quantification Analysis (WQA), the first multidimensional, structured metric framework grounded in DTW paths, which extracts interpretable geometric descriptors—such as path curvature, compression ratio, and local lag—that orthogonally capture distinct nonlinear temporal alignment characteristics. Contribution/Results: Through controlled simulations, we validate descriptor specificity; applied to large-scale fMRI data, WQA identifies schizophrenia-negative-symptom-specific alterations in brain network coupling—significantly correlated with clinical severity—undetectable by conventional DTW distance. WQA preserves computational compatibility with standard DTW implementations while substantially enhancing sensitivity, interpretability, and clinical traceability of time-series alignment analysis.

Existing time-series analysis models are restricted to numeric modalities and struggle to incorporate domain-specific textual knowledge, resulting in limited modeling capacity and a lack of high-quality multimodal benchmarks. To address this, we introduce Time-MMD—the first large-scale multimodal time-series dataset spanning nine diverse domains—featuring fine-grained semantic alignment between numeric sequences and domain-specific textual descriptions. We further propose a multi-domain multimodal time-series benchmark that systematically tackles modality contamination and the absence of cross-modal alignment. Additionally, we open-source MM-TSFlib, the first modular library for multimodal time-series forecasting, enabling joint modeling and granular evaluation. Experiments demonstrate that our approach reduces average MSE by over 15% on multimodal forecasting tasks, with gains reaching 40% in text-rich scenarios. This work advances time-series analysis from unimodal paradigms toward human-AI collaborative multimodal reasoning. Code and data are publicly available.

This work addresses the challenges of capturing local dynamics and modeling global periodic structures in irregular multivariate time series, which arise from non-uniform sampling and asynchronous variables. To this end, we propose TFMixer, a novel framework that enables end-to-end joint time–frequency modeling for the first time. TFMixer introduces a learnable non-uniform discrete Fourier transform (NUDFT) to directly handle irregular sampling, integrates a query-driven temporal patch mixing mechanism to adaptively aggregate local information, and explicitly extrapolates seasonal components via an inverse NUDFT. The final prediction is derived by fusing representations from both time and frequency domains. Extensive experiments on multiple real-world datasets demonstrate that TFMixer significantly outperforms existing methods, achieving state-of-the-art performance.

This study addresses the challenges of modeling and analyzing complex time series arising in astrophysics, meteorology, finance, and other domains by systematically integrating classical statistical methods—such as ARIMA, exponential smoothing, and state-space models—with modern machine learning techniques, including tree-based ensembles, hidden Markov models, Gaussian processes, and deep learning architectures like RNNs, CNNs, and Transformers. By distilling cross-disciplinary modeling principles, the work establishes a unified framework that combines theoretical rigor with practical guidance, offering researchers a comprehensive and extensible toolkit for time series analysis. This approach significantly enhances the capacity to handle temporal data across diverse scientific and applied contexts.

This study systematically investigates the frequency-domain encoding capabilities of the Chronos foundation model, addressing a critical gap in understanding how such models represent fundamental signal properties. Through controlled experiments using discrete sinusoidal signals and a lightweight online Minimum Description Length (MDL) probing framework, the work examines the existence, separability, and cross-spectral fidelity of internal frequency representations within the Chronos decoder. The research reveals, for the first time, a degradation in representation quality in high-frequency regions, thereby delineating both the strengths and limitations of Chronos’s frequency encoding mechanism. These findings offer novel insights into the interpretability of time-series foundation models and provide practical guidance for applications in signal processing and multimodal fusion.

Existing time series question answering (QA) benchmarks are largely confined to forecasting and anomaly detection, offering limited capacity to comprehensively evaluate a model’s temporal reasoning capabilities. To address this gap, this work proposes TSAQA—a unified, multi-task time series QA benchmark encompassing six task categories: anomaly detection, classification, feature characterization, comparison, data transformation, and temporal relationship analysis. TSAQA comprises 210,000 structured QA pairs spanning 13 domains and introduces novel QA formats including true/false, multiple-choice, and puzzle-style questions. The benchmark supports both zero-shot and instruction-tuning evaluation paradigms and is compatible with standard large language model (LLM) testing pipelines. Experimental results reveal that even the strongest commercial model, Gemini-2.5-Flash, achieves only a 65.08 average score under zero-shot settings, while fine-tuned open-source models like LLaMA-3.1-8B still exhibit substantial room for improvement, underscoring the inherent challenges of temporal understanding for current LLMs.

Existing multimodal time series methods often suffer from excessive smoothing in non-stationary environments, overlooking critical fluctuations and consequently distorting forecast shapes. To address this limitation, this work proposes the STaT architecture, which for the first time enables collaborative modeling across symbolic, temporal, and textual modalities. The symbolic modality captures structural turning points through discretization, the temporal modality models dynamic dependencies, and the textual modality injects domain knowledge to guide macro-level trends. Through a carefully designed multimodal alignment mechanism, STaT significantly enhances shape fidelity while maintaining high prediction accuracy. Empirical evaluation on eight real-world benchmarks demonstrates that STaT improves overall performance by 8.9% on average and reduces shape distortion by up to 8.5%.