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Yimiao Shao, Wenzhong Li, Kang Xia, Kaijie Lin, Mingkai Lin, Sanglu Lu

Probabilistic time series forecasting has attracted an increasing attention in machine learning community for its potential applications in the fields of renewable energy, traffic management, healthcare, etc. Previous research mainly focused on extracting long-range dependencies for point-wise prediction, which fail to capture complex temporal patterns and statistical characteristics for probabilistic analysis. In this paper, we propose a novel pattern-mixture decomposition method that decomposes long-term series into quantile drift, divergence patterns, and Gaussian mixture components, which can effectively capture the intricate temporal patterns and stochastic characteristics in time series. Based on pattern-mixture decomposition, we propose a novel Transformer-based model called QuantileFormer for probabilistic time series forecasting. It takes the the comprehensive drift-divergence mixture patterns as features, and designs a variational inference based fusion Transformer architecture to generate quantile prediction results. Extensive experiments show that the proposed method consistently boosts the baseline methods by a large margin and achieves state-of-the-art performance on six real-world benchmarks.

Kijeong Park, Sungchul Hong, Jong-June Jeon

In stock price forecasting, modeling the probabilistic dependence between stock prices within a time-series framework has remained a persistent and highly challenging area of research. We propose a novel model to explain the extreme co-movement in multivariate data with time-series dependencies. Our model incorporates a Hawkes process layer to capture abrupt co-movements, thereby enhancing the temporal representation of market dynamics. We introduce dynamic hypergraphs into our model adapting to higher-order (groupwise rather than pairwise) relationships within the stock market. Extensive experiments on real-world benchmarks demonstrate the robustness of our approach in predictive performance and portfolio stability.

Qihong Pan, Haofei Tan, Guojiang Shen, Xiangjie Kong, Mengmeng Wang, Chenyang Xu

Large language models have demonstrated remarkable generalization capabilities and strong performance across various fields. Recent research has highlighted their significant potential in time series forecasting. However, time series data often exhibit complex periodic characteristics, posing a substantial challenge in enabling these models to effectively capture latent patterns. To address this challenge, we propose a novel framework, LLM-TPF, which leverages individuality and commonality fusion to enhance time series forecasting. In the frequency domain, periodic features are extracted to reveal the intrinsic periodicity of the data, while textual prototypes are used to indicate temporal trends. In the time domain, carefully designed prompts are employed to guide the models in comprehending global information. A commonality fusion mechanism further aggregates heterogeneous information across dimensions, and three distinct language models are utilized to independently process different types of information. Extensive real-world experiments demonstrate that LLM-TPF is a powerful tool for time series forecasting, achieving superior performance compared to state-of-the-art specialized models and exhibiting exceptional generalization ability in zero-shot scenarios. Code is available at https://github.com/switchsky/LLM-TPF.

Xinhong Liu, Xiaoliang Li, Yangfan Li, Fengxiao Tang, Ming Zhao

Anomaly detection in multivariate time series data is critical across a variety of real-life applications. The predominant anomaly detection techniques currently rely on reconstruction-based methods. However, these methods often overfit the abnormal pattern and fail to diagnose the anomaly. Although some studies have attempted to prevent the incorrect fitting of anomalous data by enabling models to learn the trend of data variations, they fail to account for the dynamic nature of data distribution. This oversight can lead to the erroneous reconstruction of anomalies that do not exist. To address these challenges, we propose RTdetector, a Transformer-based time series anomaly detection model leveraging reconstruction trends. RTdetector employs a novel global attention mechanism based on reconstruction trends to learn distinguishable attention from the original sequence, thereby preserving the global trend information intrinsic to the time series. Additionally, it incorporates a self-conditioning transformer, based on reconstruction trend enhancement to achieve superior predictive performance. Extensive experiments on four datasets demonstrate that RTdetector achieves state-of-the-art results in multivariate time series data anomaly detection. Our code is available at https://github.com/CSUFUNLAB/RTdetector.

Xinhui Li, Liang Duan, Lixing Yu, Kun Yue, Yuehua Li

Multivariate time series (MTS) forecasting endeavors to anticipate the forthcoming sequence of interdependent variables through the utilization of past observations. The prevailing methodologies, relying on deep neural networks, Transformer, or information bottleneck frameworks, persist in confronting challenges such as overlooking or inadequately capturing the inter / intra-series correlations evident in practical MTS datasets. In response to these challenges, we introduce a conditional information bottleneck-based strategy for MTS forecasting, grounded in information theory. Initially, we establish a conditional information bottleneck principle to capture the inter-series correlations via conditioning on non-target variables. Subsequently, a conditional mutual information-based technique is introduced to extract intra-series correlations by conditioning historical data, ensuring temporal consistency within each variable. Lastly, we devise a unified optimization objective and propose a training algorithm to collectively capture inter / intra-series correlations. Empirical investigations on authentic datasets underscore the superiority of our proposed approach over other cutting-edge competitors. Our code is available at https: //github.com/Xinhui-Lee/CIB-MTSF.

Minhyuk Lee, Hyekyung Yoon, MyungJoo Kang

Multivariate long-term time series forecasting is critical for applications such as weather prediction, and traffic analysis. In addition, the implementation of Transformer variants has improved prediction accuracy. Following these variants, different input data process approaches also enhanced the field, such as tokenization techniques including point-wise, channel-wise, and patch-wise tokenization. However, previous studies still have limitations in time complexity, computational resources, and cross-dimensional interactions. To address these limitations, we introduce a novel CNN Autoencoder-based Score Attention mechanism (CASA), which can be introduced in diverse Transformers model-agnosticically by reducing memory and leading to improvement in model performance. Experiments on eight real-world datasets validate that CASA decreases computational resources by up to 77.7%, accelerates inference by 44.0%, and achieves state-of-the-art performance, ranking first in 87.5% of evaluated metrics. Our code is available at https://github.com/lmh9507/CASA.

Chen Hu, Rui Wang, Xiaoning Song, Tao Zhou, Xiao-Jun Wu, Nicu Sebe, Ziheng Chen

Riemannian neural networks, which generalize the deep learning paradigm to non-Euclidean geometries, have garnered widespread attention across diverse applications in artificial intelligence. Among these, the representative attention models have been studied on various non-Euclidean spaces to geometrically capture the spatiotemporal dependencies inherent in time series data, e.g., electroencephalography (EEG). Recent studies have highlighted the full-rank correlation matrix as an advantageous alternative to the covariance matrix for data representation, owing to its invariance to the scale of variables. Motivated by these advancements, we propose the Correlation Attention Network (CorAtt) tailored for full-rank correlation matrices and implement it under the permutation-invariant and computationally efficient Off-Log and Log-Scaled geometries, respectively. Extensive evaluations on three benchmarking EEG datasets provide substantial evidence for the effectiveness of our introduced CorAtt. The code and supplementary material can be found at https://github.com/ChenHu-ML/CorAtt.

Yunfeng Ge, Jiawei Li, Yiji Zhao, Haomin Wen, Zhao Li, Meikang Qiu, Hongyan Li, Ming Jin, Shirui Pan

Text-to-Time Series generation holds significant potential to address challenges such as data sparsity, imbalance, and limited availability of multimodal time series data across domains. While diffusion models have achieved remarkable success in Text-to-X (e.g., vision and audio data) generation, their use in time series generation remains limit. Existing approaches face two critical limitations: (1) reliance on domain-specific captions that generalize poorly, and (2) inability to generate time series of arbitrary length, limiting real-world use. In this work, we first introduce a new multimodal dataset containing over 600,000 high-resolution text-time series pairs. Second, we propose Text-to-Series (T2S), a diffusion-based framework that bridges the gap between natural language and time series in a domain-agnostic manner. It employs a length-adaptive VAE to encode time series of varying lengths into consistent latent embeddings. On top of that, T2S effectively aligns textual representations with latent embeddings by utilizing Flow Matching and employing DiT as the denoiser. We train T2S in an interleaved paradigm across multiple lengths, allowing it to generate sequences of arbitrary lengths. Extensive evaluations demonstrate that T2S achieves state-of-the-art performance across 13 datasets spanning 12 domains.

Mingyue Cheng, Jintao Zhang, Zhiding Liu, Chunli Liu

Intraoperative hypotension (IOH) prediction using past physiological signals is crucial, as IOH may lead to inadequate organ perfusion and significantly elevate the risk of severe complications and mortality. However, current methods often rely on static modeling, overlooking the complex temporal dependencies and the inherently non-stationary nature of physiological signals. We propose a Hybrid Multi-Factor (HMF) network that formulates IOH prediction as a dynamic sequence forecasting task, explicitly capturing both temporal dependencies and physiological non-stationarity. We represent signal dynamics as multivariate time series and decompose them into trend and seasonal components, enabling separate modeling of long-term and periodic variations. Each component is encoded with a patch-based Transformer to balance computational efficiency and feature representation. To address distributional drift from evolving signals, we introduce a symmetric normalization mechanism. Experiments on both public and real-world clinical datasets show that HMF significantly outperforms competitive baselines. We hope HMF offers new insights into IOH prediction and ultimately promotes safer surgical care. Our code is available at https://github.com/Mingyue-Cheng/HMF.

Weiqi Chen, Zhaoyang Zhu, Yifan Zhang, Lefei Shen, Linxiao Yang, Qingsong Wen, Liang Sun

The inherent non-stationarity of time series in practical applications poses significant challenges for accurate forecasting. This paper tackles the concept drift problem where the underlying distribution or environment of time series changes. To better describe the characteristics and effectively model concept drifts, we first classify them into macro-drift (stable, long-term changes) and micro-drift (sudden, short-term fluctuations). Next, we propose a unified meta-learning framework called LEAF (Learning to Extrapolate and Adjust for Forecasting), where an extrapolation module is first introduced to track and extrapolate the prediction model in latent space considering macro-drift, and then an adjustment module incorporates meta-learnable surrogate loss to capture sample-specific micro-drift patterns. LEAF’s dual-stage approach effectively addresses diverse concept drifts and is model-agnostic which can be compatible with any deep prediction model. We further provide theoretical analysis to justify why the proposed framework can handle macro-drift and micro-drift. To facilitate further research in this field, we release three electric load time series datasets collected from real-world scenarios, exhibiting diverse and typical concept drifts. Extensive experiments on multiple datasets demonstrate the effectiveness of LEAF.

Ruichu Cai, Kaitao Zheng, Junxian Huang, Zijian Li, Zhengming Chen, Boyan Xu, Zhifeng Hao

Time series imputation is one of the most challenging problems and has broad applications in various fields like health care and the Internet of Things. Existing methods mainly aim to model the temporally latent dependencies and the generation process from the observed time series data. In real-world scenarios, different types of missing mechanisms, like MAR (Missing At Random) and MNAR (Missing Not At Random), can occur in time series data. However, existing methods often overlook the difference among the aforementioned missing mechanisms and use a single model for time series imputation, which can easily lead to misleading results due to mechanism mismatching. In this paper, we propose a framework for the time series imputation problem by exploring Different Missing Mechanisms (DMM in short) and tailoring solutions accordingly. Specifically, we first analyze the data generation processes with temporal latent states and missing cause variables for different mechanisms. Sequentially, we model these generation processes via variational inference and estimate prior distributions of latent variables via a normalizing flow-based neural architecture. Furthermore, we establish identifiability results under the nonlinear independent component analysis framework to show that latent variables are identifiable. Experimental results show that our method surpasses existing time series imputation techniques across various datasets with different missing mechanisms, demonstrating its effectiveness in real-world applications.

Nasim Baharisangari, Yucheng Ruan, Chengcheng Zhao, Zhe Xu

Causal discovery in time-series datasets is critical for understanding complex systems, especially when the \textit{effectiveness} of causal relationships depends on both the \textit{duration} and \textit{magnitude} of the cause. We introduce a novel framework for causal discovery based on \textbf{Signal Temporal Logic (STL)}, enabling the extraction of interpretable causal diagrams (STL-CD) that explicitly capture these temporal dynamics. Our method first identifies statistically meaningful time intervals, then infers STL formulas that classify system behaviors, and finally employs transfer entropy to determine direct causal relationships among the formulas. This approach not only uncovers causal structure but also identifies the temporal persistence required for causal influence—an insight missed by existing methods. Experimental results on synthetic and real-world datasets demonstrate that our method achieves superior structural accuracy over state-of-the-art baselines, providing more informative and temporally precise causal models.

Yudong Zhang, Zhaoyang Sun, Xu Wang, Xuan Yu, Kai Wang, Yang Wang

Current spatio-temporal modeling techniques largely rely on the abundant data and the design of task-specific models. However, many cities lack well-established digital infrastructures, making data scarcity and the high cost of model development significant barriers to application deployment. Therefore, this work aims to enable spatio-temporal learning to cope with the problems of few-shot data modeling and model generalizability. To this end, we propose a Universal Spatio-Temporal Correlationship pre-training framework (USTC), for spatio-temporal modeling across different cities and tasks. To enhance the spatio-temporal representations during pre-training, we propose to decouple the time-frequency patterns within data, and leverage contrastive learning to maintain the time-frequency consistency. To further improve the adaptability to downstream tasks, we design a prompt generation module to mine personalized spatio-temporal patterns on the target city, which can be integrated with the learned common spatio-temporal representations to collaboratively serve downstream tasks. Extensive experiments conducted on real-world datasets demonstrate that USTC significantly outperforms the advanced baselines in forecasting, imputation, and extrapolation across cities.

Huanyao Zhang, Jiaye Lin, Wentao Zhang, Haitao Yuan, Guoliang Li

Multivariate time series forecasting involves predicting future values based on historical observations. However, existing approaches primarily rely on predefined single-scale patches or lack effective mechanisms for multi-scale feature fusion. These limitations hinder them from fully capturing the complex patterns inherent in time series, leading to constrained performance and insufficient generalizability. To address these challenges, we propose a novel architecture named Adaptive Weighted Mixture of Multi-Scale Expert Transformers (AdaMixT). Specifically, AdaMixT introduces various patches and leverages both General Pre-trained Models (GPM) and Domain-specific Models (DSM) for multi-scale feature extraction. To accommodate the heterogeneity of temporal features, AdaMixT incorporates a gating network that dynamically allocates weights among different experts, enabling more accurate predictions through adaptive multi-scale fusion. Comprehensive experiments on eight widely used benchmarks, including Weather, Traffic, Electricity, ILI, and four ETT datasets, consistently demonstrate the effectiveness of AdaMixT in real-world scenarios.

Wenzhen Yue, Yong Liu, Xianghua Ying, Bowei Xing, Ruohao Guo, Ji Shi

This paper presents FreEformer, a simple yet effective model that leverages a Frequency Enhanced Transformer for multivariate time series forecasting. Our work is based on the assumption that the frequency spectrum provides a global perspective on the composition of series across various frequencies and is highly suitable for robust representation learning. Specifically, we first convert time series into the complex frequency domain using the Discrete Fourier Transform (DFT). The Transformer architecture is then applied to the frequency spectra to capture cross-variate dependencies, with the real and imaginary parts processed independently. However, we observe that the vanilla attention matrix exhibits a low-rank characteristic, thus limiting representation diversity. To address this, we enhance the vanilla attention mechanism by introducing an additional learnable matrix to the original attention matrix, followed by row-wise L1 normalization. Theoretical analysis demonstrates that this enhanced attention mechanism improves both feature diversity and gradient flow. Extensive experiments demonstrate that FreEformer consistently outperforms state-of-the-art models on eighteen real-world benchmarks covering electricity, traffic, weather, healthcare and finance. Notably, the enhanced attention mechanism also consistently improves the performance of state-of-the-art Transformer-based forecasters. Code is available at https://anonymous.4open.science/r/FreEformer.

Min Yang, Yang An, Jinliang Deng, Xiaoyu Li, Bin Xu, Ji Zhong, Xiankai Lu, Yongshun Gong

Spatio-temporal data mining is crucial for decision-making and planning in diverse domains. However, in real-world scenarios, training and testing data are often not independent or identically distributed due to rapid changes in data distributions over time and space, resulting in spatio-temporal out-of-distribution (OOD) challenges. This non-stationarity complicates accurate predictions and has motivated research efforts focused on mitigating non-stationarity through normalization operations. Existing methods, nonetheless, often address individual time series in isolation, neglecting correlations across series, which limits their capacity to handle complex spatio-temporal dynamics and results in suboptimal solutions. To overcome these challenges, we propose Clustering Adaptive Normalization (CAN-ST), a general and model-agnostic method that mitigates non-stationarity by capturing both localized distributional changes and shared patterns across nodes via adaptive clustering and a parameter register. As a plugin, CAN-ST can be easily integrated into various spatio-temporal prediction models. Extensive experiments on multiple datasets with diverse forecasting models demonstrate that CAN-ST consistently improves performance by over 20% on average and outperforms state-of-the-art normalization methods.

Han Yan, Dongliang Chen, Guiyuan Jiang, Bin Wang, Lei Cao, Junyu Dong, Yanwei Yu

Multivariate time series forecasting is a critical focus across many fields. Existing transformer-based models have overlooked the explicit modeling of inter-variable correlations. Similarly, the graph-based methods have also failed to address the dynamic nature of multivariate correlations and the noise in correlation modeling. To overcome these challenges, we propose a novel Dynamic Graph Learning Guided Multi-Scale Transformer (DGraFormer) for multivariate time series forecasting. Specifically, our method consists of two main components: Dynamic correlation-aware graph Learning (DCGL) and multi-scale temporal transformer (MTT). The former aims to capture dynamic correlations across different time windows, filters out noise, and selects key weights to guide the aggregation of relevant feature representations. The latter can effectively extract temporal patterns from patch data at varying scales. Finally, the proposed method can capture rich local correlation graph structures and multi-scale global temporal features. Experimental results demonstrate that DGraformer significantly outperforms existing state-of-the-art models on ten real-world datasets, achieving the best performance across multiple evaluation metrics. The source code of our model is available at \url{https://anonymous.4open.science/r/DGraFormer}.

Wenchao Weng, Hanyu Jiang, Mei Wu, Xiao Han, Haidong Gao, Guojiang Shen, Xiangjie Kong

Spatio-temporal graph modeling is widely applied to spatio-temporal data, analyzing the relationships between data to achieve accurate predictions. However, despite the excellent predictive performance of increasingly complex models, their intricate architectures result in significant memory overhead and computational complexity when handling spatio-temporal data, which limits their practical applications. To address these challenges, we propose a plug-and-play SubGraph Learning (SGL) method to reduce the memory overhead without compromising performance. Specifically, we introduce a SubGraph Partition Module (SGPM), which leverages a set of learnable memory vectors to select node groups with similar features from the graph, effectively partitioning the graph into smaller subgraphs. Noting that partitioning the graph may lead to feature redundancy, as overlapping information across subgraphs can occur. To overcome this, we design a SubGraph Feature Aggregation Module (SGFAM), which mitigates redundancy by averaging node features from different subgraphs. Experiments on four traffic network datasets of various scales demonstrate that SGL can significantly reduce memory overhead, achieving up to a 56.4\% reduction in average GPU memory overhead, while maintaining robust prediction performance. The source code is available at https://github.com/wengwenchao123/SubGraph-Learning.

Shunnan Wang, Min Gao, Zongwei Wang, Yibing Bai, Feng Jiang, Guansong Pang

Large Language Models (LLMs) have recently shown promise in Time Series Forecasting (TSF) by effectively capturing intricate time-domain dependencies. However, our preliminary experiments reveal that standard LLM-based approaches often fail to capture global correlations, limiting predictive performance. We found that embedding frequency-domain signals smooths weight distributions and enhances structured correlations by clearly separating global trends (low-frequency components) from local variations (high-frequency components). Building on these insights, we propose FreqLLM, a novel framework that integrates frequency-domain semantic alignment into LLMs to refine prompts for improved time series analysis. By bridging the gap between frequency signals and textual embeddings, FreqLLM effectively captures multi-scale temporal patterns and provides more robust forecasting results. Extensive experiments on benchmark datasets demonstrate that FreqLLM outperforms state-of-the-art TSF methods in both accuracy and generalization. The code is available at https://github.com/biya0105/FreqLLM.

Hao Wang, Jindong Han, Wei Fan, Leilei Sun, Hao Liu

Spatio-temporal forecasting is pivotal in numerous real-world applications, including transportation planning, energy management, and climate monitoring. In this work, we aim to harness the reasoning and generalization abilities of Pre-trained Language Models (PLMs) for more effective spatio-temporal forecasting, particularly in data-scarce scenarios. However, recent studies uncover that PLMs, which are primarily trained on textual data, often falter when tasked with modeling the intricate correlations in numerical time series, thereby limiting their effectiveness in comprehending spatio-temporal data. To bridge the gap, we propose RePST, a semantic-oriented PLM reprogramming framework tailored for spatio-temporal forecasting. Specifically, we first propose a semantic-oriented decomposer that adaptively disentangles spatially correlated time series into interpretable sub-components, which facilitates PLM to understand sophisticated spatio-temporal dynamics via a divide-and-conquer strategy. Moreover, we propose a selective discrete reprogramming scheme, which introduces an expanded spatio-temporal vocabulary space to project spatio-temporal series into discrete representations. This scheme minimizes the information loss during reprogramming and enriches the representations derived by PLMs. Extensive experiments on real-world datasets show that the proposed RePST outperforms twelve state-of-the-art baseline methods, particularly in data-scarce scenarios, highlighting the effectiveness and superior generalization capabilities of PLMs for spatio-temporal forecasting. Codes and Appendix can be found at https://github.com/usail-hkust/REPST.