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.

Jun 3, 2026

RIDE: An Open Dataset and Benchmark for Train Delay Prediction

Train delay prediction is an important problem for both passengers and railway operators, yet progress in the field remains difficult to assess due to the lack of standardized datasets, prediction targets, and evaluation protocols. To address this gap, we introduce RIDE, an open dataset and benchmark for train delay prediction built at nationwide scale over the Belgian railway network. RIDE covers 94.5M train events, 3.6M journeys, and 35.7M weather records from 2023 to 2025. It is organized as a layered data pipeline from raw railway and weather sources to two public releases: a reusable intermediate relational dataset and model-ready benchmark datasets. The benchmark standardizes the prediction task and the training and testing data. It also provides a unified evaluation protocol that supports direct comparison across models. Using this framework, we provide the first comprehensive comparative evaluation of non-learning, statistical learning, and deep learning models. We show that learning-based methods clearly outperform non-learning models, with graph neural networks achieving the best mean performance, while the strongest learning-based models remain relatively close to one another. Beyond aggregate mean absolute error (MAE) and root mean squared error (RMSE), the framework also provides breakdowns by prediction horizon and delay change, enabling more detailed analysis of model behavior across forecasting regimes.

Clément Elliker, Mathis Le Bail, Clément Mantoux +2

LIX, École Polytechnique, IP Paris, France · e.SNCF Solutions, France

Intelligent Transportation Systems Time Series Forecasting Forecasting Benchmarks

Jun 3, 2026

Signed Dual Attention: Capturing Signed Dependencies in Time Series Forecasting

Initially developed for natural language processing, Transformer architectures and attention mechanisms are now central to a wide range of deep learning models, including applications in time series forecasting. A standard attention mechanism, however, implicitly assumes homophilic interactions, limiting its ability to model data with positive and negative dependencies, such as time series. In this work, we introduce the Signed Dual Attention, a novel attention formulation that captures both positive and negative relational patterns without additional parameters. By leveraging a dual message-passing scheme inspired by correlation structures, Signed Dual Attention propagates both supportive and contrastive information within a single shared block, effectively achieving the expressiveness of two head attention without additional parameters. This module can be seamlessly integrated into existing architectures and can yield performance gains in certain situations, requiring signed relational modeling. This approach opens a pathway toward more expressive and parameter-efficient transformers.

Balthazar Courvoisier, Tristan Cazenave

Queensfield AI Technologies, Paris, France · LAMSADE, Universit´e Paris Dauphine - PSL, Paris, France

Time Series Forecasting Transformer Attention Time Series Transformers

Jun 3, 2026

REGAIN: REconciliation GAIN-driven Auxiliary Direction Learning

Forecast reconciliation usually starts from a fixed measurement system and asks how forecasts should be projected onto a coherent space. We ask a different question: which additional linear measurements should be forecast and included in the reconciliation system? We propose REGAIN, a reconciliation-gain framework that learns normalized auxiliary directions, forecasts the induced series with a frozen forecasting oracle, and selects directions by their target-weighted loss reduction after augmented generalized least-squares reconciliation. Unlike variance-based components or predictability-based auxiliary selection, REGAIN optimizes the downstream effect of an auxiliary measurement on the final reconciled forecasts. We provide a statistical characterization showing that useful auxiliary directions must provide complementary information about unresolved target uncertainty, rather than merely being easy to forecast. The analysis also clarifies the covariance-risk reduction mechanism, the role of bias changes in realized quadratic risk, and the stability of estimated gain signals. A stagewise learning algorithm with held-out gain screening is developed, together with an optional joint refinement step. Experiments on Beijing PM2.5 and Australian Tourism data show that gain-selected measurements can improve both ordinary multivariate and hierarchical forecasts, especially when they reveal residual uncertainty not captured by the original measurement system.

Weijia Li, Shun Hu, Yanfei Kang

School of Mathematical Sciences, Beihang University, Beijing, China · School of Economics and Management, Beihang University, Beijing, China

Multivariate Time Series Forecasting Time Series Forecasting

Jun 3, 2026

Expectations vs. Realities: The Cost of MSE-Optimal Forecasting Under Conditional Uncertainty

Multi-step time series forecasting (MSF) is commonly evaluated using point-wise error metrics such as mean squared error (MSE), implicitly treating the conditional mean as a sufficient target. We show that this can be misleading under conditional uncertainty, where the conditional expectation becomes unrepresentative of typical realized values at longer horizons. We formalize this effect through a conditional uncertainty gap and prove that whenever this gap is nonzero, no deterministic predictor can simultaneously minimize MSE and match the marginal distribution of realized futures. This establishes a fundamental, model-agnostic trade-off between point accuracy and marginal realism in MSF evaluation. Using controlled stochastic dynamical systems and nine real-world forecasting benchmarks, we empirically characterize the resulting accuracy--realism frontier and \textbf{quantify the practical cost of MSE-only model selection}. As conditional uncertainty increases with forecast horizon, the attainable set expands into a pronounced Pareto front, separating MSE-optimal but under-dispersed predictors from methods that trade accuracy for realistic marginal variability. \textbf{Across benchmarks, we find that small relaxations in MSE (

\boldsymbol{\le 5\%}

) frequently unlock disproportionate gains in marginal realism, with median improvements of

\mathbf{17.3\%}

and gains exceeding

\mathbf{30\%}

in some datasets.} We further show that common forecasting strategies systematically occupy different regions of this frontier: direct multi-output predictors concentrate near the accuracy-optimal extreme, while recursive strategies and sample-based inference favors marginal realism. Together, these results expose a structural failure mode of MSE-based evaluation in long-horizon forecasting and recast strategy and inference selection as navigation of an unavoidable accuracy--realism trade-off.

Riku Green, Zahraa S. Abdallah, Telmo M Silva Filho

The University of Bristol Bristol, UK

Long-Term Time Series Forecasting Time Series Forecasting Probabilistic Time Series Forecasting

Jun 2, 2026

Metric-Aware Hybrid Forecasting for the CTF4Science Lorenz Challenge

We describe our approach to the CTF4Science Lorenz challenge, a benchmark that mixes short-horizon forecasting, long-time distribution matching, and trajectory reconstruction across nine task pairs. The key discovery is that no single model family dominated all metrics. Instead, we built a metric-aware hybrid system that assigned a different predictor to each metric family: (1) synthetic-pretrained denoisers for full-trajectory reconstruction, (2) Lorenz ODE fitting and trajectory shooting for the first 20 forecast steps, and (3) histogram-tail substitution using synthetic Lorenz libraries for long-time evaluation. A representative mature submission from this system family scored 83.83551 on the public leaderboard, and a small follow-up stack of the same ideas reached 83.85529. We focus on the cleaner intermediate system because it captures the full method while remaining simple enough to reproduce and analyze, while the final submission can be understood as a conservative extension of the same backbone.

Cen Lu

EPFL & Idiap Research Institute · Switzerland

Time Series Forecasting Forecasting Benchmarks Chaotic Time-Series Prediction

Jun 2, 2026

Stationarity-Aware Retrieval-Augmented Time Series Forecasting

Time series forecasting relies on historical patterns, but real-world series often exhibit non-stationarity and regime shifts that challenge fully parametric forecasters. Inspired by Retrieval-Augmented Generation (RAG), recent work augments forecasters by retrieving relevant historical segments and using them as external evidence at inference time. However, due to the intrinsic non-stationarity of real-world time series, a highly similar past segment does not necessarily imply a similar future, rendering similarity-only retrieval brittle and prone to redundancy. We propose Stationarity-Aware Retrieval-Augmented Time Series Forecasting (SARAF), a framework that adaptively balances relevance and diversity in retrieval. SARAF first forms a candidate pool via temporal similarity with time-aligned enhancement, then applies a diversity-aware selection strategy to cover heterogeneous historical regimes, with the diversification strength automatically modulated by dataset-level stationarity. Moreover, SARAF uses stationarity-aware aggregation to fuse the retrieved futures. Extensive experiments on eight real-world datasets show that SARAF achieves competitive forecasting performance and improves average accuracy and robustness over strong baselines, with particularly clear benefits under challenging non-stationary settings. Code: https://github.com/ShiqiaoZhou/SARAF.

Shiqiao Zhou, Holger Schöner, Zipeng Wu +3

University of Birmingham Birmingham, United Kingdom · Siemens AG Munich, Germany

Time Series Forecasting Non-Stationary Time Series Forecasting Retrieval-Augmented Time Series Forecasting

Jun 2, 2026

Adaptive Patching Is Harder Than It Looks For Time-Series Forecasting

Adaptive patching is a recent and compelling proposal for time-series Transformers: allocate finer patches where the sequence looks locally informative. This paper asks under what conditions a content-adaptive patching operator should outperform a tuned uniform one. Local heterogeneity alone is not enough: under pointwise forecasting losses, a complex-looking region is not automatically one where finer patching reduces the loss. We model patching as a budgeted bitrate allocation and derive an explicit threshold that a dynamic patching rule must satisfy to beat a well-tuned uniform baseline, then bound the achievable improvement both locally (a quadratic surrogate) and globally (a strong-convexity bound under the model's assumptions). Two structural results follow: without a coupling constraint, scalar local complexity cannot produce a non-uniform optimum under a common loss landscape; and once the backbone is trained to its representation-aware optimum, the alignment gain collapses around a well-tuned uniform patch size. To test these predictions, we run a controlled isolation study on three representative architectures, replacing each adaptive mechanism with a uniform patch-size sweep while keeping the backbone, data, and training protocol fixed. On standard long-horizon forecasting benchmarks, the validation-selected uniform baseline is competitive with the dynamic counterpart, with per-setting effects concentrated near zero and no consistent directional advantage once results are aggregated by dataset. The larger gains we do observe are method- and dataset-specific. Adaptive patching should therefore be evaluated against a tuned uniform baseline; its value depends on whether a cheap and reliable routing signal can identify where finer patches actually reduce forecasting loss.

Federico Zucchi, Yi Xie, Chao Zhang +3

ICube, University of Strasbourg, Illkirch-Graffenstaden, France · Cephalgo, Strasbourg, France · Technical University of Munich +3

Long-Term Time Series Forecasting Time Series Forecasting Time Series Transformers

Jun 2, 2026

Validation-Gated Multi-Agent Governance for Online Adaptation of Thermal-Hydraulic Surrogate Models under Operating-Regime Shift

Artificial-intelligence surrogates can support second-by-second thermal-hydraulic forecasting, but models selected and frozen offline may become condition-locked once deployed outside their pretraining envelope. This study develops a guarded continual-adaptation framework for experimental thermal-hydraulic loop data in which role-separated agents - Monitor, Diagnosis, Adaptation, Safety-Auditor, and Orchestrator - diagnose error signatures, prioritize candidate model families, and review promotions, while deterministic champion-challenger gates and background shadow learning retain final authority over model replacement. Seven surrogate families were screened by blocked three-fold cross-validation, and a temporal Fourier neural operator was selected as the initial champion for 60-s-history-to-10-s-trajectory forecasting on two held-out transients, with three seeds per adaptive mode. Static deployment gave a channel-averaged MAE of 7.06 and a 56.8% warning-exceedance ratio; rule-based adaptation reduced MAE to 6.54, whereas shadow refresh alone remained close to Static. The MA-Full mode, in which the role-separated multi-agent council reviews every evaluated stream step, achieved the lowest mean error, 5.72, and 35.8% exceedance, corresponding to a 19.0% improvement over Static. Paired bootstrap intervals against Static excluded zero, although intervals among adaptive modes overlapped and the six paired units limit broad statistical claims. Validated promotions from the neural operator to Transformer and graph neural network indicate that logged, gate-controlled adaptation can support auditable surrogate evolution while deterministic gates retain deployment authority.

Doyeong Lim, Seungyoon Lee, In Cheol Bang

Department of Nuclear Engineering, Ulsan National Institute of Science and Technology (UNIST), Ulsan, 44919, Republic of Korea

Neural Surrogate Modeling Continual Test-Time Adaptation Time Series Forecasting AI Agent Governance

Jun 2, 2026

FinStressTS: A Parametric Synthetic Benchmark for Time-Series Forecasting in Finance

Financial forecasting is difficult due to low signal-to-noise ratios, latent factors, heavy tails, regime shifts, and jumps. Real-world benchmarks offer limited failure attribution: researchers can observe underperformance, but often cannot isolate why because mechanisms are unobservable and entangled. Real financial data reveal only one realized path, making it difficult to assess tail-risk calibration or data efficiency. We introduce FinStressTS, a mechanism-aware synthetic benchmark that links model behavior to controlled structural causes. FinStressTS comprises 30 diagnostic environments around six mechanism families: volatility clustering, multi-scale persistence, heavy-tailed shocks, regime switching, self-exciting jumps, and zero-inflated processes. We evaluate two tasks: point forecasting, using NMAE across five settings, and probabilistic forecasting, using CRPS under known data-generating mechanisms. We benchmark 15 models, from classical methods (HAR, VAR) to Transformer forecasters (PatchTST, iTransformer) and deep probabilistic architectures (DeepAR, TSFlow), and use learning curves to measure sample efficiency. Our evaluation reveals three insights. First, performance is mechanism-dependent: autoregressive and linear models are highly competitive, and often outperform Transformer-based models, in several volatility-, tail-, and jump-driven environments. Second, distributional alignment matters: parametric probabilistic models such as DeepAR calibrate well in stationary settings, while flexible models can help when distributions become multimodal or sparse. Third, neural models often require more data to match simple baselines, with larger gains mainly when learning latent regimes or complex distributions. FinStressTS provides an open framework for diagnosing failure modes and advancing risk-aware forecasting.

Jiaze Sun, Kelvin J. L. Koa, Ruiyang Ni +3

National University of Singapore Singapore · National University of Singapore Asian Institute of Digital Finance Singapore · Nanyang Technological University Singapore

Financial Forecasting Time Series Forecasting Forecasting Benchmarks Synthetic Benchmark Generation Financial Time Series Finance+1

Jun 2, 2026

From Long News to Accurate Forecast: Importance-Aware Fusion and PRM-Guided Reflection for Time Series Forecasting

Incorporating news into time series forecasting is appealing because news can reveal abrupt exogenous events that historical values alone cannot recover. However, existing LLM-based news-forecasting pipelines face two practical limitations: relevant news articles often exceed the model's context window, and iterative retrieval of supplementary news is typically unguided, leading to redundant updates and slow convergence. We address these issues with a novel framework that combines importance-aware news compression and process-level retrieval supervision. First, we train an importance reward model that estimates the forecasting utility of each article and uses this signal to allocate compression budgets during sequential pairwise fusion, preserving informative content within a fixed context limit. Second, we introduce a process reward model (PRM) that ranks multiple supplementary-news candidates conditioned on the current error profile and the history of previously selected articles, replacing one-shot blind retrieval with quality-controlled selection. Both components are trained offline using historical data with ground truth; inference uses the frozen filtering logic and compression modules without any reflection loop. Experiments on finance, energy, traffic, and bitcoin forecasting benchmarks show that our method improves prediction accuracy over strong baselines, significantly reduces the number of refinement iterations compared to the iterative baseline, and remains effective when relevant articles span thousands of tokens.

Mingyang Liu, Qingcan Kang, Yuke Wang +6

Department of Computer Science, City University of Hong Kong · Work done as an intern in Huawei Noah’s Ark Lab. · Huawei Noah’s Ark Lab

Process Reward Models Financial Forecasting Time Series Forecasting LLM-Based Time Series Forecasting Retrieval-Augmented Time Series Forecasting Context Compression

Jun 1, 2026

Data-Driven Forecasting of three-Component Seismograms Using Transformer Architectures

Forecasting seismic waveforms beyond observed data remains challenging due to the nonlinear, dispersive, and multi-scale nature of seismic wave propagation. In this work, we introduce \textsc{SeismoGPT}, a transformer-based autoregressive model designed to forecast three-component seismic waveforms directly in the time domain. Forecasting is formulated as a physically constrained continuation problem in which the model receives waveform context beginning at the P-wave arrival and extending a defined time beyond the S-wave arrival, after which future motion is generated recursively without access to ground-truth samples. Evaluation is performed on synthetic seismograms spanning source depths of 5--100,km, epicentral distances of 10--90

^\circ

, and magnitudes

3 \leq M_w \leq 7

. To disentangle the effects of context length and prediction horizon, we define three evaluation configurations using a distance-normalized context ratio and fixed prediction horizons of 120 and 240,s. Across all configurations, the model achieves a median normalized cross correlation of 0.93 or higher. Analysis of representative forecasts shows that successful predictions preserve both phase coherence and spectral energy distribution. Where failure cases arise, this is primarily due to gradual phase drift during autoregressive rollout rather than unphysical signal generation. These results demonstrate that transformer-based sequence models can learn stable dynamical continuation of seismic wavefields, highlighting the potential of foundation-model approaches for physics-driven time-series forecasting. There are potential applications of this methodology in seismic warning and hazard mitigation, particularly for next-generation gravitational-wave observatories, such as the Einstein Telescope.

Waleed Esmail, Stuart Russell, Jana Klinge +2

Institut für Kernphysik, Universität Münster, Wilhelm-Klemm-Straße 9, 48149, Münster · Institut für Geophysik, Universität Münster, Corrensstraße 24, 48149, Münster · James Cook University, 1 James Cook Drive, Douglas, Queensland, 4814, Australia +1

Multivariate Time Series Forecasting Time Series Forecasting Seismology Time Series Transformers Autoregressive Modeling

Jun 1, 2026

RESCAST-100K: A Comprehensive Dataset for Cross-Domain Residential Load and Indoor Temperature Forecasting

Accurate short-term forecasting of residential energy load and indoor temperature is essential for home energy management systems, grid-level demand response, and community energy efficiency efforts. Domain adaptation and transfer learning have shown promise for improving forecasting accuracy under data heterogeneity and scarcity commonly seen in residential settings. However, progress is limited by the lack of comprehensive residential datasets: existing benchmarks are narrow in target coverage and rarely support structured cross-domain evaluation. We introduce RESCAST-100K, a large-scale residential forecasting benchmark for studying cross-domain generalization. It provides a configuration-driven interface that instantiates source and target domains along interpretable axes, including geography, climate zone, wall construction, and heating equipment, enabling systematic evaluation of transfer learning, domain adaptation, and zero-shot generalization under controlled domain shifts. The benchmark covers approximately 100,000 EnergyPlus-simulated U.S. homes derived from ResStock, with 15-minute time series for three coupled targets per home: total load, HVAC load, and indoor temperature. These are paired with weather channels, HVAC setpoints, and over 40 static building covariates. RESCAST-100K also integrates five real-world residential datasets under a unified schema, supporting sim-to-real evaluation on the same tasks. We benchmark recurrent, attention-based, and MLP-mixer architectures for zero-shot performance across domains, missing-input conditions, and forecasting tasks. Cross-attention and MLP-mixer models consistently outperform recurrent and classical transformer baselines under domain shift. RESCAST-100K is intended to aid the machine learning and building analytics communities advance cross-domain residential forecasting at home, community, and grid scale.

Jainam Dhruva, Yousaf Raza, A. B. Siddique +1

Department of Computer Science University of Kentucky Lexington, KY 40506

Multivariate Time Series Forecasting Synthetic-to-Real Domain Adaptation Time Series Forecasting Forecasting Benchmarks Building Energy Management Cross-Domain Generalization+1

Jun 1, 2026

A Systematic Evaluation of Current Architectures in Wind Power Forecasting

Interval wind speed forecasting is essential for the efficient integration of wind energy into power systems, as it accounts for the inherent uncertainty of wind resources. This study presents a systematic literature review focused on hybrid approaches to interval forecasting of wind generation, exploring the combination of deep learning, modal decomposition, and statistical methods. To guide the paper selection, Latent Dirichlet Allocation (LDA) was applied for topic modeling, enabling the identification of patterns and research trends. The findings emphasize that integrating hybrid models with decomposition techniques-such as Variational Mode Decomposition (VMD) and Ensemble Empirical Mode Decomposition (EEMD)-enhances forecast accuracy and reliability by narrowing prediction intervals without compromising coverage. Regarding interval construction, most studies adopt a dual-model strategy, independently forecasting the lower and upper bounds. Input data are commonly decomposed using techniques like EMD, EEMD, or VMD, which extract frequency-based components. These components serve as inputs to models such as LSTM or ELM, trained separately for each bound. This approach allows for targeted modeling of uncertainty, improving flexibility and precision, Interval quality is typically evaluated through metrics that balance coverage and interval width. The review also highlights challenges, including the lack of standardized evaluation metrics, computational complexity, and limited real-world validation. Overall, the study reinforces the value of interval forecasting for wind energy operations and offers insights for advancing model robustness and decision-making.

Vinicius Bortolini, Gilson Adamczuk Oliveira, Erick Oliveira Rodrigues +1

Industrial and Systems Engineering Graduate Program (PPGEPS), Federal University of Technology Parand (UTFPR), Pato Branco, Parand $5503-390, Brazil

Time Series Forecasting Wind Power Forecasting Probabilistic Time Series Forecasting Regression Prediction Intervals

Jun 1, 2026

Evaluating Transformer and LSTM Frameworks for Prediction in Ungauged Basins

Watershed networks exhibit convergent topologies in which multiple tributaries merge into downstream channels,integrating diverse upstream hydrological processes. In ungauged basins, the absence of direct observations increases uncertainty and limits the ability to anticipate extreme events. This study evaluates whether an encoder-only Transformer provides an advantage over an LSTM for upstream streamflow inference under limited hydrologic information, using retrospective simulations from the NOAA National Water Model (NWM). Across both upstream-only and combined configurations, the LSTM showed stronger overall performance than the Transformer model across the two configurations. Incorporating downstream information further boosted performance for all models, increasing median NNSE by more than 60%. Rather than treating this as a leaderboard-style comparison, we interpret the experiments as a test of architectural inductive bias for hydrologic sequence inference. The results indicate that recurrent memory remains better aligned with this upstream reconstruction task than an encoder-only Transformer, while downstream hydrologic context provides a strong auxiliary constraint that substantially improves prediction skill across architectures

Taye Akinrele, James Halgren, Noorbakhsh Amiri Golilarz +2

Dept. of Computer Science, The University of Alabama, Tuscaloosa, USA · Alabama Water Institute, USA

Transformer Time Series Forecasting Long Short-Term Memory Networks

Jun 1, 2026

Bridging the Last Mile of Time Series Forecasting with LLM Agents

Time series forecasting has advanced rapidly, especially with the emergence of foundation models that show strong zero-shot performance on numerical extrapolation. However, in real-world forecasting settings, a statistically plausible baseline is rarely the final forecast used in practice. Before a forecast becomes decision-ready, it often needs to be revised using weakly structured business context such as holiday effects, campaign plans, external events, historical analogs, and expert feedback. This practical stage remains underexplored in the forecasting literature. In this paper, we formulate this stage as the \textbf{last-mile forecasting} problem and present an LLM-agent framework that sits on top of a forecasting backbone. Our system maintains a unified forecast workspace, invokes tools to retrieve contextual evidence, and converts reasoning trajectories into explicit forecast revision actions under structural safety constraints. It also supports long-horizon forecasting through map-reduce-style decomposition and post-hoc reflection through a memory bank. The resulting system is designed to be controllable and auditable. Through real-world case studies, we show how LLM agents can bridge the gap between statistical prediction and business-ready forecasting.

Yuhua Liao, Zetian Wang, Qiangqiang Nie +1

Trip.com Group, Shanghai, China

Time Series Forecasting LLM-Based Time Series Forecasting

Jun 1, 2026

ODTQA-FoRe: An Open-Domain Tabular Question Answering Dataset for Future Data Forecasting and Reasoning

The rapid development of LLMs has significantly advanced tabular question answering, but most systems cannot perform future-oriented numerical prediction. To address this gap, we introduce a novel task, Open-Domain Tabular Question Answering for Future Data Forecasting and Reasoning, and propose the first dataset to cover time-series forecasting and forecast-based reasoning scenarios using real estate data. This task poses challenges in retrieving precise historical data, overcoming the forecasting limitations of LLMs, and standardizing responses for diverse queries. To solve the above challenges, we propose TimeFore, an LLM agent-based framework that decomposes the problem into three collaborative roles: a Retriever autonomously generates SQL to fetch data, a Forecaster invokes external time-series models for higher accuracy, and an Analyzer synthesizes the results to construct a precise and consistent final answer. Extensive experiments demonstrate the effectiveness of our TimeFore.

Zhensheng Wang, Xiaole Liu, Wenmian Yang +3

School of Artificial Intelligence, Beijing Normal University, Beijing, PR China · Faculty of Arts and Sciences, Beijing Normal University, Zhuhai, PR China · Institute of Artificial Intelligence and Future Networks, Beijing Normal University, Zhuhai, PR China +1

Table QA Time Series Reasoning Time Series QA Time Series Forecasting Forecasting Benchmarks

Jun 1, 2026

Physics-Guided Recurrent State-Space Neural Networks for Multi-Step Prediction

State-space models are traditionally based on physical knowledge, but multi-step predictions from these physical models can be poor due to model inaccuracy. Black-box deep learning has shown promise as an alternative. However, these methods rely on the availability of large datasets and potentially available physical knowledge is neglected. We propose the PG-RSSNN, a physics-guided recurrent state-space neural network that incorporates recurrent structures to enable the use of non-saturating activation functions in multi-step prediction. It mitigates the vanishing gradients and eliminates the risk of numerical divergence in training seen in existing structures that feed back state estimates. Results across multiple systems with various physical model imperfections, from linear state-space models with Gaussian noise to a robotic arm and a cascaded water tank system, show that the proposed PG-RSSNN maintains stable training behavior, and improves multi-step predictions, as compared with black-box neural networks and physics-only models, even with limited training data and when physical models are only partially known.

Ruiyuan Li, Ajay Seth, Manon Kok

Delft Center for Systems and Control, TU Delft, the Netherlands · Department of Biomechanical Engineering, TU Delft, the Netherlands

Time Series Forecasting Recurrent Neural Networks Physics-Informed ML State Space Models

Jun 1, 2026

VLBM: Variational Latent Basis Modeling for OOD Robust Multivariate Time Series Forecasting

Out of distribution (OOD) events in multivariate time series forecasting are rare but often dominate real world risk, making average case forecasting insufficient for reliable deployment. Under standard average risk training on mixed ID/OOD distributions, optimization signals from rare OOD events can be overwhelmed by frequent in distribution (ID) patterns, so strong benchmark accuracy may not translate into reliability under high impact shifts. To address this issue, we propose VLBM (Variational Latent Basis Model), a theory guided latent forecasting framework that separates stable dynamics from OOD induced deviations. VLBM learns a shared latent basis that defines a low rank subspace for stable ID dynamics, explicitly decomposes inputs into basis subspace components and orthogonal residual components, and aligns a future aware posterior with a future blind prior so that test time latent inference depends only on historical input. Across 12 benchmark tasks spanning transportation, weather, power systems, and other real world domains, including newly constructed real world OOD traffic datasets, VLBM achieves state of the art OOD robustness and ID accuracy, with average MAE and MSE gains of 15.08% and 7.74% over the strongest baseline. On a synthetic simulation dataset, VLBM also consistently achieves the best performance and better tracks OOD pulse recovery. These results support latent structured forecasting as a principled route to robust prediction under mixed ID and OOD conditions. The code is available at https://github.com/leijieruilq/VLBM_OOD_forecast.

Xudong Zhang, Jierui Lei, Jiacheng Li +3

School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing 100049, China. · Center for Machine Learning Research, Peking University, Beijing, China. · Amap, Alibaba Group, China. +2

Multivariate Time Series Forecasting Latent Variable Models Time Series Forecasting OOD Generalization

Jun 1, 2026

Why Do Time Series Models Need Long Context Windows?

Modern deep learning models for forecasting groups of time series rely on increasingly longer observation windows. However, the benefit of increasing the window size is often simply attributed to capturing long-range dependencies, and broader discussion on how global forecasting models leverage input observations has been limited. In this paper, we show that forecasting groups of time series involves two objectives: (i) generative process identification (GPI), i.e., inferring the specific process generating the input sequence, and (ii) conditional forecasting (CF), i.e., predicting future values given input observations. From this perspective, optimal predictions can be interpreted as an average over plausible data-generating processes, weighted by their likelihood given the input window. This suggests another explanation for the benefits of long context windows: they reduce the uncertainty about which specific process is generating the input time series during operation. We prove that even for processes with memory length

P

, an input window size strictly larger than

P

is necessary to achieve the minimum attainable error. Finally, we show how decoupling GPI and CF can improve computational scalability without compromising accuracy. Experiments on synthetic and real-world data validate our insights and their relevance for designing forecasting architectures.

Luca Butera, Giovanni De Felice, Andrea Cini +1

1Università della Svizzera Italiana · 2EPFL · 3Politecnico di Milano

Time Series Forecasting Long-Context Modeling

May 31, 2026

FreqLite: A Lightweight Frequency-Decomposed Linear Model with Adaptive Reversible Normalization for Robust Long-Term Time-Series Forecasting

Long-term time-series forecasting needs models that are accurate yet efficient enough for commodity hardware. Lightweight linear forecasters are remarkably strong in this regime, yet they leave two openings: reversible instance normalization (RevIN) de-normalizes the entire horizon with a single lookback statistic, which is inaccurate under non-stationarity, and time-domain trend/seasonal decomposition relies on a fixed, non-adaptive filter. We present FreqLite, an ultra-lightweight, channel-independent frequency-decomposed linear forecaster: a learnable, lossless, partition-of-unity spectral filter splits the input into bands that are forecast by per-band linear heads and, unlike low-pass-truncation approaches, the high-frequency band is retained and modeled. FreqLite is the best lightweight model on the standard long-term forecasting benchmarks and, at long lookback (L=336), attains a lower average error than a PatchTST Transformer (0.3244 vs. 0.3587 MSE) while using 4x fewer parameters, 2.2x less memory, and 2.2x less time per epoch on a single 4 GB laptop GPU; although modest in magnitude, its improvements are statistically significant under paired Wilcoxon tests across all matched cells (p < 1e-5). We further introduce Adaptive Reversible Instance Normalization (A-RevIN), a regime-adaptive reversible normalization that strictly generalizes RevIN (recovered exactly when its gate is closed), engages under non-stationarity, and reduces to RevIN without harm on stationary data. We validate this on both a real strongly non-stationary dataset (ILI, up to ~5% MSE reduction) and a controlled synthetic drift sweep in which A-RevIN's benefit and its learned gate both rise monotonically with injected non-stationarity. Every component is independently ablatable (Linear and RLinear are special cases of FreqLite), and all results are reproducible on commodity hardware.

Mirza Samad Ahmed Baig, Syeda Anshrah Gillani

Fandaqah, Al Khobar, Saudi Arabia · Hamdard University, Karachi, Pakistan

Long-Term Time Series Forecasting Frequency-Domain Feature Learning Time Series Forecasting Non-Stationary Time Series Forecasting

May 31, 2026

Feature to Dynamics: Feature-space to Autoregression strategy for Zero-shot Time Series Forecasting

Zero-shot time series forecasting aims to predict future values for previously unseen series, requiring models to generalize temporal dynamics beyond the training distribution. While recent foundation models achieve strong in-domain performance through large-scale pretraining, their effectiveness often relies on broad data coverage and implicit pattern memorization, which can limit generalization when data are scarce or source and target domains are disjoint. In this work, we propose FSA, a feature-to-strategy framework for controlled zero-shot univariate forecasting. Instead of directly modeling raw sequences in the observation space, FSA learns a structured mapping from an interpretable feature space to an autoregressive strategy space. This design introduces explicit inductive biases that disentangle global trends, periodic components, and local temporal dynamics, enabling the model to capture transferable time-series structure with fewer data assumptions. Empirical results show that, under identical pretraining data, training protocol, and comparable parameter budgets, FSA outperforms Transformer-based architectures in our controlled zero-shot setting.

Yifan Wu, Junjie Wu, Kai Wu +2

School of Artificial Intelligence, Xidian University, Xi’an, China · School of Cyber Engineering, Xidian University, Xi’an, China · Sun Yat-Sen University, Guangzhou, China

Zero-Shot Time Series Forecasting Time Series Forecasting

May 30, 2026

Hybrid Probabilistic Forecasting of Under-Five Malaria Admissions in Ghana: A Gaussian Process Regression with Holt-Winters Smoothing

Accurate malaria forecasting remains a major challenge in sub-Saharan Africa, where strong seasonality, reporting uncertainty, and non-stationary transmission dynamics reduce the reliability of conventional models. In Ghana, district-level malaria surveillance requires forecasting frameworks that are probabilistically rigorous and robust under limited data. This study proposes a hybrid framework integrating Gaussian Process Regression (GPR) with Holt-Winters exponential smoothing for modelling monthly under-five malaria admissions. GPR captures non-linear behaviour and predictive uncertainty, while Holt-Winters stabilises long-horizon forecasts and preserves seasonal structure. Using ten years of district-level data (2014-2023), performance was evaluated via rolling-origin expanding-window validation. The hybrid model achieved

R^2 = 0.9906

versus

0.8213

for Holt-Winters alone, with

94.2\%

of residuals within

\pm 2σ

bounds. Forecasts for 2024-2028 project average monthly admissions from approximately 8{,}000 to 12{,}200 cases. Spatio-temporal analysis revealed pronounced ecological heterogeneity: northern high-burden districts exhibited stable relative patterns despite large absolute fluctuations. The framework provides a scalable probabilistic approach for malaria early warning and operational planning in endemic settings, supporting Ghana's national malaria control strategy.

T. Ansah-Narh, Y. Asare Afrane, J. Bremang Tandoh

Epidemic Forecasting Time Series Forecasting Spatiotemporal Forecasting Probabilistic Time Series Forecasting Gaussian Process Regression

May 30, 2026

Bayesian Inference of Nonlinear Malaria Dynamics in Ghana via an Ensemble Markov Chain Monte Carlo Sampler

Reliable quantification of malaria dynamics in sub-Saharan Africa is hindered by short, noisy, and spatially heterogeneous surveillance records. In Ghana, health-facility data from 2014 to 2023 reveal non-linear and age-specific fluctuations in hospital admissions, yet existing approaches struggle to capture stochastic variability or provide credible uncertainty bounds. This study develops a Bayesian nonlinear inference framework that integrates a cubic baseline with a damped oscillatory kernel, estimated via an affine-invariant ensemble Markov Chain Monte Carlo sampler. The framework accommodates limited data, models parameter uncertainty, and generates probabilistic forecasts for children under five years and individuals aged five years or more. Results show strong empirical adequacy (

R^2 = 0.9958

for

<5

years;

R^2 = 0.9956

for

\geq 5

years) with residual errors below

2\%

and well-mixed posteriors confirming convergence. District-level analysis reveals pronounced spatial heterogeneity, with coefficients of variation ranging from

<0.07

in urban centres such as Kumasi to

>3.3

in peripheral districts such as Mpohor and Bia East. Forecasts for 2024-2026 indicate a gradual resurgence: from 137,000 to 149,000 cases among children under five years and from 348,000 to 375,000 cases among older individuals, with uncertainty widening over time. By producing probabilistic forecasts, this Bayesian framework provides a principled tool for anticipating malaria fluctuations and strengthening data-driven decision-making in Ghana's national malaria control strategy.

T. Ansah-Narh, Y. Asare Afrane, J. Bremang Tandoh

Ghana Space Science and Technology Institute, Ghana Atomic Energy Commission, P. O. Box LG 80, Legon, Accra, Ghana · Department of Medical Microbiology, University of Ghana Medical School, University of Ghana, Accra, Ghana

Epidemic Forecasting Bayesian Inference Time Series Forecasting Probabilistic Forecasting

May 30, 2026

EnergyMamba: An Uncertainty-Aware Graph-Enhanced Selective State Space Model for Energy Consumption Prediction

Energy consumption prediction is essential for efficient grid management, demand-side optimization, and sustainable energy planning. Although advanced machine learning methods have been employed for better prediction performance, existing works have two key limitations: (1) they usually formulate this task as a purely time-series prediction problem without explicitly modeling the spatial dependencies among different regions, and (2) they fail to provide reliable predictions with uncertainty estimates under abnormal situations such as extreme weather events. To advance existing research, we propose EnergyMamba, an uncertainty-aware spatiotemporal learning framework for accurate and reliable energy consumption prediction, which comprises two key components: (i) a novel Graph-Enhanced Selective State Space Model (GE-Mamba) that injects spatial context learned from the grid topology into the temporal dynamics, enabling coupled spatiotemporal modeling, and (ii) an Adaptive Sequential Conformalized Quantile Regression (AS-CQR) module, which includes locally adaptive normalization and an online feedback mechanism to dynamically calibrate prediction intervals under potential distribution shifts. We evaluate EnergyMamba on four large-scale real-world datasets from Florida, New York, and California. Results show EnergyMamba achieves around 5% improvement in prediction accuracy and 6% improvement in uncertainty quantification over 15 state-of-the-art baselines.

Dahai Yu, Rongchao Xu, Lin Jiang +1

Florida State University · Tallahassee, Florida, USA

Selective SSMs Time Series Forecasting Probabilistic Forecasting Conformal Prediction Spatiotemporal Forecasting Electricity Load Forecasting+1

May 29, 2026

Generalizing Multi-Scale Time-Series Modeling with a Single Operator

Multi-scale modeling has emerged as an effective design principle for time-series forecasting by capturing temporal dynamics at multiple resolutions. As no principled foundation has been established in the literature, we unify existing scaling methods into a scaling operator family, revealing a fundamental limitation of existing approaches: reliance on fixed and discrete scaling. To address this limitation, we propose SiGMA (Single Generalized Multi-scale Architecture), which enables distance-aware scaling via the learnable discrete Gaussian (LDG) kernel grounded in scale-space theory. We evaluate SiGMA comprehensively on long- and short-term forecasting benchmarks against state-of-the-art multi-scale baselines. SiGMA outperforms all competitors on both tasks, especially achieving the best performance in 13 out of 16 long-term evaluation settings. Beyond accuracy, SiGMA significantly improves training speed by up to 5.3 times and reduces memory consumption by up to 3.8 times over the strongest competitors. Code is available at https://github.com/cheonwoolee/SiGMA.

Cheonwoo Lee, Dooho Lee, Doyun Choi +1

School of Electrical Engineering, KAIST, Daejeon, Republic of Korea · Department of Computer Science and Engineering, Seoul National University, Seoul, Republic of Korea

Long-Term Time Series Forecasting Time Series Forecasting Multiscale Time-Series Modeling

May 29, 2026

STEP: Learning STructured Embeddings for Progressive Time Series

We present a novel method for learning interpretable representations of progressive time series, that is, data capturing irreversible state transitions such as degradation or task completion. Our approach uses a self-supervised contrastive objective to learn a low-dimensional latent space whose geometry is itself the interpretation: each observation becomes a point on a manifold anchored between two fixed orthogonal prototype vectors, and a trajectory becomes a path across that manifold. From this structure we read a latent compass, the polar coordinates (θ, r) of the latent vector, in which θ tracks the progression of the underlying state (e.g., from healthy to failed) and r identifies the active mode (e.g., the operating condition), without any proxy labels. We evaluate the approach against the state of the art on diverse domains, including industrial degradation, robotic tasks, and neural activity, validating three key capabilities: (1) end-state prediction, (2) multi-step forecasting, and (3) interpretable phase separation. Our method matches or improves over black-box counterparts on all of these while providing transparency about the underlying mechanisms. A simple linear regressor on top of the latent compass coordinates is competitive with deep architectures, direct quantitative evidence that the underlying state is encoded in a geometrically accessible form.

Lucas Thil, Jesse Read, Rim Kaddah +1

LIX, École Polytechnique IRT SystemX Palaiseau, France · IRT SystemX Palaiseau, France · Safran Tech Chateaufort, France

Self-Supervised Time Series Representation Learning Interpretable ML Time Series Forecasting State Tracking State Representation Learning

May 29, 2026

Kalimati Vegetable Price Index Forecasting with a Momentum Corrected Online Stacking Ensemble

Forecasting agricultural commodity prices in emerging economies is difficult due to high volatility, frequent supply disruptions, and strong cultural influences on demand. This study introduces the Kalimati Vegetable Price Index (KVPI), a new inverse-volatility weighted composite index that aggregates 135 daily wholesale commodities from Kathmandu over ten years (2013-2023). By creating a stable macro-level signal, the KVPI reduces the noise inherent in modelling individual crops. A rich set of 64 causally valid features was developed, including festival lead-lag effects, rolling statistics, and calendar variables. Fourteen forecasting models spanning statistical, tree-based, deep learning, hybrid, and transformer architectures were rigorously evaluated across short (7-day), medium (14- and 30-day), and long-term (90-day) horizons. Tree-based ensembles proved notably robust, while classical statistical models and complex transformers struggled with the noisy dataset. The proposed Momentum-Corrected Online Stacking Ensemble achieved the strongest performance, yielding a Root Mean Square Error (RMSE) of 1.771, an exceptionally low Mean Absolute Percentage Error (MAPE) of 0.68%, and explaining 84.5% of the variance (R-squared = 0.845) at the 90-day horizon. This open-source pipeline provides policymakers and supply chain actors in Nepal and similar markets with a practical, reliable tool for anticipating price movements and strengthening food security.

Sahaj Raj Malla

Department of Mathematics, Kathmandu University, Dhulikhel, Nepal

Long-Term Time Series Forecasting Time Series Forecasting Deep Ensembles

May 28, 2026

Bridging the Gap Between Natural Language and Market Dynamics via High-Dimensional Representation Learning

Traditional multi-modal financial forecasting often relies on scalar sentiment scores, which fail to capture the nuances of financial news. To address this information loss, this paper explores high-dimensional representation learning by replacing discrete polarity ratings with dense FinBERT embeddings within a Transformer-based forecasting architecture. We benchmarked various embedding strategies on the FNSPID dataset, including raw embeddings, attention-weighted aggregation, and a custom Siamese network. While the attention-based mechanism struggled with the low signal-to-noise ratio typical of financial data, the integration of Siamese-optimized embeddings outperformed both the scalar baseline and raw embedding approaches, demonstrating that preserving high-dimensional narrative context yields improved predictive accuracy for short-term stock price movements.

Yujin Jeong, Noelle Jung, Brian Y. C. Leung

Mike

Sentence Embeddings Time Series Forecasting Siamese Neural Networks Multimodal Embedding

May 28, 2026

KairosAgent: Agentic Time Series Forecasting with Fused Semantic Reasoning

Cross-domain multimodal time series forecasting is a challenging task, requiring models to integrate precise numerical comprehension, cross-domain semantic understanding, and effective multimodal fusion. Existing approaches either build Time Series Foundation Models (TSFMs) from scratch or leverage pretrained Large Language Models (LLMs). However, TSFMs often overlook semantic understanding and lack the ability to perform future-oriented semantic reasoning, and LLMs struggle with numerical comprehension and accurate quantitative forecasting. To overcome these limitations, we propose KairosAgent, a novel agentic framework for multimodal time series forecasting, including an LLM-based reasoner and a TSFM-based forecaster. KairosAgent unifies textual reasoning and numerical forecasting by dynamically invoking analytical tools to enhance the numerical understanding and semantic reasoning capabilities of LLMs. The reasoning results are subsequently fused into the TSFM pipeline, enabling more accurate and reliable future predictions. To further improve the reasoning, we curate a large-scale corpus of high-quality trajectories, alongside a reinforcement learning from forecasting paradigm with multi-turn refinement and turn-level credit assignment. Experiments demonstrate that KairosAgent achieves superior zero-shot forecasting performance while maximizing the utility of pretrained LLMs and TSFMs, presenting a promising direction for efficient and interpretable time series agents. The project page is at https://foundation-model-research.github.io/KairosAgent .

Kun Feng, Ziwei Shan, Yuchen Fang +6

ShanghaiTech University · Ant Group

Multivariate Time Series Forecasting Zero-Shot Time Series Forecasting Time Series Reasoning Time Series Forecasting LLM-Based Time Series Forecasting

May 28, 2026

From Short Histories to Long Futures: Horizon-Aware Graph Neural Networks for Long Horizon Forecasting

Accurate long-range prediction of geophysical systems is difficult due to strongly nonlinear dynamics, the high computational cost of full-physics simulations, and the error accumulation that arise when one-step autoregressive surrogates are rolled out over decades. Deep neural network can serve as efficient emulators, but most are trained only for next-step prediction and often drift or become unstable as the forecast horizon grows. We propose a multi-horizon graph neural network emulator that learns state-to-state transitions from a single current time to multiple future lead times within one unified model. The physical domain is represented as a graph, where nodes correspond to spatial locations with time-varying geophysical attributes and edges encode local spatial interactions. Given the current graph state, the model predicts the future evolution of key fields, ice thickness and ice velocities at all nodes, using a shared graph backbone with separate output branches for each target variable. To improve stability, the network predicts state increments relative to the current state, which are then added back to reconstruct future states. Training jointly optimizes all lead times with a unified regression objective, and inference uses a coarse-to-fine rollout that advances with larger jumps and selectively refines with shorter jumps to reduce drift and avoid redundant computation. Experiments on multi-decadal Pine Island Glacier simulations show that our approach achieves higher long-range accuracy and improved stability than both (i) an initial-state baseline that predicts each future time directly from the starting state and (ii) a standard single-step autoregressive rollout, producing a more reliable emulator for downstream climate and sea-level studies.

Zesheng Liu, Maryam Rahnemoonfar

Department of Computer Science and Engineering, Lehigh University, Bethlehem PA 18015, USA · Department of Civil and Environmental Engineering, Lehigh University, Bethlehem2026 PA 18015, USA

Neural Surrogate Modeling Long-Term Time Series Forecasting Time Series Forecasting Spatiotemporal Forecasting Spatiotemporal GNNs