Time series forecasting is a critical and complex task, characterized by diverse temporal patterns, varying statistical properties, and different prediction horizons across datasets and domains. Conventional approaches typically rely on a single, unified model architecture to handle all forecasting scenarios. However, such monolithic models struggle to generalize across dynamically evolving time series with shifting patterns. In reality, different types of time series may require distinct modeling strategies. Some benefit from homogeneous multi-scale forecasting awareness, while others rely on more complex and heterogeneous signal perception. Relying on a single model to capture all temporal diversity and structural variations leads to limited performance and poor interpretability. To address this challenge, we propose a Multi-Agent Forecasting System (MAFS) that abandons the one-sizefits-all paradigm. MAFS decomposes the forecasting task into multiple sub-tasks, each handled by a dedicated agent trained on specific temporal perspectives (e.g., different forecasting resolutions or signal characteristics). Furthermore, to achieve holistic forecasting, agents share and refine information through different communication topology, enabling cooperative reasoning across different temporal views.

Despite impressive performance across diverse downstream forecasting tasks, existing time series FMs possess massive network architectures and require substantial pre-training on large-scale datasets, which significantly hinders their deployment in resourceconstrained environments. In response to this growing tension between versatility and affordability, we propose SEMPO, a novel lightweight foundation model that requires pretraining on relatively small-scale data, yet exhibits strong general time series forecasting. Concretely, SEMPO comprises two key modules: 1) energyaware SpEctral decomposition module, that substantially improves the utilization of pre-training data by modeling not only the high-energy frequency signals but also the low-energy yet informative frequency signals that are ignored in current methods; and 2) Mixture-of-PrOmpts enabled Transformer, that learns heterogeneous temporal patterns through small dataset-specific prompts and adaptively routes time series tokens to prompt-based experts for parameter-efficient model adaptation across different datasets and domains. Equipped with these modules, SEMPO significantly reduces both pre-training data scale and model size, while achieving strong generalization. Extensive experiments on two large-scale benchmarks covering 16 datasets demonstrate the superior performance of SEMPO in both zero-shot and few-shot forecasting scenarios compared with state-of-the-art methods. Code and data are available at https://github.com/mala-lab/SEMPO.

Spatio-temporal forecasting is crucial in many domains, such as transportation, meteorology, and energy. However, real-world scenarios frequently present challenges such as signal anomalies, noise, and distributional shifts. Existing solutions primarily enhance robustness by modifying network architectures or training procedures. Nevertheless, these approaches are computationally intensive and resourcedemanding, especially for large-scale applications. In this paper, we explore a novel test-time computing paradigm, namely learning with calibration, ST-TTC, for spatio-temporal forecasting. Through learning with calibration, we aim to capture periodic structural biases arising from non-stationarity during the testing phase and perform real-time bias correction on predictions to improve accuracy. Specifically, we first introduce a spectral-domain calibrator with phase-amplitude modulation to mitigate periodic shift and then propose a flash updating mechanism with a streaming memory queue for efficient test-time computation.

Spatio-temporal forecasting is essential for real-world applications such as traffic management and urban computing. Although recent methods have shown improved accuracy, they often fail to account for dynamic deviations between current inputs and historical patterns. These deviations contain critical signals that can significantly affect model performance. To fill this gap, we propose STSSDL, a Spatio-Temporal time series forecasting framework that incorporates a Self-Supervised Deviation Learning scheme to capture and utilize such deviations. ST-SSDL anchors each input to its historical average and discretizes the latent space using learnable prototypes that represent typical spatio-temporal patterns. Two auxiliary objectives are proposed to refine this structure: a contrastive loss that enhances inter-prototype discriminability and a deviation loss that regularizes the distance consistency between input representations and corresponding prototypes to quantify deviation. Optimized jointly with the forecasting objective, these components guide the model to organize its hidden space and improve generalization across diverse input conditions. Experiments on six benchmark datasets show that ST-SSDL consistently outperforms state-of-the-art baselines across multiple metrics. Visualizations further demonstrate its ability to adaptively respond to varying levels of deviation in complex spatio-temporal scenarios.

Time series analysis provides essential insights for real-world system dynamics and informs downstream decision-making, yet most existing methods often overlook the rich contextual signals present in auxiliary modalities. To bridge this gap, we introduce TimeXL, a multi-modal prediction framework that integrates a prototypebased time series encoder with three collaborating Large Language Models (LLMs) to deliver more accurate predictions and interpretable explanations. First, a multimodal prototype-based encoder processes both time series and textual inputs to generate preliminary forecasts alongside case-based rationales. These outputs then feed into a prediction LLM, which refines the forecasts by reasoning over the encoder's predictions and explanations. Next, a reflection LLM compares the predicted values against the ground truth, identifying textual inconsistencies or noise. Guided by this feedback, a refinement LLM iteratively enhances text quality and triggers encoder retraining. This closed-loop workflow--prediction, critique (reflect), and refinement--continuously boosts the framework's performance and interpretability. Empirical evaluations on four real-world datasets demonstrate that TimeXL achieves up to 8.9% improvement in AUC and produces human-centric, multi-modal explanations, highlighting the power of LLM-driven reasoning for time series prediction.

This paper is concerned with online time series forecasting, where unknown distribution shifts occur over time, i.e., latent variables influence the mapping from historical to future observations. To develop an automated way of online time series forecasting, we propose a Theoretical framework for Online Time-series forecasting (TOT in short) with theoretical guarantees. Specifically, we prove that supplying a forecaster with latent variables tightens the Bayes risk--the benefit endures under estimation uncertainty of latent variables and grows as the latent variables achieve a more precise identifiability. To better introduce latent variables into online forecasting algorithms, we further propose to identify latent variables with minimal adjacent observations. Based on these results, we devise a modelagnostic blueprint by employing a temporal decoder to match the distribution of observed variables and two independent noise estimators to model the causal inference of latent variables and mixing procedures of observed variables, respectively. Experiment results on synthetic data support our theoretical claims. Moreover, plugin implementations built on several baselines yield general improvement across multiple benchmarks, highlighting the effectiveness in real-world applications.

Recent studies reveal that Large Language Models (LLMs) exhibit strong sequential reasoning capabilities, allowing them to replace specialized time-series models and serve as foundation models for complex time-series analysis. To activate the capabilities of LLMs for time-series tasks, numerous studies have attempted to bridge the gap between time series and linguistics by aligning textual representations with time-series patterns. However, it is a non-trivial endeavor to losslessly capture the infinite time-domain variability using natural language, leading to suboptimal alignment performance. Beyond representation, contextual differences, where semantics in time series are conveyed by consecutive points, unlike in text by individual tokens, are often overlooked by existing methods. To address these, we propose S2TS-LLM, a simple yet effective framework to repurpose LLMs for universal time series analysis through the following two main paradigms: (i) a spectral symbolization paradigm transforms time series into frequency-domain representations characterized by a fixed number of components and prominent amplitudes, which enables a limited set of symbols to effectively abstract key frequency features; (ii) a contextual segmentation paradigm partitions the sequence into blocks based on temporal patterns and reassigns positional encodings accordingly, thereby mitigating the structural mismatch between time series and natural language.

Time series data is ubiquitous, with forecasting applications spanning from finance to healthcare. Beyond popular deterministic methods, generative models are gaining attention due to advancements in areas like image synthesis and video generation, as well as their inherent ability to provide probabilistic predictions. However, existing generative approaches mostly involve recurrent generative operations or repeated denoising steps, making the prediction laborious, particularly for long-term forecasting. Most of them only conduct experiments for relatively short-term forecasting, with limited comparison to deterministic methods in long-term forecasting, leaving their practical advantages unclear. This paper presents TARFVAE, a novel generative framework that combines the Transformer-based autoregressive flow (TARFLOW) and variational autoencoder (VAE) for efficient one-step generative time series forecasting.

Multivariate time series (MTS) classification has attracted increasing attention across various domains. Existing methods either decompose MTS into separate univariate series, ignoring inter-variable dependencies, or jointly model all variables, which may lead to over-smoothing and loss of semantic structure. These limitations become particularly pronounced when dealing with complex and heterogeneous variable types. To address these challenges, we propose SwinGroupNet (SGN), which explores a novel perspective for constructing variable interaction and temporal dependency. Specifically, SGN processes multi-scale time series using (1) Variable Group Embedding (VGE), which partitions variables into groups and performs independent group-wise embedding; (2) Multi-Scale Group Window Mixing (MGWM), which reconstructs variable interactions by modeling both intra-group and inter-group dependencies while extracting multi-scale temporal features; and (3) Periodic Window Shifting and Merging (PWSM), which exploits inherent periodic patterns to enable hierarchical temporal interaction and feature aggregation. Extensive experiments on diverse benchmark datasets from multiple domains demonstrate that SGN consistently achieves state-of-the-art performance, with an average improvement of 4.2% over existing methods. We release the source code at https://github.com/colison/SGN.

Time series forecasting plays a pivotal role in critical domains such as energy management and financial markets. Although deep learning-based approaches (e.g., MLP, RNN, Transformer) have achieved remarkable progress, the prevailing "longsequence information gain hypothesis" exhibits inherent limitations. Through systematic experimentation, this study reveals a counterintuitive phenomenon: appropriately truncating historical data can paradoxically enhance prediction accuracy, indicating that existing models learn substantial redundant features (e.g., noise or irrelevant fluctuations) during training, thereby compromising effective signal extraction. Building upon information bottleneck theory, we propose an innovative solution termed Adaptive Masking Loss with Representation Consistency (AMRC), which features two core components: 1) Dynamic masking loss, which adaptively identified highly discriminative temporal segments to guide gradient descent during model training; 2) Representation consistency constraint, which stabilized the mapping relationships among inputs, labels, and predictions. Experimental results demonstrate that AMRC effectively suppresses redundant feature learning while significantly improving model performance. This work not only challenges conventional assumptions in temporal modeling but also provides novel theoretical insights and methodological breakthroughs for developing efficient and robust forecasting models. We have made our code available at https://github.com/MazelTovy/AMRC.