Multivariate Time Series Forecasting

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46 papers in the last four weeks, up 39% on the four weeks before. 0.3% of all new papers.

Jul 13Week of Sep 28

Latest papers 223

Sep 1, 2026cs.LG

When Does Online Adaptation Pay on the Edge? A Leakage-Free Evaluation of Warmup, Learning-Rate Selection, and Resource Trade-offs for Time-Series Forecasting

Online adaptation can help edge time-series forecasting under distribution drift, but its measured benefit is sensitive to evaluation choices. We study six public multivariate streams, including building-sensor and smart-meter data, under a leakage-free streaming protocol. We identify two additional sources of comparison bias. First, the warmup budget of the static baseline has a two-sided effect: insufficient warmup undertrains the baseline, whereas excessive warmup can degrade its pre-drift generalization. Across six dataset-backbone settings, the estimated adaptation benefit changes by 3.0 to 18.8 percentage points (pp) over the 1,000-20,000-step warmup range. Second, comparing SGD with momentum (SGD+m) and Adam at a shared default learning rate conflates optimizer quality with rate sensitivity. We select both the warmup budget and each optimizer's online rate using a held-out pre-drift validation slice without accessing test data. Under this validation-only procedure, Adam outperforms SGD+m in 310 of 360 evaluated cells, while 4 Adam cells remain below the static baseline. We further characterize accuracy against adaptation-state memory and A100-measured per-update latency for full, head-only, and calibration-based adaptation. In the evaluated PatchTST frontier settings, several parameter-efficient variants are nondominated on the adaptation-state-memory axis. Smart-meter analyses also show that reported gains depend on meter-selection rules. These findings support a validation-only commissioning procedure, while target-device latency and energy remain to be measured. Code, data, and all reported numbers: https://github.com/keiotakmin/tsf-edge-adaptation.

Takumi Fujimoto, Hiroaki Nishi

School of Science for Open and Environmental Systems, Graduate School of Science and Technology, Keio University, Yokohama, Japan

Multivariate Time Series Forecasting Learning Rate Scheduling Continual Test-Time Adaptation Edge Computing Temporal Distribution Shift

Aug 30, 2026cs.LG

Predicting the Unpredictable: LLM-powered Long-term Chaotic Time Series Forecasting under Short-term Observations

Chaotic time series forecasting is a challenging task due to its sensitivity to initial conditions and long-term unpredictability. Traditional methods typically rely on sufficient temporal trajectories to learn long-term dynamics, which limits their applicability when only short-term observations are available. While recent Large Language Models (LLMs) have shown great potential for time series forecasting, their temporal representations are not explicitly tailored to the phase-space structure and nonlinear evolution of chaotic systems. To address these issues, we propose PAC-LLM, a phase-space-aware adaptive fusion framework for long-term chaotic time series forecasting powered by LLMs. PAC-LLM leverages learned phase-space features and textual information to fully enable LLM's time series forecasting capacity. In particular, we design an auxiliary feature module and a gated weighting mechanism for multivariate coupling information fusion and selection. Extensive experiments on representative chaotic systems demonstrate that our method outperforms existing fine-tuned and zero-shot baselines in both short-term and long-term predictions. Our ablation study further confirms the effectiveness of each key component in PAC-LLM.

Yuhang Yao, Bohan Jiang

Nanjing University of Posts and Telecommunications Nanjing, China · Arizona State University Tempe, Arizona, USA

Long-Term Time Series Forecasting Chaotic Time-Series Prediction LLM-Based Time Series Forecasting Dynamical Systems Multivariate Time Series Forecasting

Aug 29, 2026cs.LG

SegTSim: A Big Data Driven Segmented Temporal Simulation Framework for Heterogeneous Multivariate Systems

Heterogeneous multivariate time-series systems exhibit segment-specific nonlinear dynamics that challenge monolithic forecasting architectures. We propose SegTSim, a big-data-driven segmented temporal simulation framework that integrates segment-specific elasticity modeling with adaptive min-gating, dynamic production relocation optimization, multi-factor data fusion with exchange-rate propagation, and a deep ensemble validation pipeline. The framework is validated on US--Japan automotive trade data from USITC repositories spanning 2015 to 2025, comprising approximately 13000 annual records. Under a 25% perturbation scenario, Japanese import volume declines by 20.4% to 0.93 billion USD, while all output variables maintain coefficients of variation below 3.5% across 1000 ensemble inference runs.

Xinhang Li, Chenxi Geng, Yujia Sun

College of Medicine and Biological Information Engineering, Northeastern University, Shenyang, China

Multivariate Time Series Forecasting Time Series Generation

Aug 28, 2026cs.LG

Learning to Difference: Adaptive Reversible Differencing (AdaRDiff) for Time Series Forecasting

Reliable long-horizon time series forecasting is an important yet difficult problem. Trends and seasonality introduce complex temporal structure that challenges learning-based forecasting models. Differencing, which subtracts nearby past values to remove such structure, is the classical remedy, but its reliance on hand-picked orders and periods has kept it largely absent from recent deep architectures. We propose \textbf{\underline{Ada}}ptive \textbf{\underline{R}}eversible \textbf{\underline{Diff}}erencing \textbf{(AdaRDiff)}, a generalized differencing approach that uses learnable weights to simplify the series through weighted differencing with previous time instants. This yields stabilized residuals on which forecasting is performed, after which the removed components are restored autoregressively to reconstruct the forecast, capturing trend and seasonality jointly through a single operator. This reconstruction admits a closed-form convolutional expression, which parallelizes on GPU and yields up to

33.7\times

speedup over the naive recurrence. We furthermore rely on a two-phase training schedule that separates temporal structure discovery from reconstruction learning, as suggested by a theoretical analysis of the gradient when using a linear forecasting model. AdaRDiff attains state-of-the-art forecast accuracy across eight benchmarks spanning electricity, weather, traffic, and energy, at negligible parameter cost. Furthermore, it is designed as a plug-and-play module: integrating AdaRDiff improves eight diverse backbones, from linear models to Transformers, in the large majority of cases, by up to

25.9\%

with a linear backbone and

18.3\%

with iTransformer.

Morad Laglil, Younes Hlal, Marouane El Hadari +2

Univ. Grenoble Alpes, CNRS, Grenoble INP, LIG, 38000 Grenoble, France · Savoye, 21600 Longvic, France

Time Series Forecasting Long-Term Time Series Forecasting Multivariate Time Series Forecasting

Aug 28, 2026cs.LG

PhyMamba: Physics-Modulated Mamba for Robust Battery Health Prognostics

Battery health prognostics is a core function in battery management systems (BMSs), yet long-horizon health forecasting from BMS signals remains challenging due to operating-condition dependency and sensor noise. In this paper, we propose PhyMamba, a two-stage physics-modulated Mamba framework that integrates electrochemical aging into sequence modelling. PhyMamba does not require explicit identification of internal aging parameters, which often relies on intrusive measurements. In stage-1, a lightweight Mamba encoder first processes BMS signals and produces a latent representation that is transformed via an aging parameterization module, into physics-informed aging features. In stage-2, a customized Mamba forecasting backbone performs multi-cycle prediction, where physics is tightly integrated to regulate the model's internal temporal updates toward degradation-consistent evolution. Experiments on three public datasets under multiple forecast horizons show that PhyMamba achieves the best aggregated performance, with an overall mean error reduction of 31.8% compared with a diverse range of baselines. PhyMamba also offers an optimized accuracy-efficiency trade-off, which supports practical deployment for robust battery health prognostics.

Sara Sameer, Yunyi Zhao, Wei Zhang +4

Information and Communications Technology Cluster, Singapore Institute of Technology, Singapore 138683

Predictive Maintenance Physics-Informed ML Mamba Multivariate Time Series Forecasting

Aug 27, 2026cs.LG

SAGE: Variate-Wise Semantic Augmentation for Vision-Language Time Series Forecasting

Time series forecasting models operate on raw numerical sequences, lacking the semantic knowledge that domain experts implicitly leverage, such as the physical meaning of each variable, its statistical behavior, and its temporal dynamics. Recent efforts to bridge this gap fall into two camps. Some rely on large language models at inference time, which is computationally expensive. Others apply uniform textual prompts at the dataset level, ignoring the heterogeneous semantics across individual variates. We propose SAGE (Seeing and Augmenting with Grounded Encoding), an end-to-end CLIP-based framework that jointly models temporal, cross-variable, textual, and visual information. The CLIP text encoder processes frequency-enhanced patches and variable tokens, while gated residual paths inject variable-specific descriptions and statistical descriptors. In parallel, the frozen CLIP vision encoder aligns rendered series with temporal representations through a training-only contrastive objective. This dual use of CLIP adds complementary semantic and visual supervision without placing an LLM in the forecasting loop. Across eight long-term benchmarks and M4, SAGE achieves state-of-the-art accuracy. Ablations confirm complementary gains from multimodal alignment and variable-level knowledge.

Haizhao Fan, Xinyi Le

Shanghai Jiao Tong University Shanghai, China

Time Series Forecasting Multivariate Time Series Forecasting Long-Term Time Series Forecasting

Aug 26, 2026cs.LG

Forecasting Multiple Observables with SCROLL: Score-Trained Uncertainty for Stochastic Dynamics

Forecasting a stochastic dynamical system rarely means a single number: one wants several observables---future state, threshold event, regime label---each with its own likelihood. Standard multi-task recipes balance per-task losses, tuned or learned. We instead compose the observables' likelihoods in per-task free-routed last-layer beliefs on a shared backbone; this absorbs unit-dependent loss scaling into likelihood parameters learned in the same gradient pass. Stochastic dynamics supply what static benchmarks cannot: computable ground truth for the predictive variance. Results land where theory puts them: on the well-specified, homoscedastic Ornstein--Uhlenbeck process the learned predictive law recovers the analytic kernel and correctly specified baselines tie. On heteroscedastic systems (stochastic Lorenz-63, real air-quality data) the belief's input-dependent variance separates: best single-run NLL on the state and regime tasks, calibration matched only by arms whose NLL it beats, at a fraction of the tuned grids' cost. On the real series the state margin holds across five rolling origins.

Pavel Prochazka

Cisco Inc.

Probabilistic Time Series Forecasting Uncertainty Quantification Multivariate Time Series Forecasting

Aug 26, 2026cs.LG

Modeling spatio-temporal locality in multi-step forecasting of geo-referenced time series

Forecasting future measurements from geographically distributed sensors is essential across many domains. However, the spatial distribution of these sensors raises multiple challenges, primarily due to spatial autocorrelation phenomena, that introduce inter-dependencies among nearby locations, that cannot therefore be treated independently. While some existing approaches can capture such phenomena, they generally model the spatial dimension globally across all locations. On the other hand, the method we propose in this paper, called SPALT, focuses on capturing spatial relationships among time series with similar trends, even if they occur at different times, thus modeling the spatio-temporal locality. SPALT leverages linear model trees, which allow us to consider the spatial autocorrelation locally: during the tree-building process, the adopted heuristics group time series exhibiting similar trends into the same node, on which additional features considering the spatial dimension are selectively injected. Additionally, we propose a new pruning strategy, based on Reduced Error Pruning, that also considers the spatio-temporal locality during the tree simplification. Designed for a multi-step setting, SPALT provides forecasts for multiple future time steps across multiple sensors simultaneously. The characteristics exhibited by SPALT can provide significant benefits in different domains, where measurements come from distributed sensors. In this paper, we focus on data produced by sensors located in multiple renewable power plants measuring their energy production at regular, short intervals. Experiments on 3 real-world datasets demonstrate the effectiveness of SPALT in forecasting the production of energy at different time horizons, and its superior performance in comparison with tree-based models and state-of-the-art neural networks that incorporate both temporal and spatial dimensions.

Annunziata D'Aversa, Gianvito Pio, Michelangelo Ceci

Time Series Forecasting Spatiotemporal Forecasting Multivariate Time Series Forecasting

Aug 25, 2026cs.LG

When Does Context Routing Help? A Systematic Study of Multi-Modal Fusion in Time Series Forecasting

Multi-modal time series forecasting methods integrate auxiliary context into temporal predictions through increasingly sophisticated fusion mechanisms. A growing body of work reports substantial gains, yet it is often unclear whether they reflect genuine use of the context or incidental architectural effects. We ask a narrower, checkable question: when can auxiliary context help a forecaster at all? We identify two dataset-level conditions that must both hold: (1) the target is not dominated by a last-value shortcut (low autocorrelation rho_h), and (2) the context carries information about the target beyond history (non-zero conditional mutual information delta; when delta=0 no predictor can benefit---a distribution-free result). Through controlled experiments on MoME (a 14.3B-parameter mixture-of-experts model, 6 datasets, 10 seeds) and four additional fusion mechanisms implemented within a single-backbone testbed (5 datasets), we find that when both conditions hold, text-conditioned expert modulation contributes a sizeable MSE reduction; when either fails, the contribution collapses to the capacity floor of the modulation pathway and carries no context-attributable signal. We establish causality through two interventions: adding a shortcut to MoME suppresses routing contribution by 77-93% across 3 datasets; progressively corrupting context quality drives the context-specific benefit from +44% to negative. We validate the autocorrelation component of our diagnostic on 27 Monash Archive datasets. We provide a calibrated pre-training diagnostic that, on the datasets we test, yields no false positives in well-powered settings. We are explicit about the asymmetry of our evidence: the negative arm is broadly reliable, while the large positive magnitudes come from a single model family (MoME) and are corroborated only in direction by the testbed.

Ruizhe Zhou, Gaoyuan Du, Xiaoyang Liu +4

Amazon.com Seattle, USA · University of Tennessee, Knoxville Knoxville, USA · WorkMagic New York, USA +1

Time Series Forecasting Multimodal Fusion Multivariate Time Series Forecasting

Aug 24, 2026cs.AI

PGP-Clinical-TimeKAN: Prior-Guided Joint Probabilistic Forecasting of Clinical Trajectories

Clinical deterioration unfolds through coupled, partially observed trajectories, not a single diagnostic label. We introduce PGP-Clinical-TimeKAN, a trajectory-first framework for joint probabilistic forecasting of multivariate physiology. It combines missingness-aware temporal encoders, a soft organ-system prior, patient-specific relations, nonlinear Kolmogorov-Arnold messages, and a low-rank multivariate Student-t head. We evaluate 24-hour histories and six-hour forecasts on a frozen MIMIC-IV-derived cohort of 6,882 patients and 54,694 windows. Across five seeds and 13 models, PGP-Clinical-TimeKAN obtains the second-lowest normalized MAE (0.37727 +/- 0.00029) and the lowest RMSE (0.52656 +/- 0.00034). It reduces MAE by 0.52% relative to deterministic TimeKAN. For probabilistic forecasting, it reaches a marginal NLL of 0.66380 and a CRPS of 0.27301. Empirical coverage is 0.533, 0.831, and 0.958 for nominal 50%, 80%, and 95% intervals. Removing relational structure causes the largest ablation loss. Increasing covariance rank improves joint likelihood but has little effect on point accuracy. A trajectory-derived risk score remains weaker than a dedicated GRU-D classifier (AUROC 0.603 versus 0.650), which limits the present clinical claim. Joint trajectory forecasting therefore provides an inspectable intermediate task, but accurate physiology forecasts alone do not ensure a calibrated event detector.

Weizhi Nie, Rihao Chang, Weijie Wang +1

Tianjin University

Time Series Forecasting Multivariate Time Series Forecasting Probabilistic Time Series Forecasting Kolmogorov-Arnold Networks

Aug 24, 2026cs.CV

Velocity-coupled Representation Refinement for Satellite Orbit Prediction

Satellite orbit prediction, which aims to forecast future orbital trajectories from historical observations, is important for collision warning and safe space operations. With advances in time-series forecasting, learning-based methods have emerged as a promising solution for satellite prediction. In orbital dynamics, a satellite state is typically described by position and velocity, where position characterizes trajectory geometry and velocity reflects its instantaneous direction and rate of change. However, most existing methods mainly focus on temporal dependencies within position sequences while rarely exploiting the intrinsic coupling between position and velocity, which is essential for modeling satellite motion. To this end, we propose OrbitNet, a velocity-aware representation learning method for accurate satellite orbit prediction. It lifts conventional position-sequence forecasting to a position-velocity coupled representation learning paradigm by exploiting relationships among satellite state variables. Specifically, we develop a velocity-coupled representation refinement strategy to enhance positional representations through cross-variable interactions between position and velocity. We further introduce orbital segment modeling, which partitions historical trajectories into temporal segments and performs segment-level temporal learning to capture local motion variations and long-range evolution patterns. Extensive experiments show that OrbitNet outperforms large time-series foundation models and representative general forecasting methods under both in-domain evaluation on Starlink and zero-shot evaluation across six unseen satellite constellations. We expect this work to encourage further exploration of satellite-aware representation learning for trajectory time-series forecasting.

Yue Yang, Zhiqiang Wu, Saiyu Qi +1

Xi’an Jiaotong University, Xi’an, China · Zhejiang University, Hangzhou, China

Trajectory Prediction Time Series Representation Learning Multivariate Time Series Forecasting

Aug 24, 2026cs.AI

Modalities Should Talk to Each Other: Dual-Stream Multimodal Learning for Long-Horizon Influenza Forecasting

Forecasting long-range influenza-like illness (ILI) matters for public health readiness. Publicly available surveillance datasets typically pair numeric epidemiological signals with textual information that is noisy, loosely structured, only indirectly related to near-term trends, and often lagged relative to the numeric signal. Fusing the two therefore requires careful design. We propose Dual-Stream Attention (DSA), a multimodal deep learning framework that forecasts 12-week-ahead ILI activity from a 36-week multimodal history by letting the numerical and textual streams condition each other. Using the Time-MMD health-domain dataset, DSA separately encodes the two modalities with a Transformer-based numerical encoder and a domain-adapted headline encoder, then couples them through a bidirectional Cross-Modal Attention (CMA) mechanism: the text (news headlines) conditions the interpretation of the numeric signal and vice versa. The CMA output then passes to a causal temporal model for forecasting. Evaluated across ten random seeds, DSA achieves a median test MSE of 0.416, versus 0.668, 0.607, and 0.851 for iTransformer, TaTS, and GPT4MTS, corresponding to mean-error reductions of 54.95%, 37.29%, and 67.23%, with paired Cohen's d of 0.555, 0.337, and 0.345, respectively, and ranks first in 100% of bootstrap draws. It also has substantially lower worst-window error than all baselines. On an external-geography dataset, DSA again ranks first among nine evaluated baselines. Ablations show the advantage does not depend on text-encoder choice or language-model fine-tuning, and that bidirectional attention outperforms either direction alone. Finally, perturbation-based faithfulness analysis shows the learned CMA is functionally informative under targeted masking, with a stronger effect in the text-to-numerical direction.

Seyed Mohammad Hossein Hashemi, Mohsen Hooshmand, Parvin Razzaghi

Department of Computer Science & Information Technology, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran

Epidemic Forecasting Long-Term Time Series Forecasting Multimodal Fusion Multivariate Time Series Forecasting Cross-Modal Attention

Aug 24, 2026cs.LG

Do Time-Series Foundation Models Pay Off for Industrial Monitoring? A Cost-Aware Empirical Study

Industrial monitoring models must detect operationally relevant deviations while satisfying target-specific data, calibration, and resource constraints. Time-series foundation models (TSFMs) promise reusable representations and zero-shot forecasts, yet evidence for their deployment value remains mixed when task definitions are heterogeneous and lightweight baselines are competitive. This work presents a protocol-aware empirical assessment across three settings: a C-MAPSS degradation-risk proxy, normal-only training for anomalous-sound detection on MIMII, and BDG2 forecasting-residual diagnostics with synthetic target perturbations. We assess classical one-class methods, compact neural autoencoders, residual forecasters, MOMENT-small, Chronos-T5, and TimesFM 2.5 in terms of anomaly-ranking performance, risk-horizon sensitivity, residual forecasting and perturbation sensitivity, and local implementation cost. Across 100 C-MAPSS engines evaluated out of fold, TCN-AE reaches fold-weighted AUROC/AUPRC 0.9570/0.8960, compared with 0.7310/0.3080 for MOMENT reconstruction; paired engine-cluster bootstrap confidence intervals exclude zero for both differences. Across five matched MIMII pump evaluations, OCSVM also exceeds MOMENT reconstruction in AUROC and AUPRC. On a fixed 12-meter BDG2 panel, TimesFM 2.5 has the lowest aligned forecast error and the highest synthetic AUROC point estimate, although synthetic AUPRC is similar across TSFM and fitted residual models. Same-device measurements show that MOMENT incurs higher latency, peak allocated VRAM, and serialized state-dictionary size than TCN-AE. Under the evaluated frozen and zero-shot settings, TSFMs are task-dependent deployment options rather than default replacements for fitted lightweight models.

Guan-Hua Wen, Kuan-Yu Chen

Department of Computer Science and Information Engineering National Taiwan University of Science and Technology Taipei, Taiwan

Time-Series Foundation Models Time-Series Anomaly Detection Industrial Anomaly Detection Multivariate Time Series Forecasting

Aug 23, 2026q-fin.MF

Arbitrage-Aware Multi-Step Forecasting of Implied Volatility Surfaces: Modelling Surface Trajectories Using Latent Diffusion

Implied volatility surfaces summarise the option market and are central to many financial applications. Forecasting their future evolution requires modelling two-dimensional geometry, temporal dependence, and predictive uncertainty while preserving economic admissibility. We propose a conditional latent diffusion framework for generating joint 30-step trajectories of implied volatility surfaces and underlying returns. An arbitrage-aware autoencoder learns a low-dimensional surface representation, while the diffusion model captures the conditional joint evolution. Evaluated on SPX surfaces, the framework generates realistic probabilistic multi-step scenarios while also outperforming the persistence benchmark in point forecasting.

Dominik Manuel Buchegger, Lukas Gonon

University of St.Gallen St.Gallen, Switzerland

Quantitative Finance Probabilistic Forecasting Multivariate Time Series Forecasting Conditional Diffusion Models Latent Diffusion Models

Aug 23, 2026cs.CL

Semantics or Structure? Auditing Text Sensitivity in Multimodal Time-Series Forecasting

Multimodal time-series forecasting has emerged as a promising paradigm in which natural-language context is expected to improve predictive performance. Recent multimodal foundation models, including Aurora, as well as early- and late-fusion approaches such as MM-TSFlib and TaTS, report substantial gains over unimodal baselines on the Time-MMD benchmark, attributing these improvements to textual information. However, whether these models are actually sensitive to the semantic content of the text remains unverified. We address this question through controlled text perturbations, attribution analyses, and probes of Aurora's text pathway. On Time-MMD, swapping each row's text for any other real text (empty, constant, within-domain shuffled, or cross-domain) moves mean MSE by less than

0.5\%

on all three architectures. The improvement reported in the literature is recovered when a co-shipped numeric column is removed without touching text. We conclude that, on this benchmark and within this family of frozen-encoder architectures, text content is not the operative signal behind the reported gains. To support future work on text integration in multimodal foundation models for structured data, we release our perturbation protocol and evaluation harness as a reusable diagnostic toolkit.

Karthik Sridhar, Atharva Gupta, Nishant Pradhan +3

Birla AI Labs, Mumbai, India · BITS Pilani, Pilani, India · KIIT, Bhubaneswar, India

Multimodal Foundation Models Multimodal Model Evaluation Multivariate Time Series Forecasting

Aug 21, 2026cs.LG

ConceptTS: LLM-Guided Concept Bottlenecks for Interpretable Multivariate Time-Series Forecasting

State-of-the-art multivariate time-series forecasters can model complex temporal and cross-variable dependencies, yet their opaque representations provide limited insight into why a particular forecast is produced. This lack of transparency restricts their use in settings where practitioners must understand and assess the factors underlying a prediction. We introduce ConceptTS, an interpretable forecasting framework that organizes its predictions around named, human-readable concepts. ConceptTS uses a large language model to propose task-relevant concepts and generate executable labeling rules, translating the language model's domain knowledge into direct supervision without costly manual concept annotation. The proposed concepts are organized into three complementary bottlenecks that describe the historical context, local forecast intervals, and the full forecast horizon. A shared decoder combines representations derived from their predicted activations to construct the forecast, making the model's decision process explicit and supporting direct concept-level interventions. Experiments on the Beijing Multi-Site Air Quality dataset show that ConceptTS achieves accuracy competitive with strong black-box baselines while producing semantically meaningful concept activations.

Yichen Jiang, Yueqiao Chen, Dongyu Liu

Department of Electrical Engineering Stanford University Stanford, CA, USA · Department of Computer Science University of California, Davis Davis, CA, USA

Multivariate Time Series Forecasting Explainable Time Series Forecasting Concept Bottleneck Models

Aug 21, 2026cs.LG

Fuzzy-MoE: Interpretable Regime-Conditioned Expert Routing for Non-Stationary Multivariate Time Series Forecasting

In non-stationary multivariate time series, different variables and samples often exhibit heterogeneous latent dynamic states, while existing deep forecasting models usually compress them into a unified end-to-end mapping, leading to suboptimal modeling of time-varying dynamics and limited interpretability regarding which forecasting mechanism is activated under different latent states. To overcome these limitations, we reformulate time series forecasting as a unified framework of latent temporal state identification and interpretable expert routing, and propose Fuzzy-MoE, a fuzzy logic-based dynamic Mixture-of-Experts model. Fuzzy-MoE consists of multiple parallel expert mapping networks and a dual-view fuzzy router. By jointly exploiting local convolutional dynamics and global segmented statistics, the router infers latent temporal states and computes expert activation strengths through learnable Gaussian membership functions, enabling explicit IF-THEN rule-based expert selection. This fine-grained routing strategy allows different variables within the same sequence to activate different experts, effectively capturing heterogeneous temporal dynamics while improving model interpretability. Experimental results on multiple public time series benchmark datasets show that Fuzzy-MoE significantly outperforms mainstream forecasting methods in forecasting accuracy. Moreover, fuzzy memberships and rule activations provide interpretable routing diagnostics, demonstrating the effectiveness of the proposed framework in both forecasting performance and mechanism transparency. Unlike traditional MoE models that use black-box routing, Fuzzy-MoE`s routing is based on clear, interpretable fuzzy rules. This makes the expert selection transparent and traceable.

Lan Guo, Jie Xiao, Zhao Su +5

School of Information Science and Engineering, Lanzhou University · School of Computing and Information Technology, University of Wollongong · Department of Data Science and AI, Monash University

Multivariate Time Series Forecasting Non-Stationary Time Series Forecasting Explainable Time Series Forecasting Mixture-of-Experts Models

Aug 20, 2026cs.LG

CLaST: Context-aware Contrastive VAE for Probabilistic Time Series Forecasting

Probabilistic forecasting models are widely used for time series forecasting in domains such as energy systems, finance, medicine, and transportation. In recent years, deep generative models have shown strong results on probabilistic forecasting, yet many conventional approaches struggle to capture internal temporal dependencies, leading to latent representations with limited expressive power. To address this limitation, we propose \textit{CLaST}, a VAE framework for probabilistic multivariate time series forecasting. Unlike existing generative models, CLaST learns embeddings that preserve contextual similarity between observations through our contrastive loss function. Experiments across nine widely adopted benchmarks demonstrate that CLaST consistently surpasses strong baseline methods. In short-term forecasting tasks, our approach achieves improvements of up to

16.4\%

in CRPS and

14.4\%

in NMAE over the second-best method. Furthermore, in long-term prediction CLaST attains superior overall performance, exceeding the second-best method by up to

48.6\%

and

25.1\%

in CRPS and NMAE, respectively.

Alexander Marusov, Dmitry Anikin, Petr Sokerin +3

Applied AI Institute Moscow, Russia

Variational Autoencoders Multivariate Time Series Forecasting Self-Supervised Time Series Representation Learning Time Series Representation Learning Probabilistic Time Series Forecasting

Aug 20, 2026cs.LG

Scale-Aware Pretraining of Time Series Foundation Models via Multi-Patch Token Alignment and Hybrid Masking

Pretraining time series foundation models across heterogeneous datasets necessitates effective handling of varying sampling frequencies. Current methods either employ dataset-specific patch sizes and separate FFNs, leading to fragmented representations, or enforce a fixed patch size that neglects inherent temporal variations. To address this, we propose SATS, featuring a scale-aware token alignment mechanism that treats patch size as an explicit notion of scale. By incorporating a contrastive-inspired alignment regularizer, SATS aligns representation spaces across scales while preserving distinct modeling capacities. Furthermore, a hybrid masking strategy combining random and contiguous masking is introduced to capture multi-scale temporal structures. Experimental results on LSTF benchmarks demonstrate that SATS achieves a 9.2% improvement in MSE and an 8.3% gain in GIFT-Eval MASE compared to competitive baselines. Notably, SATS consistently delivers SOTA performance while achieving a 65.6% increase in model efficiency over advanced baselines, highlighting its effectiveness and scalability in time series pretraining.

Taihua Chen, Xiang Ma, Yixin Zhang +3

Time-Series Foundation Models Self-Supervised Pre-Training Multiscale Time-Series Modeling Multivariate Time Series Forecasting

Aug 20, 2026cs.AI

Rethinking Patch Based Multivariate Time Series Forecasting with Semantic Structured Partitioning

Multivariate time series forecasting (MTSF) is a fundamental task in many real world applications. Existing patch based forecasting methods generally fall into three categories: fixed partitioning, multi-scale partitioning, and extendable partitioning. Fixed partitioning often breaks meaningful temporal boundaries, multi-scale partitioning may introduce redundant representations across scales, and extendable partitioning improves flexibility but still lacks an explicit mechanism for organizing semantic structure and modeling interactions among heterogeneous temporal patterns. To address these limitations, we propose SCPaT, a Transformer based framework built on semantic structured partitioning. SCPaT first decomposes input sequences into semantically consistent units through adaptive semantic unit generation, then constructs a dynamic semantic graph to model directed dependencies among these units and organize them into higher order semantic blocks. Based on these structured representations, an importance aware routing mechanism adaptively dispatches different semantic blocks to different experts for customized modeling. Extensive experiments on 12 real world datasets demonstrate the effectiveness of SCPaT.

Zhiquan Huang, Jiazhe Wang, Linjing Xue +3

School of Information Engineering, Henan University of Science and Technology, Luoyang, 471023, Henan, China · School of Software, Henan University of Science and Technology, Luoyang, 471000, Henan, China

Multivariate Time Series Forecasting Time Series Forecasting Time Series Transformers

Aug 20, 2026cs.LG

StationPDE: Station-Oriented Surface PDE Learning for Multi-Station Multivariate Weather Forecasting

Multi-station multivariate weather forecasting aims to forecast future weather variables at multiple weather stations from historical surface observations. Existing station forecasting models learn statistical dependencies among discrete stations, but lack explicit physical evolution. Meanwhile, PDE-based weather models provide interpretable physical dynamics, yet require continuous fields and upper-air variables unavailable in surface station data. To bridge this gap, we propose StationPDE, a station-oriented surface PDE learning model. StationPDE constructs a terrain-aware continuous surface field from discrete station observations and decomposes its physical evolution into surface wind transport and upper-air inference. Surface wind transport explicitly evolves observable weather variables, while upper-air inference uses learnable horizontal diffusion to approximate the missing influence of unavailable upper-air variables. A parallel data-driven diffusion branch captures complementary motion patterns, and an adaptive router integrates the two forecasts for station-level multivariate forecasting. Experiments on Weather2K and MeteoNet show that StationPDE consistently outperforms state-of-the-art baselines, reducing MSE by about

9.6\%

on average compared with the strongest baseline.

Xiao Wang, Changjian Chen, Rongwen Li +3

Hunan University.

Multivariate Time Series Forecasting PDE Operator Learning Spatiotemporal Forecasting Weather Forecasting

Aug 18, 2026stat.ML

SPACE: Sample-cloud Predictive Adaptive Conformal Ellipsoids for Multivariate Time-Series Forecasting

Modern probabilistic time-series forecasters often express uncertainty through forecast samples. While typically converted into nominal prediction regions using empirical quantiles, these model-implied sets lack formal coverage guarantees and frequently deviate from nominal targets under distribution shift. Existing multivariate conformal methods can calibrate these regions online, but they typically estimate geometry from historical residuals using fixed or accumulating look-back windows. This reliance on the past limits their ability to exploit the instantaneous dependence structure of current predictions and leaves them vulnerable to stale-regime contamination. To address this, we propose SPACE, a conformal wrapper for sample-generating multivariate forecasters. SPACE constructs ellipsoidal joint prediction regions by estimating time-local covariance geometry directly from the current forecast sample cloud, calibrating the region's radius via a dynamic backward window-selection scheme. Across diverse multivariate datasets, probabilistic forecasters, and conformal baselines, SPACE consistently brings realized joint and rolling coverage closer to the nominal target, achieving superior coverage-efficiency tradeoffs relative to competing wrappers.

Baishi Li, Kelvin J. L. Koa, Ke-Wei Huang

Conformal Prediction Multivariate Time Series Forecasting Probabilistic Time Series Forecasting Adaptive Conformal Inference

Aug 17, 2026cs.LG

SCENARIODIFF: A Scenario-level Guidance Framework for Multimodal Time Series Forecasting--Extended Version

Textual context such as news, reports, and logs can provide valuable signals for time series forecasting, especially when future dynamics are driven by external events that are not yet visible in historical values. Existing multimodal forecasting methods often either ask large language models (LLMs) to predict numerical values directly or fuse text and time series implicitly, making contextual influence difficult to interpret and control. We propose SCENARIODIFF, a hierarchical contextual reasoning framework for multimodal time series forecasting under noisy and weakly aligned documents. SCENARIODIFF organizes contextual information into three levels: a Historical Context Agent extracts stepwise evidence from raw documents, a Scenario Agent produces a qualitative scenario description for the forecast horizon, and an Anchor Guidance Agent generates sparse anchor points for event-relevant future regions. These structured signals condition a Multimodal Diffusion Transformer, while Anchor Blended Sampling locally refines generated trajectories without retraining. Experiments on the Time-MMD benchmark show that SCENARIODIFF is especially effective in event-driven domains, demonstrating the value of explicit hierarchical scenario guidance for multimodal time series forecasting. Our full implementation is available at https://anonymous.4open.science/r/ScenarioDiff_ICDM-2C4C

Tuan-Binh Tran, Dat Nguyen Cong, Duc-Trong Le +2

Time Series Forecasting Multivariate Time Series Forecasting Multimodal Diffusion Models

Aug 17, 2026cs.LG

AsyTO: Asymmetric Temporal Operator for Parameter-Efficient Multivariate Time Series Forecasting

Multivariate time-series forecasting faces a structural dilemma: sharing one temporal predictor across variables is parameter-efficient but forces heterogeneous variables through an identical history-to-future map, whereas learning an independent predictor per variable restores flexibility at a cost that grows with the product of variable count, context length, and horizon. We argue that this dilemma dissolves once the object being compressed is the forecasting operator rather than the observed series. Auditing per-variable linear history-to-future maps across standard benchmarks, we find that a phase-locked seasonal component paired with a compact residual operator outperforms a dense phase-blind reference in most audited settings. The residual transport is also directional: lag-invariant alternatives consistently underperform asymmetric history-to-future maps. Guided by this structure, we propose AsyTO, an Asymmetric Temporal Operator that factorizes the tensor of per-variable operators into shared but distinct history-reading and future-writing temporal modes with per-variable mode-wise gains, complemented by a low-rank periodic prototype and a cycle-separable factorization of the temporal modes. Each forecast reads only its own variable's history, so parameters and compute grow linearly in the number of variables. Across eleven benchmarks and multiple forecast horizons, AsyTO attains the best lightweight error in 30 of 44 dataset-horizon settings, locating at the accuracy-compute Pareto frontier.

Xiachong Lin, Du Yin, Hao Xue +5

Multivariate Time Series Forecasting Time Series Forecasting

Aug 12, 2026q-fin.CP

AI-Driven Multiscenario Interest Rate Forecasting: A Proof of Concept for Banking Asset Management

This study focuses on developing an AI-supported prototype for multiperspective interest rate forecasting that combines classical econometric models with modern artificial intel-ligence methods. Tested in a major European bank, the system enables more precise and flexible prediction of interest rate developments, supporting strategic decision-making in Asset-Liability Management (ALM). It integrates topic modeling, sentiment analysis, econometric forecasting, and market-based analyses within an interactive platform. Leveraging AI to analyze large volumes of financial documents and market data enables the identification of monetary policy trends and sentiment signals at an early stage. The core econometric model is a Bayesian vector autoregression (BVAR) that enables simulation-based scenario analyses to evaluate economic developments from multiple perspectives. The system's innovation lies in its integration of several forecasting approaches that consolidate previously separate information sources and present them transparently and interpretably. Financial analysts and risk managers thus gain a better basis for making decisions, allowing them to assess interest rate risks more accurately and manage market movements more proactively. While the prototype demonstrates how AI can transform interest rate management in banking, further development is required to optimize real-time data integration and regulatory compliance. Even at this stage, the study shows that multi-perspective, AI-driven forecasting provides substantial added value for banks by increasing transparency, strengthening evidence-based decision-making, and improving risk management.

Ekkehardt Bauer, Dirk Holländer, David Scholz +4

zeb.rolfes.schierenbeck.associates Ltd. · zeb Institute for Financial Services, University Witten/Herdecke

Multivariate Time Series Forecasting Financial Time Series Finance

Aug 12, 2026cs.LG

Air Quality Station Simulation via LSTM and Attention-Based Modelling

Poor air quality in urban areas is driven by a complex chain of processes and presents a significant public health concern. To better understand and control the mechanisms that determine air quality, cities deploy networks of measurement stations, and launch initiatives for collecting denser data about the concentration of pollutants in the atmosphere. Extracting insights from the stations relies on their reliable and uninterrupted operation. However, hardware is susceptible to faults and black- outs that may result in data unavailability, which affects the overall quality of analyses. In this paper, we present a deep-learning model, called SATADL, which can infer complex relations and output multiple-hour-ahead air-quality forecasts. The goal of the model is to simulate the mea- surements of an unresponsive station until its operation is restored. The architecture of the model, which allows it to extract information from different aspects of the data, is described in detail and a careful examination of all of its components is provided. We demonstrate the performance of SATADL on four sets of air quality stations from around the world, by using it to simulate the concentration of PM10 for periods of hypothetical failures of one of the measurement stations, lasting for as long as 48 hours. A selection of baseline and published deep learning models were trained and used as a benchmark. The results show that SATADL per- forms better across different prediction windows, for both coefficient of determination and root mean squared error, demonstrating its suitability as a virtual proxy station.

Alexander Kostadinov, Petar O. Hristov, Dessislava Petrova-Antonova

GATE Institute Sofia University “St Kliment Ohridski” 5 James Bourchier Blvd, 1164, Sofia

Multivariate Time Series Forecasting Time Series Imputation Air Quality Prediction

Aug 10, 2026cs.AI

AirFlow: Context Preserving and Multi-Rate State Modeling for Air Quality Forecasting

Accurate air quality forecasting is essential for public health and urban environmental management, but remains challenging because pollutant channels differ in periodicity and distribution drift, while their concentration trajectories contain both multi-scale dependencies and rapid changes. Recent methods have improved spatial dependency learning and meteorological covariate modeling. However, pollutant channels are still passed through the same normalization rule and temporal backbone, using a shared latent representation for channel-specific distributions and changes at different rates. To address this limitation, we propose AirFlow, a pollutant-aware dual-stream framework that operates on station multivariate observations without additional graph propagation or predefined signal decomposition. Specifically, AirFlow designs two novel blocks: (1) a statistic-guided normalization routing mechanism that selects a normalization path for each pollutant according to its 24-hour autocorrelation and distribution drift; and (2) a hierarchical dual-stream state model that combines multi-scale state space propagation with learnable response coefficients, where gated bidirectional cross-attention exchanges information and adaptively fuses the resulting representations. Experiments on real-world data from multiple cities show that AirFlow achieves the best performance in 34 of 36 metrics comparisons, with reductions of up to 11.11% root mean square error over the state-of-the-art baseline. AirFlow also requires only 0.0483M parameters and 0.0215G FLOPs, achieving high forecasting accuracy with low computational overhead.

Fan Yang, Nan Chen, Yijie Dong +2

School of Software Technology, Zhejiang University Hangzhou, Zhejiang 310000, China

Multivariate Time Series Forecasting Air Quality Prediction Non-Stationary Time Series Forecasting Multiscale Time-Series Modeling State Space Models

Aug 7, 2026cs.AI

QFCQT: A Chaotically Gated Quantformer Framework for Volatile Time-Series Forecasting

Forecasting non-stationary time series remains difficult due to long-range dependencies, local volatility bursts, structural shifts, and nonlinear oscillatory behaviors. Although Transformer-based forecasters are effective for modeling long-term temporal dependencies, their feed-forward blocks typically rely on smooth static activations that are insufficiently sensitive to abrupt regime changes. Motivated by quantitative Transformer designs and oscillator-based nonlinear activations, we propose QFCQT, short for Quantum-Fractal-inspired Chaotically Gated Quantformer, for robust forecasting under complex volatile dynamics. Here, "quantum-fractal-inspired" denotes a computational analogy based on soft oscillator superposition and multi-scale nonlinear responses, rather than a formal quantum-mechanical or fractal-theoretic derivation. QFCQT consists of three main components: (1) a Quantformer-style numerical encoder that directly processes multivariate inputs via linear embedding; (2) a learnable Lee-oscillator activation module that maps scalar pre-activations to dynamic oscillatory responses and summarizes them through Max-over-Time pooling; and (3) a smooth-chaotic gated fusion mechanism that adaptively balances conventional smooth activations and chaos-sensitive responses. Furthermore, instead of using a single fixed oscillator, QFCQT employs a soft superposition of eight parameterized Lee oscillator families to adaptively capture different nonlinear response patterns across regimes. Experiments on ETTh1, ETTh2, and A-share Stock Index benchmarks show that QFCQT consistently outperforms strong baselines, including Informer, LogTrans, LSTMa, HAT, and COTN.

Junkai Lin, Siqi Hou, Raymond Lee

Faculty of Science and Technology, Beijing Normal-Hong Kong Baptist University, Zhuhai, China · Guangdong Provincial Key Lab of Interdisciplinary Research and Application for Data Science (BNBU), Zhuhai, China

Multivariate Time Series Forecasting Time Series Forecasting Neural Network Activation Functions Non-Stationary Time Series Forecasting Time Series Transformers

Aug 7, 2026cs.LG

When GNNs Fail: Quantifying and Overcoming Temporal Correlation Volatility in Time Series

Modeling multivariate time series by representing them as graphs, where individual series act as nodes and pairwise temporal corre- lations serve as edges, has gained significant traction. Recent advances in Graph Neural Networks (GNNs) have demonstrated strong perfor- mance by assuming a static graph topology and aggregating information from neighboring series. In this work, we investigate the representa- tional power of GNNs for forecasting under both static and dynamic settings (i.e., when pairwise correlations evolve drastically over time) and identify critical limitations in current architectures. To formalize this, we first propose Temporal Correlation Volatility (TCV), a model- agnostic metric designed to quantify the distributional evolution of these latent structures. We establish a clear connection between TCV and performance degradation, demonstrating that many popular models, including Transformers, generalize poorly in high-TCV settings and are often outperformed by simple structure-agnostic baselines. To address these limitations, we propose Graph Layer for Inference in Dynamic En- vironments (GLIDE), a novel GNN layer enhanced by two theoretically grounded design mechanisms: (D1) Path-based Message Passing, which captures path-based neighborhoods and (D2) Static and Dynamic Propagation Separation, which identifies optimal dynamics via local static approximation. These components significantly improve learning under dynamic topology while preserving robustness in static scenarios. Ex- tensive experiments on synthetic and real-world benchmarks show that GLIDE improves average performance by up to 45.6% across static and dynamic settings, with the largest gain reaching 85.7%. The source code is available at https://github.com/ChenS676/GLIDE.

Chen Shao, Yue Wang, Zhenyi Zhu +4

Karlsruhe Institute of Technology, Germany · The Hong Kong University of Science and Technology, Hong Kong SAR · East China Normal University, China +1

Multivariate Time Series Forecasting Temporal GNNs GNN Expressivity Dynamic Graph Learning

Aug 7, 2026cs.LG

Accounting Graph Transformer for Short-History Multi-KPI Forecasting in Small Businesses

Small businesses often have only 12-24 months of accounting history, yet planning and risk workflows require coordinated forecasts across financial statements. We study joint 12-month forecasting of 13 income-statement, balance-sheet, cash-flow, and working-capital key performance indicators (KPIs) from 71 monthly ledger series. We introduce the Accounting Graph Transformer (AGT), which represents each ledger series as a masked token, exchanges information through typed attention on a fixed accounting-relation graph, pools target-specific context, and fuses it with a gated three-month recency path. Across 11,993 forecast origins from 1,060 unseen companies, AGT achieves sample-weighted KPI-macro mean absolute error (MAE)

0.6990 \pm 0.0013

over three independent seeds, compared with

0.7378 \pm 0.0014

for the strongest baseline, LightGBM. At the pre-specified seed 42, a paired company-clustered bootstrap gives a LightGBM-minus-AGT difference of 0.0395 with 95% confidence interval (CI)

[0.0350,0.0439]

. AGT is best on all 13 KPIs against LightGBM, TimeMixer, and SOFTS in the matched seed-42 comparison, while final-architecture ablations show that relational attention, accounting topology, and the recency path each improve validation and test accuracy. On 7,094 additional unseen companies with origins sampled from January-May 2025, AGT obtains 0.7548 MAE versus 0.7694 for SOFTS. A single 5.3M-parameter model produces 156 aligned forecasts without company-specific fitting, providing one forecasting layer for integrated planning, liquidity, and working-capital analysis.

Shrutendra Harsola, Vignesh Subrahmaniam

Foresight-AI, Intuit Bangalore, India

Multivariate Time Series Forecasting Financial Forecasting Financial Time Series Graph Transformer