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.

Apr 27, 2026cs.LG

End-to-End Learning for Partially-Observed Time Series with PyPOTS

Partially-observed time series (POTS) is ubiquitous in real-world applications, yet most existing toolchains separate missing-value handling from downstream learning, which limits reproducibility and overall performance. This tutorial introduces PyPOTS, an open-source Python ecosystem for end-to-end data mining and machine learning on POTS. We present practical workflows spanning missingness simulation, data preprocessing, model training, and evaluation across core tasks, including imputation, forecasting, classification, clustering, and anomaly detection. The tutorial consists of two parts: Part I emphasizes hands-on application for practitioners through unified APIs and benchmark-oriented experiments. Part II targets developers and researchers, focusing on extending PyPOTS with custom models, domain-specific constraints, and contribution-ready engineering practices. Participants will gain both conceptual understanding and implementation experience for building robust, transparent, and reusable POTS pipelines in research and production settings. PyPOTS is publicly available at https://github.com/WenjieDu/PyPOTS

Wenjie Du, Yiyuan Yang, Tianxiang Zhan +1

PyPOTS Research · PyPOTS Research & Univ. of Oxford · Squirrel Ai Learning

Irregular Time-Series Modeling Time Series Imputation Incomplete Data Imputation Learning with Missing Data Time Series Forecasting

Apr 27, 2026cs.LG

DecompKAN: Decomposed Patch-KAN for Long-Term Time Series Forecasting

Accurate time series forecasting in scientific domains such as climate modeling, physiological monitoring, and energy systems benefits from both competitive predictions and model transparency. This work proposes DecompKAN, a lightweight attention-free architecture that combines trend-residual decomposition, channel-wise patching, learned instance normalization, and B-spline Kolmogorov-Arnold Network (KAN) edge functions. Each KAN edge learns an explicit, inspectable 1D scalar function over learned patch-embedding coordinates that can be directly visualized. On standard benchmarks, DecompKAN achieves best or tied-best MSE on 15 of 32 dataset-horizon combinations among selected published baselines, and achieves best or tied-best MSE on 20 of 36 comparisons under a controlled same-recipe evaluation across 9 datasets including the physiological PPG-DaLiA benchmark. The architecture shows particular strength on datasets with smooth temporal dynamics (Solar -17%, ECL -10% vs. iTransformer, Weather) and physiological time series. Visualization of learned edge functions reveals qualitatively different latent nonlinearities across domains. Ablation analysis shows that the architectural pipeline (decomposition, patching, normalization) drives performance more than the choice of nonlinear layer, while the KAN formulation enables inspection of learned latent transformations.

Naveen Mysore

Long-Term Time Series Forecasting Explainable Time Series Forecasting Time Series Forecasting Kolmogorov-Arnold Networks

Apr 27, 2026cs.AI

Context-Aware Hospitalization Forecasting Evaluations for Decision Support using LLMs

Medical and public health experts must make real-time resource decisions, such as expanding hospital bed capacity, based on projected hospitalization trends during large-scale healthcare disruptions (e.g., operational failures or pandemics). Forecasting models can assist in this task by analyzing large volumes of resource-related data at the facility level, but they must be reliable for decision-making under real-world data conditions. Recent work shows that large language models (LLMs) can incorporate richer forms of context into numerical forecasting. Whereas traditional models rely primarily on temporal context (i.e., past observations), LLMs can also leverage non-temporal public health context such as demographic, geographic, and population-level features. However, it remains unclear how these models should be used to produce stable or decision-relevant predictions in real-world healthcare settings. To evaluate how LLMs can be effectively used in this setting, we evaluate three approaches across 60 counties with low-,mid-, and high-hospitalization intensities in the United States: direct LLM-based forecasting, classical time-series models, and a context-augmented hybrid pipeline (HybridARX) that incorporates LLM-derived signals into structured models. Because the goal is operational decision-making rather than error minimization alone, we evaluate performance with bias and lead-lag alignment in addition to standard forecasting metrics. Our results show that HybridARX improves over classical ARX by yielding more stable and better-calibrated forecasts, particularly when incorporating noisy contextual signals into structured time-series models. These findings suggest that, in non-stationary healthcare resource forecasting, LLMs are most useful when embedded within structured hybrid models.

Rhea Makkuni, Ananya Joshi

Johns Hopkins University Baltimore, USA

Healthcare Time Series Forecasting LLM-Based Time Series Forecasting

Apr 26, 2026cs.LG

Machine Learning and Deep Learning Models for Short Term Electricity Price Forecasting in Australia's National Electricity Market

Short term electricity price forecast is essential in competitive power markets, yet electricity price series exhibit high volatility, irregularity, and non-stationarity. This phenomenon is pronounced in the South Australian region of the National Electricity Market, where high renewable penetration drives price volatility and frequent negative price intervals, while structural changes such as the transition to five-minute settlement further complicate forecast. To address these challenges, this study develops a unified benchmark framework. Under identical data preprocessing, feature engineering with lag features, rolling statistics, cyclic temporal encodings, and so on, and an 85% to 15% chronological train test split, six algorithms are systematically compared, including AWMLSTM, CatBoost, GBRT, LSTM, LightGBM, and SVR. The results show that for price prediction, tree-based models, especially GBRT with an R squared value of 0.88, generally outperform LSTM and SVR. However, all models achieve a mean absolute percentage error above 90%, and more than 65% of GBRT predictions have relative errors above 10%, which highlights the inherent difficulty of price forecast. For demand prediction, all models perform substantially better than in price prediction. AWMLSTM and GBRT achieve an R2 value of 0.96 with mean absolute percentage error below 32%, and GBRT has 74.37% of samples within 5% error, while LSTM and SVR perform less accurately in both tasks. Future improvements should focus on hybrid models such as tree plus transformers, data augmentation for extreme events, and error correction to better capture price spikes.

Wei Lu, Jay Wang, Dingli Duan +3

School of Engineering, Computer & Mathematical Sciences, Auckland University of Technology (AUT), Auckland 1010, New Zealand · Department of Thermal Energy and Power Engineering, Yantai University, Yantai, China · Department of Building Environment and Equipment, School of Civil Engineering, Hefei University of Technology, Hefei, China +1

Gradient-Boosted Decision Trees Electricity Price Forecasting Time Series Forecasting Forecasting Benchmarks

Apr 26, 2026cs.AI

Time-Series Forecasting in Safety-Critical Environments: An EU-AI-Act-Compliant Open-Source Package / Zeitreihenprognose in sicherheitskritischen Umgebungen: Ein KI-VO-konformes Open-Source-Paket

With spotforecast2-safe we present an integrated Compliance-by-Design approach to Python-based point forecasting of time series in safety-critical environments. A review of the relevant open-source tooling shows that existing compliance solutions operate consistently outside of the library to be used - e.g. as scanners, templates, or runtime layers. spotforecast2-safe takes the inverse approach and anchors the requirements of Regulation (EU) 2024/1689 (the EU AI Act, in German: KI-VO), of IEC 61508, of the ISA/IEC 62443 standards series, and of the Cyber Resilience Act within the library: in application-programming-interface contracts, persistence formats, and continuous-integration gates. The approach is operationalised by four non-negotiable code-development rules (zero dead code, deterministic processing, fail-safe handling, minimal dependencies) together with the corresponding process rules (model card, executable docstrings, CI workflows, Common-Platform-Enumeration (CPE) identifier, REUSE-conformant licensing, release pipeline). Interactive visualisation, hyperparameter tuning and automated machine learning (AutoML), as well as deep-learning and large-language-model backends are deliberately excluded, because each of these components either enlarges the attack surface, introduces non-determinism, or impairs reproducibility. A bidirectional traceability matrix maps every regulatory provision onto the corresponding mechanism in the code; an end-to-end example of European-market electricity generation, transmission, and consumption forecasting demonstrates the application. The package is open-source and available under Affero General Public License (AGPL) 3.0-or-later.

Thomas Bartz-Beielstein, Eva Bartz

Bartz & Bartz GmbH, 51643 Gummersbach, Deutschland

AI Assurance Time Series Forecasting AI Governance

Apr 26, 2026cs.LG

Autocorrelation Reintroduces Spectral Bias in KANs for Time Series Forecasting

Existing theory suggests that Kolmogorov-Arnold Networks (KANs) can overcome the spectral bias commonly observed in neural networks under the assumption that inputs are statistically independent. However, this assumption does not hold in time series forecasting (TSF), where inputs are lagged observations with strong temporal autocorrelation. Through theoretical analysis and empirical validation, we obtain an unexpected finding: temporal autocorrelation reintroduces spectral bias in KANs, and the bias becomes increasingly pronounced as the degree of autocorrelation increases. This suggests that standard KANs may face substantial difficulties in TSF with strongly autocorrelated inputs. To address this problem, we introduce the Discrete Cosine Transform (DCT) to reduce the correlations among the network inputs. As expected, experimental results reveal that DCT preprocessing substantially reduces the observed low-frequency preference in TSF. This result also corroborates that the spectral bias of KANs in TSF tasks is indeed induced by the autocorrelation among input variables.

Chen Zeng, Jiahui Wang, Qiao Wang

School of Information Science and Engineering, Southeast University, Nanjing, China · School of Economics and Management, Southeast University, Nanjing, China · both the School of Information Science and Engineering and the School of Economics and Management, Southeast University, Nanjing, China

Time Series Forecasting Kolmogorov-Arnold Networks

Apr 26, 2026cs.LG

Interpretable Physics-Informed Load Forecasting for U.S. Grid Resilience: SHAP-Guided Ensemble Validation in Hybrid Deep Learning Under Extreme Weather

Accurate short-term electricity load forecasting is a cornerstone of U.S. grid reliability; however, prevailing deep learning models remain opaque, limiting operator trust during extreme weather. A unified, interpretable, physics-informed ensemble framework is proposed, integrating a Convolutional Neural Network (CNN) branch for local feature extraction and a Transformer branch for long-range dependency modeling; the branches are fused through a validation-optimized weighted ensemble and regularized by a physics-informed loss derived from the piecewise parabolic temperature-demand relationship of the Electric Reliability Council of Texas (ERCOT) system. Post-hoc interpretability is provided through SHapley Additive exPlanations (SHAP) with the DeepExplainer backend, yielding global and event-level attributions. Using eight years of ERCOT hourly load data (2018-2025) fused with Automated Surface Observing System (ASOS) records from three Texas stations, the framework achieves 713 MW MAE, 812 MW RMSE, and 1.18% MAPE on the test window. For Hampel-flagged extreme events, MAPE falls by 20.7% relative to its Transformer branch and by 40.5% relative to its CNN branch; an ablation confirms that the parabolic and ramp constraints drive a 14.7% RMSE reduction. SHAP analysis reveals a regime shift: temperature dominates under normal operation, whereas wind speed and precipitation become more influential during cold fronts and heatwaves.

Md Abubakkar, Sajib Debnath, Md. Uzzal Mia

Dept. of Computer Science, Midwestern State University, Dallas, TX, USA · O&M Analytics, AES Clean Energy, The AES Corporation, Louisville, CO, USA · Dept. of Information and Communication Engineering, Pabna University of Science and Technology, Bangladesh

Hybrid CNN-Transformer Architectures Time Series Forecasting Physics-Informed ML Electricity Load Forecasting Power Systems

Apr 25, 2026cs.LG

GeoCert: Certified Geometric AI for Reliable Forecasting

Forecasting systems in science must be accurate, physically consistent, and certifiably reliable. Most existing models address prediction, constraint enforcement, and verification separately, limiting scalability and interpretability. We introduce GeoCert, a geometric AI framework that unifies forecasting, physical reasoning, and formal verification within a single differentiable computation. GeoCert formulates forecasting as evolution along a hyperbolic manifold, where negative curvature induces contraction dynamics, intrinsic robustness, and logarithmic-time certification. A hierarchical constraint architecture separates universal physical laws from domain-specific dynamics, enabling certified generalization across energy, climate, finance, and transportation systems. GeoCert achieves state-of-the-art accuracy while reducing computational cost by 97.5% and maintaining better certification rates. By embedding verification into the geometry of learning, GeoCert transforms forecasting from empirical approximation to formally verified inference, offering a scalable foundation for trustworthy, reproducible, and physically grounded scientific AI.

Regina Zhang, Zongru Li, Honggang Wen +4

Department of Biomedical Informatics & Data Science, Yale University, US · School of Computing and Data Science, Nanyang Technological University, Singapore. · Department of Computer Science, The University of Hong Kong, Hong Kong SAR +1

Neural Network Verification Time Series Forecasting Physics-Informed ML Certified Robustness

Apr 24, 2026cs.LG

Liquid Neural Network Models for Natural Gas Spot Price Time-Series Forecasting

Natural gas is undoubtedly an essential component of the global energy system. Accurate short-term forecasting of natural gas price is challenging due to pronounced volatility driven by seasonal demand patterns, geopolitical developments, and shifting macroeconomic conditions. The nonlinear dynamics and frequent regime changes can limit the effectiveness of traditional time-series models. In this study, we explore the use of Liquid Neural Networks (LNNs) for short-horizon forecasting of the Henry Hub spot price, a primary benchmark for pricing. LNNs are designed to adapt continuously to evolving temporal patterns through dynamic internal state updates, making them well suited for nonstationary price behavior. By improving forecast accuracy in volatile market conditions, this work aims to reduce uncertainty and enhance decision support across energy trading and power market applications.

Yiqian Liu, Jiayi Niu, Adam Kelleher +1

Department of Data Science, Columbia University New York, NY, USA

Liquid Neural Networks Time Series Forecasting Non-Stationary Time Series Forecasting

Apr 24, 2026cs.LG

FETS Benchmark: Foundation Models Outperform Dataset-specific Machine Learning in Energy Time Series Forecasting

Driven by the transition towards a climate-neutral energy system, accurate energy time series forecasting is critical for planning and operation. Yet, it remains largely a dataset-specific task, requiring comprehensive training data, limiting scalability, and resulting in high model development and maintenance effort. Recently, foundation models that aim to learn generalizable patterns via extensive pretraining have shown superior performance in multiple prediction tasks. Despite their success and strong potential to address challenges in energy forecasting, their application in this domain remains largely unexplored. We address this gap by presenting the Foundation Models in Energy Time Series Forecasting (FETS) benchmark. We (1) provide a structured overview of energy forecasting use cases along three main dimensions: stakeholders, attributes, and data categories; (2) collect and analyze 54 datasets across 9 data categories, guided by typical stakeholder interests; (3) benchmark foundation models against classical machine learning approaches across different forecasting settings. Foundation models consistently outperform dataset-specific optimized machine learning approaches across all settings and data categories, despite the latter having seen the full historic target data during training. In particular, covariate-informed foundation models achieve the strongest performance. Further analysis reveals a strong correlation between predictive performance and spectral entropy, performance saturation beyond a certain context length, and improved performance at higher aggregation levels such as national load, district heating, and power grid data. Overall, our findings highlight the strong potential of foundation models as scalable and generalizable forecasting solutions for the energy domain, particularly in data-constrained and privacy-sensitive settings.

Marco Obermeier, Marco Pruckner, Florian Haselbeck +1

Julius-Maximilians-Universität Würzburg, Modeling and Simulation Lab, Am Hubland, Würzburg, 97074, Germany · Weihenstephan-Triesdorf University of Applied Sciences, Smart Farming, Am Staudengarten 1, Freising, 85354, Germany · Weihenstephan-Triesdorf University of Applied Sciences, Digital Energy Transition, Hans-Carl-von-Carlowitz-Platz 3, Freising, 85354, Germany

Time Series Forecasting Forecasting Benchmarks Electricity Load Forecasting Time-Series Foundation Models

Apr 23, 2026cs.LG

Hybrid Deep Learning Approach for Coupled Demand Forecasting and Supply Chain Optimization

Supply chain resilience and efficiency are vital in industries characterized by volatile demand and uncertain supply, such as textiles and personal protective equipment (PPE). Traditional forecasting and optimization approaches often operate in isolation, limiting their real-world effectiveness. This paper proposes a Hybrid AI Framework for Demand-Supply Forecasting and Optimization (HAF-DS), which integrates a Long Short-Term Memory (LSTM)-based demand forecasting module with a mixed integer linear programming (MILP) optimization layer. The LSTM captures temporal and contextual demand dependencies, while the optimization layer prescribes cost-efficient replenishment and allocation decisions. The framework jointly minimizes forecasting error and operational cost through embedding-based feature representation and recurrent neural architectures. Experiments on textile sales and supply chain datasets show significant performance gains over statistical and deep learning baselines. On the combined dataset, HAF-DS reduced Mean Absolute Error (MAE) from 15.04 to 12.83 (14.7%), Root Mean Squared Error (RMSE) from 19.53 to 17.11 (12.4%), and Mean Absolute Percentage Error (MAPE) from 9.5% to 8.1%. Inventory cost decreased by 5.4%, stockouts by 27.5%, and service level rose from 95.5% to 97.8%. These results confirm that coupling predictive forecasting with prescriptive optimization enhances both accuracy and efficiency, providing a scalable and adaptable solution for modern textile and PPE supply chains.

Nusrat Yasmin Nadia, Md Habibul Arif, Habibor Rahman Rabby +3

Department of Information Technology, Washington University of Science and Technology, , Alexandria, 22314, VA, USA · Department of Information Technology, University of the Potomac, , Washington, D.C., 20005, DC, USA · Department of Computer Science, Campbellsville University, , Louisville, 40220, KY, USA +2

Time Series Forecasting

Apr 22, 2026cs.LG

StormNet: Improving storm surge predictions with a GNN-based spatio-temporal offset forecasting model

Storm surge forecasting remains a critical challenge in mitigating the impacts of tropical cyclones on coastal regions, particularly given recent trends of rapid intensification and increasing nearshore storm activity. Traditional high fidelity numerical models such as ADCIRC, while robust, are often hindered by inevitable uncertainties arising from various sources. To address these challenges, this study introduces StormNet, a spatio-temporal graph neural network (GNN) designed for bias correction of storm surge forecasts. StormNet integrates graph convolutional (GCN) and graph attention (GAT) mechanisms with long short-term memory (LSTM) components to capture complex spatial and temporal dependencies among water-level gauge stations. The model was trained using historical hurricane data from the U.S. Gulf Coast and evaluated on Hurricane Idalia (2023). Results demonstrate that StormNet can effectively reduce the root mean square error (RMSE) in water-level predictions by more than 70% for 48-hour forecasts and above 50% for 72-hour forecasts, as well as outperform a sequential LSTM baseline, particularly for longer prediction horizons. The model also exhibits low training time, enhancing its applicability in real-time operational forecasting systems. Overall, StormNet provides a computationally efficient and physically meaningful framework for improving storm surge prediction accuracy and reliability during extreme weather events.

Noujoud Nader, Stefanos Giaremis, Clint Dawson +3

Center for Computation and Technology, Louisiana State University, Baton Rouge, 70803, LA, US. · Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, 54124, Greece. · Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, 78712, TX, US.

Time Series Forecasting Spatiotemporal Forecasting Spatiotemporal GNNs

Apr 22, 2026cs.LG

Cold-Start Forecasting of New Product Life-Cycles via Conditional Diffusion Models

Forecasting the life-cycle trajectory of a newly launched product is important for launch planning, resource allocation, and early risk assessment. This task is especially difficult in the pre-launch and early post-launch phases, when product-specific outcome history is limited or unavailable, creating a cold-start problem. In these phases, firms must make decisions before demand patterns become reliably observable, while early signals are often sparse, noisy, and unstable We propose the Conditional Diffusion Life-cycle Forecaster (CDLF), a conditional generative framework for forecasting new-product life-cycle trajectories under cold start. CDLF combines three sources of information: static descriptors, reference trajectories from similar products, and newly arriving observations when available. Here, static descriptors refer to structured pre-launch characteristics of the product, such as category, price tier, brand or organization identity, scale, and access conditions. This structure allows the model to condition forecasts on relevant product context and to update them adaptively over time without retraining, yielding flexible multi-modal predictive distributions under extreme data scarcity. The method satisfies consistency with a horizon-uniform distributional error bound for recursive generation. Across studies on Intel microprocessor stock keeping unit (SKU) life cycles and the platform-mediated adoption of open large language model repositories, CDLF delivers more accurate point forecasts and higher-quality probabilistic forecasts than classical diffusion models, Bayesian updating approaches, and other state-of-the-art machine-learning baselines.

Ruihan Zhou, Zishi Zhang, Jinhui Han +2

Guanghua School of Management, Peking University, Beijing 100871, China · Department of Industrial Engineering and Decision Analytics, The Hong Kong University of Science and Technology, Hong Kong SAR, China

Time Series Forecasting Conditional Diffusion Models Probabilistic Time Series Forecasting

Apr 22, 2026cs.LG

A Wasserstein GAN-based climate scenario generator for risk management and insurance: the case of soil subsidence

According to the United Nations Office for Disaster Risk Reduction (2025), the average annual cost of natural catastrophes increased from 70--80 billion USD between 1970 and 2000 to 180--200 billion USD between 2001 and 2020. Reports from organizations such as the IFOA and the WWF highlight the need for the insurance sector to adapt to this rapidly evolving context by developing medium- to long-term strategies that go beyond the one-year horizon of prudential regulations such as Solvency II. This paper introduces an artificial intelligence framework based on Conditional Generative Adversarial Networks (Conditional GANs) to generate future spatio-temporal trajectories of climatic indices. The approach focuses on the Soil Wetness Index (SWI), a key indicator used in France to assess drought severity. Drought accounts for approximately 30% of the indemnities paid under the French natural catastrophe insurance scheme. The proposed model, SwiGAN, simulates plausible drought propagation patterns up to 2050 for a region of France particularly exposed to this hazard. By generating realistic sequences of SWI maps, SwiGAN provides insights into drought dynamics under climate change scenarios and supports the design of adaptive risk management and insurance strategies. The methodology is also generalizable to other climate-related perils and actuarial applications such as economic scenario generation.

Antoine Heranval, Olivier Lopez, Didier Ngatcha +1

BioSP · Biostatistiques et Processus Spatiaux (BioSP), INRAE, Avignon, France · CREST +3

Financial Services Time Series Forecasting Conditional Generative Modeling Generative Adversarial Networks

Apr 21, 2026cs.LG

A Multi-Plant Machine Learning Framework for Emission Prediction, Forecasting, and Control in Cement Manufacturing

Cement production is among the largest contributors to industrial air pollution, emitting ~3 Mt NOx/year. The industry-standard mitigation approach, selective non-catalytic reduction (SNCR), exhibits low NH3 utilization efficiency, resulting in operational inefficiencies and increased reagent costs. Here, we develop a data-driven framework for emission control using large-scale operational data from four cement plants worldwide. Benchmarking nine machine learning architectures, we observe that prediction error varies ~3-5x across plants due to variation in data richness. Incorporating short-term process history nearly triples NOx prediction accuracy, revealing that NOx formation carries substantial process memory, a timescale dependence that is absent in CO and CO2. Further, we develop models that forecast NOx overshoots as early as nine minutes, providing a buffer for operational adjustments. The developed framework controls NOx formation at the source, reducing NH3 consumption in downstream SNCR. Surrogate model projections estimate a ~34-64% reduction in NOx while preserving clinker quality, corresponding to a reduction of ~290 t NOx/year and ~58,000 USD/year in NH3 savings. This work establishes a generalizable framework for data-driven emission control, offering a pathway toward low-emission operation without structural modifications or additional hardware, with potential applicability to other hard-to-abate industries such as steel, glass, and lime.

Sheikh Junaid Fayaz, Nestor D. Montiel-Bohorquez, Wilson Ricardo Leal da Silva +4

Civil and Environmental Engineering, Indian Institute of Technology Delhi, Hauz Khas, 110016, New Delhi, India · Politecnico di Milano, Department of Energy, Lambruschini 4A, 20156, Milan, Italy · Fuller Technologies, 2450 Copenhagen, Denmark +1

Time Series Forecasting

Apr 20, 2026cs.AI

Quantum inspired qubit qutrit neural networks for real time financial forecasting

This research investigates the performance and efficacy of machine learning models in stock prediction, comparing Artificial Neural Networks (ANNs), Quantum Qubit-based Neural Networks (QQBNs), and Quantum Qutrit-based Neural Networks (QQTNs). By outlining methodologies, architectures, and training procedures, the study highlights significant differences in training times and performance metrics across models. While all models demonstrate robust accuracies above 70%, the Quantum Qutrit-based Neural Network consistently outperforms with advantages in risk-adjusted returns, measured by the Sharpe ratio, greater consistency in prediction quality through the Information Coefficient, and enhanced robustness under varying market conditions. The QQTN not only surpasses its classical and qubit-based counterparts in multiple quantitative and qualitative metrics but also achieves comparable performance with significantly reduced training times. These results showcase the promising prospects of Quantum Qutrit-based Neural Networks in practical financial applications, where real-time processing is critical. By achieving superior accuracy, efficiency, and adaptability, the proposed models underscore the transformative potential of quantum-inspired approaches, paving the way for their integration into computationally intensive fields.

Kanishk Bakshi, Kathiravan Srinivasan

School of Computer Science and Engineering, Vellore Institute of Technology, Vellore 632014, India.

Quantitative Finance Time Series Forecasting Quantum-Inspired ML Quantum Neural Networks

Apr 20, 2026cs.LG

CAARL: In-Context Learning for Interpretable Co-Evolving Time Series Forecasting

In this paper we investigate forecasting coevolving time series that feature intricate dependencies and nonstationary dynamics by using an LLM Large Language Models approach We propose a novel modeling approach named ContextAware ARLLM CAARL that provides an interpretable framework to decode the contextual dynamics influencing changes in coevolving series CAARL decomposes time series into autoregressive segments constructs a temporal dependency graph and serializes this graph into a narrative to allow processing by LLM This design yields a chainofthoughtlike reasoning path where intermediate steps capture contextual dynamics and guide forecasts in a transparent manner By linking prediction to explicit reasoning traces CAARL enhances interpretability while maintaining accuracy Experiments on realworld datasets validate its effectiveness positioning CAARL as a competitive and interpretable alternative to stateoftheart forecasting methods

Etienne Tajeuna, Patrick Asante Owusu, Armelle Brun +1

Explainable Time Series Forecasting Time Series Forecasting LLM-Based Time Series Forecasting Non-Stationary Time Series Forecasting In-Context Learning

Apr 19, 2026eess.SP

SPaRSe-TIME: Saliency-Projected Low-Rank Temporal Modeling for Efficient and Interpretable Time Series Prediction

Time series forecasting is traditionally dominated by sequence-based architectures such as recurrent neural networks and attention mechanisms, which process all time steps uniformly and often incur substantial computational cost. However, real-world temporal signals typically exhibit heterogeneous structure, where informative patterns are sparsely distributed and interspersed with redundant observations. This work introduces \textbf{SPaRSe-TIME}, a structured and computationally efficient framework that models time series through a decomposition into three complementary components: saliency, memory, and trend. The proposed approach reformulates temporal modeling as a projection onto informative subspaces, where saliency acts as a data-dependent sparsification operator, memory captures dominant low-rank temporal patterns, and trend encodes low-frequency dynamics. These components are integrated through a lightweight, adaptive mapping that enables simplified, selective, and interpretable temporal reasoning. Extensive experiments on diverse real-world datasets demonstrate that SPaRSe-TIME achieves competitive predictive performance compared to recurrent and attention-based architectures, while significantly reducing computational complexity. The model is particularly effective in structured time series with clear temporal components and provides explicit interpretability through component-wise contributions. Furthermore, analysis reveals both the strengths and limitations of decomposition-based modeling, highlighting challenges in highly stochastic and complex multivariate settings. Overall, SPaRSe-TIME offers a principled alternative to monolithic sequence models, bridging efficiency, interpretability, and performance, and providing a scalable framework for time series learning.

K. A. Shahriar

Department of Electrical and Electronic Engineering Bangladesh University of Engineering and Technology Dhaka-1205, Bangladesh

Time Series Forecasting Time Series Decomposition

Apr 18, 2026stat.ML

Extraction of informative statistical features in the problem of forecasting time series generated by It{ô}-type processes

In this paper, we consider the problem of extraction of most informative features from time series that are regarded as observed values of stochastic processes satisfying the It{ô} stochastic differential equations with unknown random drift and diffusion coefficients. We do not attract any additional information and use only the information contained in the time series as it is. Therefore, as additional features, we use the parameters of statistically adjusted mixture-type models of the observed regularities of the behavior of the time series. Several algorithms of construction of these parameters are discussed. These algorithms are based on statistical reconstruction of the coefficients which, in turn, is based on statistical separation of normal mixtures. We obtain two types of parameters by the techniques of the uniform and non-uniform statistical reconstruction of the coefficients of the underlying It{ô} process. The reconstructed coefficients obtained by uniform techniques do not depend on the current value of the process, while the non-uniform techniques reconstruct the coefficients with the account of their dependence on the value of the process. Actually, the non-uniform techniques used in this paper represent a stochastic analog of the Taylor expansion for the time series. The efficiency of the obtained additional features is compared by using them in the autoregressive algorithms of prediction of time series. In order to obtain pure conclusion that is not affected by unwanted factors, say, related to a special choice of the architecture of the neural network prediction methods, we used only simple autoregressive algorithms. We show that the use of additional statistical features improves the prediction.

Victor Korolev, Mikhail Ivanov, Tatiana Kukanova +4

Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics · Moscow Center for Fundamental and Applied Mathematics · Federal Research Center “Computer Science and Control”, Russian Academy of Sciences +2

Stochastic Differential Equations Time Series Forecasting

Apr 18, 2026eess.SP

TimeRFT: Stimulating Generalizable Time Series Forecasting for TSFMs via Reinforcement Finetuning

Time Series Foundation Models (TSFMs) advance generalization and data efficiency in time series forecasting by unified large-scale pretraining. But TSFMs remain lacking when adapting to specific downstream forecasting tasks for two reasons. First, the non-stationary and uncertain nature of time series data lead to inevitable temporal distribution shifts between historical training and future testing data, while current Supervised FineTuning (SFT)-based methods are prone to overfitting and may degrade generalization. Second, training data availability varies across forecasting tasks, requiring TSFMs to generalize well under diverse data regimes. To address these challenges, we introduce the Time series Reinforcement Finetuning (TimeRFT) paradigm for TSFM downstream adaptation, which consists of two task-specific training recipes: i) A forecasting quality-based temporal reward mechanism that conducts a multi-faceted evaluation of the contribution of each prediction step to overall forecasting accuracy. ii) A forecasting difficulty-based data selection strategy to identify time series samples with generalizable predictive patterns and informative training signals. Extensive experiments demonstrate TimeRFT can consistently outperform SFT-based adaptation methods across various real-world forecasting tasks and training data regimes, enhancing prediction accuracy and generalization against unforeseen distribution shifts.

Siyang Li, Yize Chen, Zijie Zhu +4

HKUST(GZ) Guangzhou, China · University of Alberta Edmonton, Canada · Alibaba Cloud Guangzhou, China +3

Time Series Forecasting OOD Generalization Non-Stationary Time Series Forecasting RL Fine-Tuning Time-Series Foundation Models

Apr 18, 2026q-fin.ST

The CTLNet for Shanghai Composite Index Prediction

Shanghai Composite Index prediction has become a hot issue for many investors and academic researchers. Deep learning models are widely applied in multivariate time series forecasting, including recurrent neural networks (RNN), convolutional neural networks (CNN), and transformers. Specifically, the Transformer encoder, with its unique attention mechanism and parallel processing capabilities, has become an important tool in time series prediction, and has an advantage in dealing with long sequence dependencies and multivariate data correlations. Drawing on the strengths of various models, we propose the CNN-Transformer-LSTM Networks (CTLNet). This paper explores the application of CTLNet for Shanghai Composite Index prediction and the comparative experiments show that the proposed model outperforms state-of-the-art baselines.

Haibin Jiao

Independent Researcher

Multivariate Time Series Forecasting Hybrid CNN-Transformer Architectures Time Series Forecasting

Apr 17, 2026cs.LG

Chronax: A Jax Library for Forecasting and Conformal Inference

Time-series forecasting is central to many scientific and industrial domains, such as energy systems, climate modeling, finance, and retail. While forecasting methods have evolved from classical statistical models to automated, and neural approaches, the surrounding software ecosystem remains anchored to the traditional Python numerical stack. Existing libraries rely on interpreter-driven execution and object-oriented abstractions, limiting composability, large-scale parallelism, and integration with modern differentiable and accelerator-oriented workflows. Meanwhile, today's forecasting increasingly involves large collections of heterogeneous time series data, irregular covariates, and frequent retraining, placing new demands on scalability and execution efficiency. JAX offers an alternative paradigm to traditional stateful numerical computation frameworks based on pure functions and program transformations such as just-in-time compilation and automatic vectorization, enabling end-to-end optimization across CPUs, GPUs, and TPUs. However, this modern paradigm has not yet been fully incorporated into the design of forecasting systems. We introduce Chronax, a JAX-native time-series forecasting library that rethinks forecasting abstractions around functional purity, composable transformations, and accelerator-ready execution. By representing preprocessing, modeling, and multi-horizon prediction as pure JAX functions, Chronax enables scalable multi-series forecasting, model-agnostic conformal uncertainty quantification, and seamless integration with modern machine learning and scientific computing pipelines.

Xan Carey, Arsh Singh, Yash Deshmukh +8

Simulacrum New York City, NY, USA

Time Series Forecasting

Apr 17, 2026cs.LG

Convolutionally Low-Rank Models with Modified Quantile Regression for Interval Time Series Forecasting

The quantification of uncertainty in prediction models is crucial for reliable decision-making, yet remains a significant challenge. Interval time series forecasting offers a principled solution to this problem by providing prediction intervals (PIs), which indicates the probability that the true value falls within the predicted range. We consider a recently established point forecasts (PFs) method termed Learning-Based Convolution Nuclear Norm Minimization (LbCNNM), which directly generates multi-step ahead forecasts by leveraging the convolutional low-rankness property derived from training data. While theoretically complete and empirically effective, LbCNNM lacks inherent uncertainty estimation capabilities, a limitation shared by many advanced forecasting methods. To resolve the issue, we modify the well-known Quantile Regression (QR) and integrate it into LbCNNM, resulting in a novel interval forecasting method termed LbCNNM with Modified Quantile Regression (LbCNNM-MQR). In addition, we devise interval calibration techniques to further improve the accuracy of PIs. Extensive experiments on over 100,000 real-world time series demonstrate the superior performance of LbCNNM-MQR.

Miaoxuan Zhu, Yi Yu, Yuyang Li +2

Southeast University

Quantile Regression Time Series Forecasting Uncertainty Calibration Regression Prediction Intervals

Apr 16, 2026cs.LG

Assessing the Performance-Efficiency Trade-off of Foundation Models in Probabilistic Electricity Price Forecasting

Large-scale renewable energy deployment introduces pronounced volatility into the electricity system, turning grid operation into a complex stochastic optimization problem. Accurate electricity price forecasting (EPF) is essential not only to support operational decisions, such as optimal bidding strategies and balancing power preparation, but also to reduce economic risk and improve market efficiency. Probabilistic forecasts are particularly valuable because they quantify uncertainty stemming from renewable intermittency, market coupling, and regulatory changes, enabling market participants to make informed decisions that minimize losses and optimize expected revenues. However, it remains an open question which models to employ to produce accurate forecasts. Should these be task-specific machine learning (ML) models or Time Series Foundation Models (TSFMs)? In this work, we compare four models for day-ahead probabilistic EPF (PEPF) in European bidding zones: a deterministic NHITS backbone with Quantile-Regression Averaging (NHITS+QRA) and a conditional Normalizing-Flow forecaster (NF) are compared with two TSFMs, namely Moirai and ChronosX. On the one hand, we find that TSFMs outperform task-specific deep learning models trained from scratch in terms of CRPS, Energy Score, and predictive interval calibration across market conditions. On the other hand, we find that well-configured task-specific models, particularly NHITS combined with QRA, achieve performance very close to TSFMs, and in some scenarios, such as when supplied with additional informative feature groups or adapted via few-shot learning from other European markets, they can even surpass TSFMs. Overall, our findings show that while TSFMs offer expressive modeling capabilities, conventional models remain highly competitive, emphasizing the need to weigh computational expense against marginal performance improvements in PEPF.

Jan Niklas Lettner, Hadeer El Ashhab, Veit Hagenmeyer +1

Karlsruhe Institute of Technology · Karlsruhe, Germany

Electricity Price Forecasting Time Series Forecasting Probabilistic Forecasting Time-Series Foundation Models Probabilistic Time Series Forecasting Power Systems

Apr 13, 2026cs.LG

TempusBench: An Evaluation Framework for Time-Series Forecasting

Foundation models have transformed natural language processing and computer vision, and a rapidly growing literature on time-series foundation models (TSFMs) seeks to replicate this success in forecasting. While recent open-source models demonstrate the promise of TSFMs, the field lacks a comprehensive and community-accepted model evaluation framework. We see at least four major issues impeding progress on the development of such a framework. First, existing evaluation frameworks comprise benchmark forecasting tasks derived from often outdated datasets (e.g., M3), many of which lack clear metadata and overlap with the corpora used to pre-train TSFMs. Second, these frameworks evaluate models along a narrowly defined set of benchmark forecasting tasks, such as forecast horizon length or domain, but overlook core statistical properties such as non-stationarity and seasonality. Third, domain-specific models (e.g., XGBoost) are often compared unfairly, as existing frameworks do not enforce a systematic and consistent hyperparameter tuning convention for all models. Fourth, visualization tools for interpreting comparative performance are lacking. To address these issues, we introduce TempusBench, an open-source evaluation framework for TSFMs. TempusBench consists of 1) new datasets which are not included in existing TSFM pretraining corpora, 2) a set of novel benchmark tasks that go beyond existing ones, 3) a model evaluation pipeline with a standardized hyperparameter tuning protocol, and 4) a tensorboard-based visualization interface. We provide access to our code on GitHub: https://github.com/Smlcrm/TempusBench and maintain a live leaderboard at https://smlcrm.com/tempusbench.

Denizalp Goktas, Gerardo Riaño-Briceño, Omkar Tekawade +14

Simulacrum New York City, NY, USA

Time Series Forecasting Forecasting Benchmarks Time-Series Foundation Models

Apr 7, 2026cs.LG

On Dominant Manifolds in Reservoir Computing Networks

Understanding how training shapes the geometry of recurrent network dynamics is a central problem in time-series modeling. We study the emergence of low-dimensional dominant manifolds in the training of Reservoir Computing (RC) networks for temporal forecasting tasks. For a general linear continuous-time reservoir in the infinite-data limit, we show that the training data generate an invariant subspace of the trained reservoir, whose dimension equals the number of dominant modes. We then specialize to a simplified diagonal linear reservoir, where we link the dominant eigenvalues and eigenvectors to the spectrum of a backward Dynamic Mode Decomposition matrix, which yields a finite-dimensional approximation of the backward-time Koopman operator of the system generating the training data. We illustrate the emergence of these dominant modes during training in simulation, and discuss how the analysis may be extended to nonlinear RC via tangent dynamics and differential p-dominance.

Noa Kaplan, Alberto Padoan, Anastasia Bizyaeva

Time Series Forecasting Reservoir Computing Neural Network Training Dynamics

Apr 7, 2026cs.LG

Channel-wise Retrieval for Multivariate Time Series Forecasting

Multivariate time series forecasting often struggles to capture long-range dependencies due to fixed lookback windows. Retrieval-augmented forecasting addresses this by retrieving historical segments from memory, but existing approaches rely on a channel-agnostic strategy that applies the same references to all variables. This neglects inter-variable heterogeneity, where different channels exhibit distinct periodicities and spectral profiles. We propose CRAFT (Channel-wise retrieval-augmented forecasting), a novel framework that performs retrieval independently for each channel. To ensure efficiency, CRAFT adopts a two-stage pipeline: a sparse relation graph constructed in the time domain prunes irrelevant candidates, and spectral similarity in the frequency domain ranks references, emphasizing dominant periodic components while suppressing noise. Experiments on seven public benchmarks demonstrate that CRAFT outperforms state-of-the-art forecasting baselines, achieving superior accuracy with practical inference efficiency.

Junhyeok Kang, Jun Seo, Soyeon Park +4

LG AI Research, Republic of Korea

Multivariate Time Series Forecasting Time Series Forecasting Temporal IR Retrieval-Augmented Time Series Forecasting

Mar 23, 2026cs.LG

Rethinking Multimodal Fusion for Time Series: Text Modalities Need Constrained Fusion

Recent advances in multimodal learning have motivated the integration of auxiliary modalities such as text or vision into time series (TS) forecasting. However, most existing methods provide limited gains, often improving performance only in specific datasets or relying on architecture-specific designs that limit generalization. In this paper, we show that multimodal models with naive fusion strategies (e.g., simple addition or concatenation) often underperform unimodal TS models, which we attribute to the uncontrolled integration of auxiliary modalities which may introduce irrelevant information. Motivated by this observation, we explore various constrained fusion methods designed to control such integration and find that they consistently outperform naive fusion methods. Furthermore, we propose Controlled Fusion Adapter (CFA), a simple plug-in method that enables controlled cross-modal interactions without modifying the TS backbone, integrating only relevant textual information aligned with TS dynamics. CFA employs low rank adapters to filter irrelevant textual information before fusing it into temporal representations. We conduct over 20K experiments across various datasets and TS/text models, demonstrating the effectiveness of the constrained fusion methods. Code is available at: https://github.com/seunghan96/cfa.

Seunghan Lee, Jun Seo, Jaehoon Lee +7

LG AI Research Seoul, South Korea

Cross-Modal Learning Time Series Forecasting Multimodal Fusion

Mar 20, 2026stat.ML

Deep Time-Series Forecasting in 10 Years: A Survey

Autocorrelation is a common property of time-series, where each observation is dependent on its predecessors. In deep time-series forecasting, it raises two central challenges: (1) designing backbone architectures to model autocorrelation in history sequences, and (2) devising loss functions to model autocorrelation in label sequences. Recent studies have made strides in tackling these challenges, but a systematic survey examining both aspects remains lacking. To bridge this gap, this paper reviews deep time-series forecasting from an autocorrelation modeling perspective, offering two contributions beyond existing surveys. First, it introduces a taxonomy that jointly covers both backbone architectures and loss functions, whereas prior surveys provide limited coverage of the latter. Second, it analyzes the motivations and insights underlying the surveyed literature from a unified autocorrelation perspective, providing a holistic overview of the field's evolution. Additional resources and details are available at https://github.com/Master-PLC/Awesome-TSF-Papers.

Hao Wang, Licheng Pan, Qingsong Wen +12

School of Intelligence Science and Technology, Peking University, Beijing 100871, China · School of Cyber Science and Technology, Zhejiang University, Hangzhou, Zhejiang 310027, China · Squirrel AI Learning, Bellevue, WA 98004, USA +7

Time Series Forecasting

Mar 19, 2026stat.ML

Extending SSMs with the Exponentially Weighted Signature

We introduce the exponentially weighted signature (EWS), a continuous-time model that computes iterated integrals of a path, where each increment is weighted by the matrix exponential of a learnable generator over elapsed clock time. We prove that it solves a linear controlled differential equation, keeps the group-like structure and the universality of the signature, and satisfies a modified Chen identity, enabling a parallel scan. At depth one the EWS is a state-space model (SSM), and we map linear time-invariant SSMs, Mamba channels and Mamba-

2

heads to it in closed form. The EWS extends SSMs through an arbitrary matrix generator, a clock that generalises the step size to causal functionals of the input, and higher truncation depths that are non-linear in the path within a single layer. Empirically, the EWS achieves the highest average accuracy and rank on six long time-series classification datasets, where depth generally helps. Learned clocks prove necessary for state tracking on formal language tasks, and at depth one, the EWS matches or exceeds competing SSMs on regression and forecasting with far fewer parameters.

Alexandre Bloch, Benjamin Walker, Joël Mouterde +3

Mathematical Institute, University of Oxford · SKF · Department of Mathematics, Imperial College London

Dynamical Systems Time Series Classification Time Series Forecasting State Space Models