Time Series Forecasting

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Latest papers 667

139 papers in the last four weeks, up 101% on the four weeks before. 0.9% of all new papers.

Sep 27, 2026cs.CL

CAME: Company-Aware Evidence-Memory Experts for Interpretable Quarter-Ahead Revenue Forecasting

Quarter-ahead revenue forecasting requires company-scale numerical accuracy, strict temporal validity, and company-specific interpretation of narrative disclosures. LLMs can distill textual evidence but can produce scale-misaligned forecasts, whereas history-based anchors are stable but miss forecast-time signals such as product transitions, supply constraints, and management guidance. We introduce CAME (Company-Aware Evidence-Memory Experts), a residual-forecasting framework that refines a no-leakage statistical anchor when current semantic evidence and prior error patterns justify an adjustment. On a development-inclusive rolling backtest of 336 company-quarters from 12 large public technology and platform firms, CAME achieves the lowest aggregate point-estimate error among the reported methods, with statistically supported macro-sMAPE gains over the matched Statistical Anchor, and outperforms History + Guidance on all six aggregate metrics. CAME also links adjustments to source-linked evidence cards and guarded memory traces, supporting forecast inspection, provenance, and failure localization.

Ya-Wen Wu, Meng-Fen Chiang, Kuang-Da Wang +1

National Yang Ming Chiao Tung University, Hsinchu, Taiwan

Financial Forecasting Time Series Forecasting Explainable Time Series Forecasting

Sep 27, 2026physics.ao-ph

BridgeCast: Bridging Ocean Wave Forecasts to Reanalysis via Flow Matching with Exogenous Variables

Ocean wave forecasting is essential for maritime safety, offshore operations, and coastal resilience, yet remains challenging due to systematic biases in physics-based models. Physical models, while widely used, rely on approximations and parameterizations that limit their accuracy under complex ocean-atmosphere conditions. To enhance ocean wave forecasting, we propose BridgeCast, within a physics-AI hybrid framework for bias correction. BridgeCast is a probabilistic model based on conditional flow matching (CFM) that learns to transform physical model forecasts into reanalysis-like fields. It treats physical forecasts as corrupted observations and employs a continuous-time generative process to bridge their distribution toward that of reanalysis data. BridgeCast is parameterized by a Transformer-based architecture that enables spatiotemporal modeling, incorporation of exogenous atmospheric variables, and flexible inference via both ordinary and stochastic differential equation formulations. Extensive experiments on real-world datasets demonstrate that BridgeCast consistently outperforms state-of-the-art baselines across regions and forecast lead times.

Siyu Gan, Dongsheng Luo, Kunxiaojia Yuan +2

Johns Hopkins University · Singapore Management University · University of Houston +1

Spatiotemporal Forecasting Time Series Forecasting Probabilistic Forecasting

Sep 26, 2026cs.CV

Distributed Hydrological Modeling in the Feature Space

Accurate forecasting of river discharge and floods is very challenging. River dynamics are affected by storage, meteorological forcing, and flow propagation at different spatial and temporal scales. Forecasting thus requires a framework that considers the upstream-to-downstream flow through river networks across grid cells and catchments. This modeling is known in hydrology as distributed modeling and routing. Existing deep learning approaches either ignore this topology, operate on lumped catchments, or route predicted physical quantities through a separate graph or physical routing model. We instead introduce feature-space routing: a topology-aware state-space operator embedded directly in the forecasting dynamics. At every forecast step, the operator gathers latent states from upstream grid cells and causally updates the downstream state according to the known river network. This preserves the physical connectivity of the river system while allowing the propagated state itself to be learned end-to-end and allows the model to predict river discharge considering both local dynamics and neighboring upstream contributions. To address uncertainty and provide probabilistic forecasts, we minimize the fair continuous ranked probability score (fCRPS) as a training objective. Our experiments on the European Flood Awareness System (EFAS) and observational data for river discharge forecasting demonstrate that encoding the physical structure of river networks explicitly in the feature space substantially improves the forecasting skill, particularly in an ungauged setting. Our approach achieves state-of-the-art results on both reanalysis and observational data and is able to forecast maps of river discharge at 1 arcminute and 6-hourly resolution up to 10 days lead time.

Mohamad Hakam Shams Eddin, Maria Luisa Taccari, Yikui Zhang +3

Max Planck Institute for Biogeochemistry, Germany · European Centre for Medium-Range Weather Forecasts (ECMWF), United Kingdom · Institute of Bio- and Geosciences Agrosphere (IBG-3), Research Centre Jülich, Germany +2

Flood Forecasting Time Series Forecasting

Sep 26, 2026cs.LG

Predicting the Financial Impact of Supply Chain Risk for Major AI-Related Semiconductor Firms: A Heterogeneous Graph Patch Transformer Approach

Modern semiconductor production relies on a globally distributed, multi-tier supply chain in which financial stress at one firm spreads with a delay and eventually affects the revenue, inventory, and profitability of the companies that design AI chips. Most firms see only their direct partners, and prior predictive research has mainly targeted market-based risk measures, so few tools forecast how supply chain stress will appear in reported financials. In this study, we propose a heterogeneous graph patch transformer that forecasts these quarterly changes one and two quarters ahead. Learning from a 15,186-company network over 60 quarters, the proposed model fuses quarterly fundamentals with macro-trade, event, and disaster signals through learned gates, carries risk across supplier, customer, ownership, and headquarters relations through typed, direction-specific propagation, and encodes the propagated histories with patch-based tokenization. In preliminary experiments on 116 focal semiconductor firms, the proposed model achieves the lowest error on every target at both horizons, and its profitability advantage widens at the two-quarter horizon. These forecasts can help supply chain managers and investors act before disruptions appear in reported financials.

Jianna Hur, Sagar Samtani

Data Science and Artificial Intelligence Lab (DSAIL), Kelley School of Business Indiana University, Bloomington, IN, USA

Financial Forecasting Supply Chain Management Time Series Forecasting Graph Transformer

Sep 26, 2026cs.LG

SIFT: Enhancing Time Series Foundation Models via Semantic Invariance and Structural Fidelity Fine-Tuning

Time Series Foundation Models (TSFMs) have achieved remarkable zero-shot performance through extensive pre-training on massive time series datasets. Nevertheless, due to the low-dimensional properties and diverse structural patterns of time series data, performing naive fine-tuning on TSFMs often leads to overfitting and falling into the mean-prediction trap. To address these challenges, we propose SIFT, a robust adaptation method that enhances time series foundation models by preserving Semantic Invariance and structural Fidelity throughout the fine-Tuning process. We employ semantic-invariant adversarial augmentation, which utilizes semantic spectrum decomposition to partition the semantic space and then generates perturbations within the non-core semantic subspace to bolster the model's robustness against these perturbations, mitigating overfitting. We implement a component-based structural fidelity enhancement, which facilitates component-wise mixup and imposes a reconstruction objective to improve the model's ability to preserve structural fidelity, alleviating the mean-prediction trap. Extensive experiments on representative TSFMs covering 10 real-world datasets demonstrate that SIFT can significantly enhance the performance of TSFMs.

Yi Tang, Tengxue Zhang, Yang Shu +3

East China Normal University, Shanghai, China · Chang’an University, Xi’an, China

Time-Series Foundation Models Time Series Forecasting Time Series Data Augmentation

Sep 26, 2026cs.LG

STRIDE: State-Transition Representation via Increment Dynamics and Evolution

We introduce STRIDE (State-Transition Representation via Increment Dynamics and Evolution), which defines states through derivative fingerprints and learns local functions for state transitions (qpairs), recasting continuous forecasting as transition prediction. Trailing convolution windows estimate local joint-transition frequencies, whose lagged differences form a high-dimensional increment trajectory. Proper orthogonal decomposition (POD) gives coordinate paths, jointly forecast by sparse dynamics with memory. Recombining their forecasts and applying history-anchored inversion recovers future transition distributions; sampled state paths select local functions to generate continuous forecasts. Three-seed experiments compare STRIDE against fourteen baselines across nine benchmark families. Five independent Markov and hidden-state baselines cover all 230 evaluated tasks, with 220 complete whole-horizon pairs. Against these comparators, system-weighted late-Energy win fractions range from 73.6% to 78.5% on 190 multi-step pairs; against DLinear, the fraction is 77.3% on 72 paired multi-step tasks. Matched controls examine the intermediate representation. On 64 independently initialized Aizawa trajectories, late-Energy reductions against four matched controls range from approximately 24% to 56%, with all four prespecified contrasts passing Holm correction. These results connect transition-statistic prediction to continuous probabilistic forecasting, with substantial long-horizon gains in the matched Aizawa study.

Yuchen Xiong, Siming Huang, Jianfeng Sun

Time Series Forecasting Probabilistic Time Series Forecasting Latent Dynamics Modeling State Representation Learning Chaotic Time-Series Prediction

Sep 26, 2026cs.LG

DiffPTS: Rethinking Diffusion ELBO for Probabilistic Time Series Forecasting

Probabilistic time series forecasting requires modeling and predicting complex and time-varying distributions. Recently, Denoising Diffusion Probabilistic Model (DDPM)-based approaches have shown promise by equipping the dif- fusion process with pretrained mean and variance estimators to accommodate distributional shift. However, these methods typically follow the standard DDPM framework and consider only partial components of the evidence lower bound (ELBO), treating the training of estimators as designed regression tasks separate from the variational inference framework. To address this, we rethink the ELBO under the Location-Scale Noise Model (LSNM) and find that it naturally induces a Gaussian negative log likelihood objective for the estimators and inherently defines a joint training objective that unifies recent diffusion paradigms for probabilistic forecasting. Building on this principled ELBO reformulation, we propose Diff- PTS, a general framework that enables end-to-end optimization of all components within the ELBO. Across multiple benchmarks, DiffPTS consistently outperforms recent models, achieving state-of-the-art performance with an average CRPS/MSE reduction of over 14.53%/16.55% compared to existing diffusion-based methods. The code is available at https://github.com/wwy155/DiffPTS.

Weiwei Ye, Dongyuan Li, Hangchen Liu +3

The University of Tokyo · Harbin Institute of Technology, Shenzhen

Time Series Forecasting Probabilistic Time Series Forecasting Diffusion Models Variational Inference

Sep 25, 2026cs.LG

Model-Agnostic Online Certificate-Driven Calibration for Time Series Forecasting Under Distribution Shift

Time series out-of-distribution generalization requires forecasters to remain reliable when deployment dynamics differ from training conditions due to covariate shift, concept shift, and temporal dependence. Probably Approximately Correct Bayesian domain adaptation provides computable certificates by decomposing target risk into a source risk term, a source-to-target mismatch term, and a complexity term, but standard analyses rely on independent sampling and distributional stability, assumptions that are violated in time series by serial dependence and nonstationary shift. We propose a model-agnostic online martingale Probably Approximately Correct Bayesian framework that yields finite-sample certificates under temporal dependence and distribution shift. The certificate replaces independent-sample concentration with martingale concentration that adapts to loss scale and predictable variation. We use the certificate as a surrogate regularizer for online calibration by training a gated residual Bayesian head on top of a fixed forecasting backbone, producing a corrective update that reverts to the backbone prediction when the gate is closed. Online calibration combines a source risk anchor, a posterior-shift penalty, and a time-adaptive mismatch term computed from target windows observed before forecasting. It follows a predict-then-update protocol in which outcomes become available only after forecasting and are used to update subsequent predictions. Experiments across convolutional, attention-based, and large language model-based forecasters show improved stability and accuracy under covariate and concept shift.

Chenfeng Huang, Zixuan Ma, George Michailidis

Department of Statistics and Data Science, University of California, Los Angeles, Los Angeles, California, USA

Time Series Forecasting OOD Generalization Model Calibration Temporal Distribution Shift PAC-Bayesian Generalization Bounds

Sep 25, 2026cs.AI

UQ-LOB: Uncertainty-Aware Limit Order Book Mid-Price Forecasting

Forecasting short-horizon mid-price movements from limit order book (LOB) data is central to algorithmic trading, yet most deep LOB forecasters are point predictors: they output a direction or a displacement, but never indicate which of their forecasts can be trusted. We introduce UQ-LOB, a lightweight, encoder-agnostic uncertainty quantification module that attaches to any pretrained LOB encoder and, in the spirit of attentive neural processes, conditions each forecast on a context set of recently completed windows whose outcomes are already realised. The UQ-regression variant outputs a calibrated Gaussian over the future tick displacement, while the UQ-classification variant outputs a categorical distribution over down/up/stationary. Both expose a scalar confidence (predicted signal-to-noise ratio or class probability) that supports selective prediction. On 5.2 billion LOB events across seven cryptocurrency assets and horizons of 5, 10 and 15 seconds, UQ-regression attains near-nominal 68% interval coverage, and restricting to the most confident 10% of predictions raises directional macro F1 by 0.11-0.15 for UQ-regression and 0.05-0.11 for UQ-classification, at every horizon. On large, economically meaningful moves, the tightest confidence tier reaches a directional F1 of 0.88 (down) and 0.83 (up) at the 5-second horizon.

Derrick Gilchrist Edward Manoharan, Eljas Linna, Kestutis Baltakys +2

Data Science Research Centre Tampere University Tampere, Finland

Uncertainty Quantification Selective Prediction Financial Forecasting Time Series Forecasting Probabilistic Forecasting

Sep 25, 2026cs.CL

ViSTA: A Simple Bridge Extends Visual Alignment to Clinical Time-Series Understanding in Multimodal LLMs

Clinical prediction models estimate risk from patient measurements, while large language models support medical text understanding and question answering. Yet their language capabilities do not ensure accurate prediction from structured, high-dimensional clinical time series. Improving this ability would connect risk estimation with flexible questions about a patient's evolving condition. We introduce ViSTA, a compact adapter that incorporates irregular numerical measurements into a pretrained vision-language model's chart representations. It learns corrections to visual tokens while leaving all pretrained parameters unchanged. On MIMIC-IV, ViSTA has the highest mean scores among the compared adaptations on all four metrics for acute kidney injury and mortality prediction across models with 2-9 billion parameters. With 0.516 million trainable parameters, the 2-billion-parameter model reaches an area under the ROC curve of 0.7376 for acute kidney injury, compared with GPT-5.6 Sol's 0.7380 with text input and high reasoning effort. Training for temporal question answering yields 69.27% accuracy at 4 billion parameters with over 90% fewer trainable parameters than low-rank adaptation using charts or numerical text, at a 2.82-4.88 percentage-point accuracy gap. ViSTA extends pretrained language models to numerical prediction and temporal questions.

Junyi Gao, Yu Shi, Pingzhao Hu +1

Centre for Medical Informatics, University of Edinburgh · Health Data Research UK · Biostatistics Division, Dalla Lana School of Public Health, University of Toronto +1

VLM Adaptation Medical VLMs Time Series QA Time Series Forecasting

Sep 25, 2026cs.LG

More Sensors Only One Field: Rethinking Continual Spatio-Temporal Forecasting

Continual spatio-temporal forecasting supports traffic management and environmental monitoring under evolving dynamics and expanding sensor networks. However, conventional graph-based continual learning methods tie forecasting representations to the current sensor layout, so sensor expansion can alter the representation of learned spatial relationships. Our key insight is that sensor expansion changes the evidence available about a process without necessarily changing the dynamics to be learned. We propose STFO (Spatio-Temporal Field Operator), which parameterizes forecasting knowledge as a shared field-evolution operator and handles changing sensor layouts through observation and query interfaces. Normalized coordinate-based aggregation lifts irregular sensor histories onto a fixed latent grid, enabling reuse of learned spatial maps across observation sets without sensor-specific parameters. To accommodate process drift, a spectral descriptor summarizes variation across spatial scales and conditions Fourier propagation and attention to adapt operator responses to the current spatial regime. Coordinate-based decoding queries the evolved field at sensor locations and combines spatial corrections with local-history predictions. Experiments on PEMS-Stream, CA-Stream, and AIR-Stream demonstrate state-of-the-art average forecasting performance. STFO-Large reduces average MAE over DOL by 8.4% on PEMS-Stream and 4.7% on CA-Stream. Our code is available at https://github.com/Xielewei/Spatio-Temporal-Field-Operator.

Lewei Xie, Haoyu Zhang, Jiajun Zhou +6

City University of Hong Kong (Dongguan) · City University of Hong Kong · Zhuhai College of Science and Technology +1

Spatiotemporal Forecasting Time Series Forecasting Neural Operators

Sep 25, 2026cs.LG

WorldTS: World Modeling for Multimodal Covariate-aware Time Series Forecasting

Time series forecasting is typically framed as learning a direct mapping from historical to future observations in the observation space. However, sequences of observations generally provide only a partial view of the dynamics of the underlying system, with future observations being shaped by latent dynamics. Recent latent-space forecasting methods thus achieve improved performance by predicting future observations from latent-space representations of historical observations rather than directly forecasting future observations in the observation space. Next, while future observations are also shaped by external factors, how to incorporate external, often multimodal, information into forecasting, so that it can shape latent-state formation and evolution directly, remains underexplored. We propose WorldTS, a world-modeling based forecasting framework that integrates multimodal covariates directly into the forecasting to further improve forecasting performance. Specifically, WorldTS employs a two-stage training strategy. First, it learns forecasting-relevant latent state dynamics conditioned on multimodal covariates, yielding encoded future states. Next, the learned state dynamics are frozen, and an observation decoder is trained to map the predicted future states back to future observations. Extensive experiments on 21 real-world datasets offer insight into WorldTS and its effectiveness.

Yuhan Zhu, Xiangfei Qiu, Hanyin Cheng +5

East China Normal University · Aalborg University

Time Series Forecasting Multivariate Time Series Forecasting World Model Learning

Sep 25, 2026cs.LG

Aurora-X: Built for Extreme Time Series Forecasting

Time series foundation models (TSFMs) enable cross-domain forecasting, but their development as general-purpose forecasters remains constrained by underexplored training potential and limited architectural versatility. To address these challenges, we introduce Aurora-X, a billion-scale TSFM with a progressive curriculum and a unified architecture. We first use channel-independent pretraining to learn temporal patterns, then introduce cross-variable dependencies, varied context and horizon lengths, and future covariates if available during midtraining. Variable-resolution post-training further enables an adjustable temporal span per token at inference. With fixed model weights, this supports longer histories under a fixed token budget or fewer tokens for the same history, enabling test-time scaling. With a versatile architecture, Aurora-X supports cross-variable modeling, covariate conditioning, and parallel decoding of future patches for probabilistic forecasting. These are supported by a novel pattern-guided mixture-of-experts that expands model capacity through sparse activation and uses shallow patch similarities to constrain deep-layer routing, guiding expert specialization across heterogeneous time series. Furthermore, we propose an implicit quantile network head that predicts arbitrary quantiles to characterize predictive distributions, enhancing probabilistic forecasting flexibility. Comprehensive experiments on GIFT-Eval, TIME, FEV-Bench, TFB, and DAG-Bench demonstrate state-of-the-art forecasting performance against pretrained TSFMs and task-specific supervised models.

Xingjian Wu, Chenjuan Guo, Xiangfei Qiu +6

East China Normal University

Time Series Forecasting Time-Series Foundation Models Multivariate Time Series Forecasting Long-Term Time Series Forecasting Probabilistic Time Series Forecasting

Sep 25, 2026cs.LG

EPOC: Endpoint-Preserving Online Correction With Compressed Residual State for Multi-Horizon Time Series Forecasting

Completed forecasts provide residual feedback, but retaining full residual blocks increases auxiliary state. We propose Endpoint-Preserving Online Correction (EPOC) with a compressed residual state. It stores low-order discrete cosine transform (DCT) coefficients and the final value of the preceding residual block. Each channel shares the endpoint across component-wise online ridge regressions using current-forecast coefficients. We evaluate eight multivariate series, DLinear and PatchTST, three seeds, and two training variants: 96 matched fixed-base conditions at a 24-step horizon. EPOC achieves mean condition-wise reductions in mean squared error (MSE) and mean absolute error (MAE) of 15.40% and 9.35% from the uncorrected base, respectively, with a median of 6,352 B in retained auxiliary arrays. EPOC also outperforms the

δ

-Adapter, COSA, FAC, and OMPB in paired MSE on most conditions while retaining less state. Full ELF achieves the largest mean MSE reduction, 19.29%, but its median retained state is 474,048 B (

\times

75 relative to EPOC). Equal-size summary controls favor the endpoint by 1.65--2.20% in paired MSE; a coefficient-reconstructed endpoint yields similar accuracy to the observed endpoint, highlighting its role as a shared input. Increasing the retained DCT component count from 4 to 8 adds 1.00 percentage point of MSE reduction for 5,728 B. On jointly trained bases, EPOC lowers MSE by 16.69--20.15% relative to globally blended TEFL-style adapters applied to the same base. Code and numerical records are available at https://github.com/keiotakmin/endpoint-preserving-residual-correction.

Takumi Fujimoto, Hiroaki Nishi

School of Science for Open and Environmental Systems, Graduate School of Science and Technology, Keio University, Yokohama 223-8522, Japan · Department of System Design, Faculty of Science and Technology, Keio University, Yokohama 223-8522, Japan

Multivariate Time Series Forecasting Residual Learning Time Series Forecasting

Sep 25, 2026cs.AI

EXAONE Demand 1.0: A Time Series Foundation Model for Demand Forecasting

Time series foundation models (TSFMs) are pretrained on series from diverse domains, where demand series make up only a small fraction. Demand data has properties that such corpora rarely contain: Short histories, frequent zeros, censoring by stock-outs, and exogenous events that the series does not record. To this end, we propose EXAONE Demand, built on 1) a demand-specific corpus and 2) a demand-aware adapter. For the corpus, we assemble 11.3M series and 48.4B observations from 73 sources, and a synthetic generator supplies the behaviour that open demand data under-represents. For the adapter, we attach low-rank branches to a frozen general-domain backbone, one for each of the four demand classes (smooth, intermittent, erratic, and lumpy), and a router that reads eight scale-free statistics of the input series decides how much each branch contributes. We build EXAONE Demand in two versions, one trained on real-world and synthetic demand together and one trained on the synthetic corpus alone. On 22 held-out datasets, both versions outperform 36 TSFMs, and real-world demand adds a gain over synthetic data alone.

Seunghan Lee, Sangjun Han, Jun Seo +9

LG AI Research

Time Series Forecasting Time-Series Foundation Models

Sep 25, 2026physics.ao-ph

On the Limits of Univariate Deep Learning for Significant Wave Height Forecasting

This study conducts a systematic hyperparameter search across five deep learning architectures, DLinear, LSTM, PatchTST, ResAttLstm, and Mamba2, and nine context lengths (1-168 h) for single-station significant wave height (Hs) forecasting on NDBC buoy 41009, followed by re-evaluation of the best configurations on a 47-buoy, 37-year corpus. The five families converge to a common performance level on the multi-buoy evaluation (between-family SD = 0.0014 m^2, 0.8% of the grand mean), a spread dwarfed by the 4.83x cross-dataset MSE shift between buoy corpora. All multi-buoy trials beat persistence (mean skill +0.062), but no architecture consistently outperforms the others. On the single-buoy experiment, skill peaks at 12-24 h where five trials fall below persistence, per-family Q4/Q3 test MSE ratios range from 2.4 to 2.6, and deep models underperform persistence for the most extreme 1% of waves. These findings are consistent with the interpretation that persistence already captures the dominant linear-inertial signal in univariate Hs, and that architecture engineering under this univariate input setting has reached diminishing returns: cross-buoy variance, not model class, dominates forecast error. Future work should prioritise atmospheric covariates, zero-shot cross-buoy transfer, and decomposition of Hs into swell and wind-sea components. By establishing a rigorous reference baseline for what univariate Hs models can and cannot achieve, this study provides a benchmark against which future multivariate and physics-informed approaches can be calibrated, and offers practical guidance for lightweight buoy-level forecasting in mid-latitude storm-dominated and swell-mixed environments.

Yilin Zhai, Hongyuan Shi, Zaijin You

Shandong Key Laboratory Of Estuary And Coast & Nuclear Environment, Ludong University, Shandong, 264025, Yantai, China · School of Hydraulic and Civil Engineering, Ludong University, Shandong, 264025, Yantai, China · Institute of Coastal Research, Ludong University, Yantai, 264025, Shandong, China +1

Time Series Forecasting Forecasting Benchmarks

Sep 24, 2026cs.LG

Neuralized Multi-Wavelet Decomposition for Time Series Classification and Forecasting

Time series analysis is fundamental in domains such as finance, healthcare, and meteorology. Real-world time series often exhibit multiscale characteristics shaped by diverse latent factors, resulting in intricate temporal patterns and rich frequency structures. However, existing approaches typically focus on either frequency-domain decomposition or time-domain pattern extraction in isolation, neglecting their joint structure. This decoupled modeling limits representation expressiveness and undermines performance in tasks requiring simultaneous temporal and spectral reasoning. To address this gap, we propose m-WCN, a novel end-to-end deep learning framework that neuralizes multi-wavelet decomposition for joint extraction of temporal patterns and frequency components. By approximating the classical GHM multi-wavelet transform with trainable convolutional operators and enforcing orthogonality constraints, m-WCN produces interpretable multi-resolution representations. Built on this foundation, we introduce two task-specific architectures: TFBC for time series classification, which boosts discriminative features across frequency scales, and FTB for forecasting, which ensembles frequency-aware predictors. Extensive experiments on 64 UCR datasets and seven public forecasting benchmarks demonstrate the effectiveness of our approach. Built on the neuralized m-WCN, our TFBC and FTB outperform various baseline models across diverse datasets, achieving average improvements of 19.97% in classification and 19.92% in forecasting tasks.

Xiaohan Jiang, Jingyuan Wang, Jiahao Ji +3

School of Computer Science and Engineering, Beihang University, Beijing, China · School of Computer Science and Engineering and the School of Economics and Management, Beihang University, Beijing, China · School of Computer Science and Engineering, Beihang University, Beijing, China, and are also with the MOE Engineering Research Center of Advanced Computer Application Technology, Beihang University, China +1

Time Series Classification Frequency-Domain Feature Learning Time Series Forecasting Wavelet Methods Multiscale Time-Series Modeling

Sep 24, 2026cs.LG

Downside-Controlled Online Forecast Combination under Delayed and Revised Outcomes

Post-hoc correction adjusts a forecaster that cannot be retrained, such as a foundation model, but a correction fitted where errors are stable can hurt where they shift. We aim for downside control: not much worse than the starting forecast. We combine the frozen forecaster, a static corrector and an online corrector on the simplex, using only losses that mature after the horizon. Across seven benchmarks and four base models, two of them foundation models, the worst deterioration over 28 pairs at the main horizon is 0.15% and gains reach 11.5%. On day-ahead load for seven European bidding zones it lowers mean MSE in all seven zones, while single correctors raise mean MSE by up to 102% where the published forecast is most accurate. Three empirical conditions on expert speed, stream length and outcome alignment, each fixed by a documented failure, delimit its scope. Learning from the provisional outcome improves four zones on the settled one; learning on the settled outcome restores all seven.

Minkyoung Kim, Hyunjung Byun, Yohan Lee +1

Graduate School of Information, Yonsei University, Seoul, 03722, South Korea

Time Series Forecasting Online Learning

Sep 24, 2026cs.LG

The Cost of Long Memory: State, Context, and Stability Complexity in Sequence Models

Long-range temporal dependence poses a resource question for sequence models: for a specified predictive-memory law, how much state, context, or dynamical criticality is required in order to forecast accurately? We study this question directly in forecasting risk. For algebraically decaying predictive memory, we prove matching upper and lower approximation bounds for exponential and finite-state modes. The best

r

-mode forecast error decays as

e^{-Θ(\sqrt r)}

, so reaching forecast error

τ

needs

r=Θ(\log^2(1/τ))

states or modes. Earlier curse-of-memory results establish broad limitations of stable recurrent models under different approximation notions; here both sides match for one canonical predictive target in forecast risk, which fixes the optimal resource exponent for that target. We then show that genuine fractional long memory changes the geometry itself. In particular, forecast error is measured after fractional integration, prediction from a finite context of length

L

has an exact

1/L

leading order, and a fixed fractional strength

d

keeps the square-log state-complexity law. Near the short-memory boundary, we identify the relevant

d^2

and

d^4

scales and give a uniform constructive law in the intermediate regime. For nonlinear contextual recurrences with uniformly contractive state dynamics, we derive an exponential first-chaos envelope and an explicit necessary condition that relates forecast accuracy to the contraction margin. Vanishing forecasting error on an algebraic target forces the recurrence quantitatively toward criticality, a condition that is necessary and not by itself sufficient. Finite-sample Kullback--Leibler calculations further connect the predictive geometry to statistical information. Theorem-matched experiments with contractive state-space, gated recurrent, and attention models reproduce the state and stability predictions.

Yuheng Song

School of Management, Huazhong University of Science and Technology

Time Series Forecasting Recurrent Neural Networks State Space Models

Sep 23, 2026cs.LG

Learning Collective Dynamics with Differentiable Gaussian Representations

Collective responses depend on individual differences, contact opportunities, and accumulated experience. Learning their dynamics from aggregate counts requires connecting a population's response distribution to both current observations and future behavior. We introduce Differentiable Gaussian Dynamics (DGD), which learns this connection through three components: a Gaussian mixture representing heterogeneous response propensities, differentiable aggregation of contact intensity and behavioral probabilities, and feedback recurrence that updates subsequent responses. Reparameterized integration and temporal recurrence let aggregate prediction errors jointly train the distribution, observation functions, and feedback parameters. On four windows from KuaiRand-Pure and Online Retail II, DGD achieves lower joint behavioral negative log-likelihood than a DeepAR adaptation with a joint-behavior head. In Retail 2010, its one-day behavioral-count MAE is 4.71 versus 6.88 for this adaptation. Learning the distribution reduces behavioral negative log-likelihood by 10.82% relative to a fixed Gaussian in KuaiRand's standard-recommendation window; removing feedback dynamics raises joint KL from 0.0340 to 0.2577 in a controlled experiment. These results establish the value of learning population representations and their feedback process from aggregate observations. Code is available at https://github.com/OranAi-Ltd/oransim.

Jianxiang Ma, Mingfu Zhang, Xiaocui Yang +3

School of Computer Science and Engineering, Northeastern University, Shenyang 110819, China · OranAI, Shenzhen 518057, China · OranAI Ltd., City of Industry, CA 91748, USA

Dynamical Systems Time Series Forecasting Recommender Systems

Sep 23, 2026cs.LG

fable.intermittent: benchmarking probabilistic forecasting methods for intermittent time series

Intermittent time series are common in spare-parts demand and retail sales. Since the cost of forecast errors is typically asymmetric, decisions such as inventory control require the full predictive distribution rather than a point forecast. Many probabilistic forecasting methods have been proposed; their implementations, however, are scattered across different software frameworks, making it difficult to compare them systematically. We introduce fable

.

intermittent, an R package that implements several probabilistic forecasting methods for intermittent series within the fable framework. The package allows several models to be fitted and evaluated on a collection of time series through a single, simple forecasting pipeline. We also introduce TWEES, a new exponential smoothing model with a Tweedie predictive distribution. Fitting TWEES requires repeated evaluation of the computationally demanding Tweedie density. We also release the R package tweedieDistr, whose implementation of the Tweedie distribution is substantially faster than the existing one while preserving the same numerical accuracy. We evaluate the methods implemented in fable

.

intermittent on four datasets, also released in the package.

Stefano Damato, Lorenzo Zambon, Giorgio Corani +1

SUPSI, Istituto Dalle Molle di Studi sull’Intelligenza Artificiale (IDSIA), Lugano, Switzerland

Time Series Forecasting Forecasting Benchmarks Probabilistic Time Series Forecasting

Sep 23, 2026cs.LG

SGA: Uncertainty Quantification for Multi-Step Forecasting in Time Series Foundation Models

The recent emergence of Time Series Foundation Models (TSFMs) has significantly advanced multi-step forecasting performance, enabling accurate predictions over extended future horizons. However, existing TSFMs often suffer from significantly inherent uncertainty, which typically manifests as derived forecast branches emerging at each time step and spreading to subsequent steps; different forecast branches often exhibit varying forecasting performance, thereby undermining the credibility of TSFM forecasts. In this paper, we propose the Slicing-Graphing-Alignment (SGA) method to quantify the uncertainty of multi-step TSFM forecasts. The proposed SGA first characterizes the topology of all potential forecast branches using a directed acyclic graph, such that the graph complexity bounds the uncertainty of multi-step forecasts, and then precisely measures the graph complexity by integrating both topological information and TSFM-inherent stochasticity. Experimental results conducted on 11 TSFMs and 27 datasets demonstrate that (i) SGA achieves the best performance when ranking predictive errors with uncertainty estimates; (ii) SGA works with a more extensive and more precise sampling coverage than those of existing UQ methods, deriving a quantification mechanism fundamentally different from those of established ones; and (iii) larger model scales of TSFMs correlate with lower uncertainty estimates of multi-step forecasts, suggesting another empirical scaling law for uncertainty quantification of multi-step TSFM forecasts.

Xin-Yu Hu, Shuang Liang, Cheng Feng +1

National Key Laboratory for Novel Software Technology, Nanjing University, China. · School of Intelligent Science and Technology, Nanjing University, China. · Siemens Data and AI Research, Beijing, China. +1

Uncertainty Quantification Time Series Forecasting Time-Series Foundation Models

Sep 23, 2026cs.LG

Time-Series Foundation Models That Understand Data Revisions

Historical observations are not always fixed: statistical agencies revise previously published values as new evidence arrives. Forecasting from a contemporary download can therefore expose a model to information unavailable at the date it purportedly made a prediction. We propose VINTAGE-TS, a revision-aware adaptation of a time-series foundation model that distinguishes observation time from information-availability time. Its targets are the next period's first-published value and the value available a fixed number of days after that publication; neither is declared final truth. A joint predictive distribution preserves dependence between these targets and exposes uncertainty about their difference. We specify an ALFRED-based rolling evaluation, a matched Chronos-2 comparison, conventional and revision-aware baselines, and a separate audit of pretraining overlap. The accompanying software implements validity-interval reconstruction, delayed-label filtering, a frozen-backbone adapter interface, and reproducible diagnostics. An executed synthetic demonstration and a 25-configuration sensitivity suite verify the workflow, expose variation across seeds and revision regimes, and illustrate how hindsight contamination changes measured performance. Thirty one automated tests check temporal and integration contracts. Real ALFRED and Chronos-2 experiments have not been executed; no empirical foundation-model advantage is claimed.

Taimoor Ahmad

Superior University Lahore, Pakistan

Time Series Forecasting Temporal Data Leakage Time-Series Foundation Models Probabilistic Time Series Forecasting

Sep 23, 2026cs.AI

Sparse-Observation Atmospheric Thermal Forecasting with Physics-Informed Neural Networks for Climate-Aware Digital Twins

Short-horizon forecasts of atmospheric temperature are needed to support climate-aware digital-twin systems, but such forecasts must be produced where thermal observations are incomplete. This study evaluates a physics-informed neural network for potential-temperature forecasting, constrained by a pressure-coordinate thermodynamic advection-source equation and a diabatic-source closure fit from the preceding 12-hour period and frozen before future-time training. Using hourly ERA5 reanalysis at three pressure levels, the model is evaluated as a conditional hindcast at lead times of one, two and three hours against persistence, local-trend, and two matched neural-network baselines, one of which receives the same future meteorological forcing as the PINN, helping distinguish the physical constraint from access to future forcing. In an Oklahoma development case, mean RMSE improvement over the strongest baseline grew from 8.1% at one hour to 23.8% at three hours; under an observation-density sweep down to 5% of candidate locations, this 3-hour advantage remained 14.6--16.9%, with no evidence that lower density improves performance. Under a fixed protocol transferred to an Alabama heat event with three virtual-observation layouts, three-hour improvement ranged 19.7-24.4% with consistent origin-level wins. A parallel Montana stress test, in which fixed pressure levels intersected complex terrain, produced a three-hour degradation of roughly 17.5%, identifying a terrain-related applicability limit of the formulation. Together, these results indicate that the physics constraint's benefit grows with forecast horizon, persists under severe observation sparsity, and transfers across regions, but is bounded by the validity of a fixed vertical-coordinate representation over complex terrain, evidence relevant to physics-constrained components of climate-aware forecasting and digital-twin systems.

Tannaz Goodarzvand Chegini, Elyas Shivanian, Behzad Karimi +1

Department of Mathematical Sciences / Montana State University, Bozeman, Montana, US · Department of Mathematics / Imam Khomeini International University, Qazvin, Iran · Department of Electrical and Computer Engineering, Montana State University, Bozeman, Montana, US +1

Weather Forecasting Time Series Forecasting Physics-Informed ML

Sep 22, 2026astro-ph.SR

PROSWIN: Probabilistic Solar Wind Speed Forecasting Using Deep Distributional Regression From Solar Images

Accurately predicting fast solar wind conditions is challenging, as uncertainties are large and unquantified by traditional single-value prediction models. In particular, the risks of high-speed solar wind streams (HSSs), which can cause damage to technological infrastructure, cannot be reliably assessed without probabilistic forecasts. We present PROSWIN, a probabilistic machine learning model that forecasts the hourly solar wind speed (SWS) at Earth with a four-day lead time. The approach combines solar images and magnetograms using a deep neural network coupled to a distributional regression algorithm. Because standard error metrics underweight the relevance of HSS peaks, we further introduce the prediction score, a model-selection metric that jointly rewards timeline and HSS peak accuracy. On 14 years of data, our forecast achieves very well-calibrated uncertainties (<1% average deviation). Using the continuous ranked probability score (CRPS), a metric that assesses distributional accuracy, we obtain a timeline CRPS of 41.0 km/s, an HSS peak CRPS of 45.3 km/s, and a prediction score of 42.3 km/s. We find that the 171 Å channel is an important complement to the typically used 193 Å and 211 Å channels and that the prediction score for model selection improves the applicability of the model. Compared to selected models from the literature, ours is the only one that is accurate for both timeline and HSS peak values, rather than trading one off against the other. These results support the advantages of probabilistic over single-value solar wind models. The introduced methods are also transferable to other forecasting problems.

Daniel Collin, Yuri Shprits, Luca Chiarabini +3

Space Physics and Space Weather, GFZ Helmholtz Centre for Geosciences, Potsdam, Germany · Department of Electrical Engineering and Computer Science, Technical University of Berlin, Berlin, Germany · Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany +5

Time Series Forecasting Probabilistic Time Series Forecasting

Sep 21, 2026cs.LG

When Tomorrow Becomes Today: Self-Evolving Policies for Agentic Time-Series Forecasting

Agentic time series forecasting concerns systems whose underlying mechanisms evolve, making the relative effectiveness of numerical models, reasoning strategies, and intervention rules inherently time-varying. Consequently, a time series agent must adapt the forecasts it produces and the orchestration policy that determines which components to trust and how to coordinate them. The deployment process naturally provides supervision for this adaptation as forecast horizons elapse and realized targets reveal the effectiveness of earlier decisions. Committing all numerical expert forecasts and candidate agent paths before target observation allows each realized outcome to evaluate the entire alternative set, providing delayed feedback without additional annotation. However, existing time series agents primarily incorporate prior experience through forecast refinement, reflection, or retrieval, without systematically converting realized outcomes into persistent updates to the joint orchestration policy governing later origins. To exploit this delayed feedback systematically, we introduce TimEvolve, a frozen-backbone time series agent that converts each realized outcome into persistent joint updates of expert trust, agent path selection, and intervention strength. A temporally ordered predict, reveal, and update protocol applies this feedback to subsequent forecasts. Experiments across eight Time-MMD domains show that TimEvolve achieves the best average MSE and MAE ranks among fifteen methods and the lowest errors on both metrics in seven domains. These results demonstrate the value of learning forecasting policies from the futures encountered during deployment.

Yifan Hu, Xilin Dai, Zhiyuan Qu +4

Ant International · Tsinghua University · The Chinese University of Hong Kong

Time Series Forecasting Self-Evolving Agents

Sep 21, 2026cs.AI

TimeLitmus: A Diagnostic Benchmark for Cross-Modal Understanding and Explanation Faithfulness in Event-Conditioned Time-Series Prediction

Large language models (LLMs) are increasingly used to make predictions from numerical time-series histories and textual events. Yet accuracy alone cannot reveal whether correct answers reflect effective integration of the two inputs or instead arise from event polarity, unimodal priors, or superficial cues. Likewise, plausible explanations may rationalize predictions without faithfully reflecting the evidence that drives model behavior. We introduce TimeLitmus, a diagnostic benchmark for cross-modal understanding and explanation faithfulness in event-conditioned time-series prediction. TimeLitmus contains 4,856 evaluation records across Finance and Traffic, combining natural prediction with controlled counterfactual and contrastive interventions, explanation-targeted faithfulness tests, and systematic shortcut controls. Across ten representative LLMs, standard prediction accuracy substantially overstates reliable cross-modal understanding: Hard Paired Contrast (HPC) pair correctness peaks at only 19.2% in Finance and 11.7% in Traffic, and all ten models show lower-than-expected consistency on Finance series-side controls. Models often recognize scenario relations explicitly yet fail to apply them during independent prediction. Explanation faithfulness shows a similar gap: in Traffic, most models cite the manipulated temporal factor in over 90% of cases, while behavioral support remains below 22%. Human annotators outperform LLMs on matched controlled and hard-pair diagnostics, confirming that these distinctions are recoverable from the inputs. Natural-only adaptation yields selective gains in evidence selection and input sensitivity, but not consistent gains in controlled or hard-pair behavior. The benchmark, evaluation suite, and supervised adaptation data will be released publicly.

Jie Gong, Maowei Jiang, Zhiwei Liu +6

School of Artificial Intelligence, Wuhan University, China · Nanjing Audit University, China · The University of Manchester, United Kingdom +3

LLM Evaluation LLM-Based Time Series Forecasting Multimodal Model Evaluation Faithfulness of Language Model Explanations Time Series Forecasting

Sep 21, 2026cs.LG

GraphToolbox: A Configurable Python Framework for Graph Neural Network Forecasting

Electricity forecasting often involves spatially related signals observed over regions, substations, and feeders, and Graph Neural Networks (GNNs) provide a natural way to represent these relations. Building a complete GNN forecasting experiment is nonetheless laborious, because graph construction, model selection, training, aggregation, and interpretation sit in incompatible tools. We present GraphToolbox, an open-source Python framework that unifies these stages in one configurationdriven pipeline built on PyTorch Geometric. It offers data-driven graph construction, an adapter that instantiates and trains 51 of the 65 PyTorch Geometric convolutions together with the recurrent cells of PyTorch Geometric Temporal, online expert aggregation, forecasting interpretability, and significance testing on cached forecasts. We evaluate the pipeline in two case studies. On French regional load, the 48 convolutions included in the complete forecasting sweep fall in a band from 1.14% to 1.60% error, online aggregation lowers this to 0.98%, and the graph models improve on classical additive and boosting baselines. On net-load, direct graph models are less accurate than a classical additive model, while forecasting each physical component separately improves them without closing that gap. Both comparisons use the same experimental interface, illustrating the role of GraphToolbox in systematic architectural evaluation.

Eloi Campagne, Yvenn Amara-Ouali, Yannig Goude +1

CB · LMO, CELESTE · EDF R\&D +1

Time Series Forecasting Electricity Load Forecasting Spatiotemporal GNNs

Sep 21, 2026cs.LG

Overlay_dx - Automating forecasting evaluation

Traditional evaluation metrics provides numerical values but often lack comprehensibility, hindering effective differentiation of model performances. Our work addresses this challenge by introducing overlay_dx, a novel evaluation metric measuring the performance of time series prediction models. Overlay_dx is a visual metric that represents the percentage of predictions falling within a confidence interval around actual values. Additionally, once evaluation results are plotted, overlay_dx computes the area under the overlay curve, providing a quantitative measure of alignment between predicted and actual values across different thresholds and predictions. Through extensive experiments, we demonstrate that our approach offers a unified evaluation framework that combines both visual and numerical assessments, enabling improved model comparison and providing valuable insights for further research and optimization efforts in time series prediction.

Long Ngo, Mohammed Amine Chamli, Jonathan Rivalan +1

Smile, Asnières, France

Time Series Forecasting Forecasting Benchmarks

Sep 21, 2026cs.LG

$t_0$ : A Time-Series Foundation Model for Forecasting with Context

We present

t_0

, a family of open-weights foundation models for forecasting with multivariate context. We release its first two members:

\texttt{t0-alpha}

and

\texttt{t0-beta}

, respectively 102M and 256M parameters. Both condition their forecasts on target history, past covariates, and known-future covariates, without task-specific retraining. Their transformer layers alternate attention along time and across variates. They produce probabilistic forecasts through quantile predictions. Pretraining combines curated public data with synthetic generator families constructed to contain covariate-to-target dependencies. On GIFT-Eval,

\texttt{t0-alpha}

reaches an aggregate CRPS of 0.4941, and

\texttt{t0-beta}

a CRPS of 0.4738 and a MASE of 0.6865, third on both and within 4.0% of the best zero-shot TSFM. On fev-bench they score 42.2 and 46.7 in skill, the latter third again and 2.0 points behind the leader. We analyze

\texttt{t0-alpha}

in depth. Known-future covariates raise its skill by 6.3 percentage points across 30 tasks. The report also examines its calibration, its rollout strategy on long horizons, and its robustness to missing data. On the Victoria electricity-demand benchmark,

\texttt{t0-beta}

is among the most accurate models with a context of nearly a year. In an independent Macrocosm evaluation of hourly ERCOT prices over 29 months, both cut the MAE of the lagged-price baseline by 38%.

Lucas Meyer, Claudio Sole, Huikan Xiang +6

The Forecasting Company · Macrocosm

Multivariate Time Series Forecasting Zero-Shot Time Series Forecasting Time Series Forecasting Time-Series Foundation Models Probabilistic Time Series Forecasting