Time Series Forecasting

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Time series forecasting studies how to predict future observations from past values, often across multiple horizons and with missing data, changing regimes, or external drivers such as weather and events. Methods range from classical autoregressive and exponential-smoothing models to recurrent networks, Transformers, state-space models, decomposition and frequency-based approaches, graph models, and pretrained foundation models; probabilistic methods also estimate uncertainty. Current work increasingly combines historical patterns with covariates, retrieval, domain knowledge, and online adaptation, while targeting applications from energy and weather to health, transport, and finance. A central tension is that larger or more complex models do not reliably beat simple baselines, and benchmark accuracy may not reflect robustness, forecast structure, uncertainty calibration, or downstream decision value.

Latest papers

886 papers113 papers in the last four weeks, down 19% on the four weeks before. 0.7% of all new papers.

Apr 26, 2026

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, 2026

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, 2026

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, 2026

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, 2026

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, 2026

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 Supply Chain Optimization

Apr 22, 2026

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, 2026

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, 2026

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, 2026

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, 2026

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, 2026

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, 2026

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 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, 2026

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, 2026

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, 2026

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, 2026

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, 2026

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, 2026

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 15, 2026

Outperforming Self-Attention Mechanisms in Solar Irradiance Forecasting via Physics-Guided Neural Networks

Accurate Global Horizontal Irradiance (GHI) forecasting is critical for grid stability, particularly in arid regions characterized by rapid aerosol fluctuations. While recent trends favor computationally expensive Transformer-based architectures, this paper challenges the prevailing "complexity-first" paradigm. We propose a lightweight, Physics-Informed Hybrid CNN-BiLSTM framework that prioritizes domain knowledge over architectural depth. The model integrates a Convolutional Neural Network (CNN) for spatial feature extraction with a Bi-Directional LSTM for capturing temporal dependencies. Unlike standard data-driven approaches, our model is explicitly guided by a vector of 15 engineered features including Clear-Sky indices and Solar Zenith Angle - rather than relying solely on raw historical data. Hyperparameters are rigorously tuned using Bayesian Optimization to ensure global optimality. Experimental validation using NASA POWER data in Sudan demonstrates that our physics-guided approach achieves a Root Mean Square Error (RMSE) of 19.53 W/m^2, significantly outperforming complex attention-based baselines (RMSE 30.64 W/m^2). These results confirm a "Complexity Paradox": in high-noise meteorological tasks, explicit physical constraints offer a more efficient and accurate alternative to self-attention mechanisms. The findings advocate for a shift towards hybrid, physics-aware AI for real-time renewable energy management.

Mohammed Ezzaldin Babiker Abdullah, Rufaidah Abdallah Ibrahim Mohammed

Omdurman Islamic University, Omdurman, Sudan.

Solar Irradiance Forecasting Solar Power Forecasting Time Series Forecasting Physics-Informed ML Convolutional RNNs

Apr 14, 2026

Bias-Corrected Adaptive Conformal Inference for Multi-Horizon Time Series Forecasting

Adaptive Conformal Inference (ACI) provides distribution-free prediction intervals with asymptotic coverage guarantees for time series under distribution shift. However, ACI only adapts the quantile threshold -- it cannot shift the interval center. When a base forecaster develops persistent bias after a regime change, ACI compensates by widening intervals symmetrically, producing unnecessarily conservative bands. We propose Bias-Corrected ACI (BC-ACI), which augments standard ACI with an online exponentially weighted moving average (EWM) estimate of forecast bias. BC-ACI corrects nonconformity scores before quantile computation and re-centers prediction intervals, addressing the root cause of miscalibration rather than its symptom. An adaptive dead-zone threshold suppresses corrections when estimated bias is indistinguishable from noise, ensuring no degradation on well-calibrated data. In controlled experiments across 688 runs spanning two base models, four synthetic regimes, and three real datasets, BC-ACI reduces Winkler interval scores by 13--17% under mean and compound distribution shifts (Wilcoxon p < 0.001) while maintaining equivalent performance on stationary data (ratio 1.002x). We provide finite-sample analysis showing that coverage guarantees degrade gracefully with bias estimation error.

Ankit Lade, Sai Krishna J., Indar Kumar

Adaptive Conformal Inference Time Series Forecasting Conformal Prediction Regression Prediction Intervals Distribution Shift Robustness

Apr 14, 2026

Beyond Weather Correlation: A Comparative Study of Static and Temporal Neural Architectures for Fine-Grained Residential Energy Consumption Forecasting in Melbourne, Australia

Accurate short-term residential energy consumption forecasting at sub-hourly resolution is critical for smart grid management, demand response programmes, and renewable energy integration. While weather variables are widely acknowledged as key drivers of residential electricity demand, the relative merit of incorporating temporal autocorrelation - the sequential memory of past consumption; over static meteorological features alone remains underexplored at fine-grained (5-minute) temporal resolution for Australian households. This paper presents a rigorous empirical comparison of a Multilayer Perceptron (MLP) and a Long Short-Term Memory (LSTM) recurrent network applied to two real-world Melbourne households: House 3 (a standard grid-connected dwelling) and House 4 (a rooftop solar photovoltaic-integrated household). Both models are trained on 14 months of 5-minute interval smart meter data (March 2023-April 2024) merged with official Bureau of Meteorology (BOM) daily weather observations, yielding over 117,000 samples per household. The LSTM, operating on 24-step (2-hour) sliding consumption windows, achieves coefficients of determination of R^2 = 0.883 (House 3) and R^2 = 0.865 (House 4), compared to R^2 = -0.055 and R^2 = 0.410 for the corresponding weather-driven MLPs - differences of 93.8 and 45.5 percentage points. These results establish that temporal autocorrelation in the consumption sequence dominates meteorological information for short-term forecasting at 5-minute granularity. Additionally, we demonstrate an asymmetry introduced by solar generation: for the PV-integrated household, the MLP achieves R^2 = 0.410, revealing implicit solar forecasting from weather-time correlations. A persistence baseline analysis and seasonal stratification contextualise model performance. We propose a hybrid weather-augmented LSTM and federated learning extensions as directions for future work.

Prasad Nimantha Madusanka Ukwatta Hewage, Hao Wu

School of Computing and Information Technology Victoria University, Sydney, NSW, Australia

Electricity Load Forecasting Time Series Forecasting Multivariate Time Series Forecasting Long Short-Term Memory Networks

Apr 14, 2026

A Physics-Aware Framework for Short-Term GPU Power Forecasting of AI Data Centers

AI data centers experience rapid fluctuations in power demand due to the heterogeneity of computational tasks that they have to support. For example, the power profile of inference and training of large language models (LLMs) is quite distinct and big divergences can result in the instability of the underlying electricity grid. In this paper we propose, to the best of our knowledge, the first physics-informed DLinear time-series model that can accurately forecast power utilization of an AI data center 5-80 minutes (short-term forecasting) into the future. The physics, based on a multi-node lumped thermal resistance-capacitance (RC) network consistent with Newton's law of cooling, is captured using newly derived time-dependent ordinary differential equations (ODE) that separately models and interlinks power consumption with the GPU compute and memory utilization and temperature. The resulting model, that we refer to as PI-DLinear, trained and evaluated on a real AI data center dataset and is not only more accurate than the state-of-the-art (SOTA) models tested, but the forecast profile respects the underlying physics under power throttling and load transient events. Relative to the SOTA transformer-based and non-transformer-based models, improvements in forecasting accuracy (averaged across all look-back and prediction windows) range from 0.782%-39.08% for MSE, 0.993%-51.82% for MAE, and 0.370%-22.28% for RMSE.

Mohammad AlShaikh Saleh, Sanjay Chawla, Sertac Bayhan +2

College of Science and Engineering, Hamad Bin Khalifa University, Doha, Qatar · Qatar Computing Research Institute, Hamad Bin Khalifa University, Doha, Qatar · Qatar Environment and Energy Research Institute, Hamad Bin Khalifa University, Doha, Qatar +1

Physics-Informed Forecasting Time Series Forecasting Electricity Load Forecasting Data Center Energy Management Physics-Informed ML

Apr 13, 2026

Beyond Sequential Prediction: Learning Financial Market Dynamics in Volatile and Non-Stationary Environments through Sentiment-Conditioned Generative Modelling

The problem of time-series forecasting in non-stationary and complex environments is a challenging task in machine learning, especially with heterogeneous numerical and textual data present. Traditional statistical models like AutoRegressive Integrated Moving Average (ARIMA) are based on the assumptions of linearity and stationarity, whereas recurrent neural networks like Long Short-Term Memory (LSTM) models do not necessarily represent distributional properties in highly volatile settings. This paper proposes a hybrid model that combines Generative Adversarial Networks (GANs) with Natural Language Processing (NLP)-based sentiment analysis to enable sentiment-conditioned time-series prediction. The model integrates adversarial learning on numerical sequences with contextual sentiment representations derived from unstructured text, enabling them to be jointly modelled to capture temporal dynamics and exogenous information. These results demonstrate the promise of hybrid generative and language-aware methods to enhance prediction robustness in non-stationary environments.

Alexis Lazanas, Spyridon Karpouzis

Department of Mechanical Engineering and Aeronautics, University of Patras, Rion-Patras, Greece · FICC Market Risk, BNP Paribas CIB, London, United Kingdom

Time Series Forecasting Non-Stationary Time Series Forecasting Conditional Generative Modeling Generative Adversarial Networks

Apr 13, 2026

INTARG: Informed Real-Time Adversarial Attack Generation for Time-Series Regression

Time-series forecasting aims to predict future values by modeling temporal dependencies in historical observations. It is a critical component of many real-world systems, where accurate forecasts improve operational efficiency and help mitigate uncertainty and risk. More recently, machine learning (ML), and especially deep learning (DL)-based models, have gained widespread adoption for time-series forecasting, but they remain vulnerable to adversarial attacks. However, many state-of-the-art attack methods are not directly applicable in time-series settings, where storing complete historical data or performing attacks at every time step is often impractical. This paper proposes an adversarial attack framework for time-series forecasting under an online bounded-buffer setting, leveraging an informed and selective attack strategy. By selectively targeting time steps where the model exhibits high confidence and the expected prediction error is maximal, our framework produces fewer but substantially more effective attacks. Experiments show that our framework can increase the prediction error up to 2.42x, while performing attacks in fewer than 10% of time steps.

Gamze Kirman Tokgoz, Onat Gungor, Tajana Rosing +1

San Diego State University, San Diego, CA, USA · University of California, San Diego, CA, USA

Adversarial Attacks Time Series Forecasting

Apr 13, 2026

Physics-Informed State Space Models for Reliable Solar Irradiance Forecasting in Off-Grid Systems

The stable operation of off-grid photovoltaic systems requires accurate, computationally efficient solar forecasting. Contemporary deep learning models often suffer from massive computational overhead and physical blindness, generating impossible predictions. This paper introduces the Physics-Informed State Space Model (PISSM) to bridge the gap between efficiency and physical accuracy for edge-deployed microcontrollers. PISSM utilizes a dynamic Hankel matrix embedding to filter stochastic sensor noise by transforming raw meteorological sequences into a robust state space. A Linear State Space Model replaces heavy attention mechanisms, efficiently modeling temporal dependencies for parallel processing. Crucially, a novel Physics-Informed Gating mechanism leverages the Solar Zenith Angle and Clearness Index to structurally bound outputs, ensuring predictions strictly obey diurnal cycles and preventing nocturnal errors. Validated on a multi-year dataset for Omdurman, Sudan, PISSM achieves superior accuracy with fewer than 40,000 parameters, establishing an ultra-lightweight benchmark for real-time off-grid control.

Mohammed Ezzaldin Babiker Abdullah

Department of Electrical and Electronic Engineering, Faculty of Engineering Sciences, Omdurman Islamic University, Omdurman, Sudan

Solar Irradiance Forecasting Time Series Forecasting State Space Models Physics-Informed ML

Apr 13, 2026

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 Time Series Modeling

Apr 12, 2026

Designing a double deep reinforcement learning selection tool for resilient demand prediction

The use of artificial intelligence in supply chain forecasting has attracted many scientific studies for several decades. However, the process of selecting an appropriate forecasting solution becomes a daunting task. This complexity arises due to the distinct features inherent to each dataset. Research to tackle this issue has been performed since the eighties but recent development of demand forecasting has opened new perspectives. This research aims to enhance automatic forecasting model selection by proposing a novel architecture that acts as a double deep reinforcement learning agent, selecting automatically a forecasting model from the forecasting committee at the time of prediction. Moreover, a novel early-stopping approach based on average reward convergence has been introduced to expedite training time. To evaluate the model's performance, an empirical study was conducted utilizing grocery sales datasets and snack demands datasets. The experimental results demonstrate the robustness of the proposed approach when compared to state-of-the-art methods.

Bilel Abderrahmane Benziane, Benoit Lardeux, Ayoub Mcharek +1

DataLab, Generix Group, 8 Rue Simone IFF, 75012, Paris, France

Model Selection Time Series Forecasting Reinforcement Learning Automated Machine Learning

Apr 12, 2026

WaveMoE: A Wavelet-Enhanced Mixture-of-Experts Foundation Model for Time Series Forecasting

Time series foundation models (TSFMs) have recently achieved remarkable success in universal forecasting by leveraging large-scale pretraining on diverse time series data. Complementing this progress, incorporating frequency-domain information yields promising performance in enhancing the modeling of complex temporal patterns, such as periodicity and localized high-frequency dynamics, which are prevalent in real-world time series. To advance this direction, we propose a new perspective that integrates explicit frequency-domain representations into scalable foundation models, and introduce WaveMoE, a wavelet-enhanced mixture-of-experts foundation model for time series forecasting. WaveMoE adopts a dual-path architecture that jointly processes time series tokens and wavelet tokens aligned along a unified temporal axis, and coordinates them through a shared expert routing mechanism that enables consistent expert specialization while efficiently scaling model capacity. Preliminary experimental results on 16 diverse benchmark datasets indicate that WaveMoE has the potential to further improve forecasting performance by incorporating wavelet-domain corpora.

Shunyu Wu, Jiawei Huang, Weibin Feng +6

Sun Yat-sen University · Xiaomi Corporation · National University of Singapore

Time Series Forecasting Time-Series Foundation Models Frequency-Domain Time Series Modeling Mixture-of-Experts Models Frequency-Domain Feature Learning

Apr 11, 2026

Daily Predictions of F10.7 and F30 Solar Indices with Deep Learning

The F10.7 and F30 solar indices are the solar radio fluxes measured at wavelengths of 10.7 cm and 30 cm, respectively, which are key indicators of solar activity. F10.7 is valuable for explaining the impact of solar ultraviolet (UV) radiation on the upper atmosphere of Earth, while F30 is more sensitive and could improve the reaction of thermospheric density to solar stimulation. In this study, we present a new deep learning model, named the Solar Index Network, or SINet for short, to predict daily values of the F10.7 and F30 solar indices. The SINet model is designed to make medium-term predictions of the index values (1-60 days in advance). The observed data used for SINet training were taken from the National Oceanic and Atmospheric Administration (NOAA) as well as Toyokawa and Nobeyama facilities. Our experimental results show that SINet performs better than five closely related statistical and deep learning methods for the prediction of F10.7. Furthermore, to our knowledge, this is the first time deep learning has been used to predict the F30 solar index.

Zhenduo Wang, Yasser Abduallah, Jason T. L. Wang +6

Institute for Space Weather Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA · Department of Computer Science, New Jersey Institute of Technology, Newark, NJ 07102, USA · Center for Solar-Terrestrial Research, New Jersey Institute of Technology, Newark, NJ 07102, USA +3

Space Weather Forecasting Time Series Forecasting Solar Physics