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.

May 12, 2026cs.LG

Investigating simple target-covariate relationships for Chronos-2 and TabPFN-TS

Time Series Foundation Models (TSFMs) have recently achieved state-of-the-art performance, often outperforming supervised models in zero-shot settings. Recent TSFM architectures, such as Chronos-2 and TabPFN-TS, aim to integrate covariates. In this paper, we design controlled experiments based on simple target-covariate relationships to assess this integration capability. Our results show that TabPFN-TS captures these relationships more effectively than Chronos-2, especially for short horizons, suggesting that the strong benchmark performance of Chronos-2 does not automatically translate into optimal modeling of simple covariate-target dependencies.

Gaspard Berthelier, Mariia Baranova, Andrei-Tiberiu Pantea +4

EDF R&D, Palaiseau · Inria Sophia-Antipolis, Université Côte d’Azur · Université Paris Cit'e

Multivariate Time Series Forecasting Time Series Forecasting Time-Series Foundation Models

May 12, 2026cs.LG

ECTO: Exogenous-Conditioned Temporal Operator for Ultra-Short-Term Wind Power Forecasting

Accurate ultra-short-term wind power forecasting is critical for grid dispatch and reserve management, yet remains challenging due to the non-stationary, condition-dependent nature of wind generation. Meteorological exogenous variables carry substantial predictive information, but the most informative variable combination varies across sites, operating conditions, and prediction horizons. Existing deep learning approaches either treat exogenous inputs as generic auxiliary channels through uniform mixing or soft gating, or rely on fixed preprocessing steps such as PCA, without exploiting the physical structure of meteorological variables. We propose ECTO (Exogenous-Conditioned Temporal Operator), a unified framework that decomposes exogenous variable modeling into two complementary modules. Physically-Grounded Variable Selection (PGVS) performs hierarchical, group-aware sparse selection over exogenous variables using a domain-informed physical prior and sparsemax activations, producing a compact, condition-adaptive exogenous context. Exogenous-Conditioned Regime Refinement (ECRR) routes the forecast through learned regime experts that apply gain--bias calibration and horizon-specific corrections via a mixture-of-experts paradigm. Experiments on three wind farms spanning different climates, capacities (66--200 MW), and exogenous dimensions (11--13 variables) demonstrate that ECTO achieves the lowest MSE across all sites, with relative improvements over the strongest baseline ranging from 2.2% to 5.2%, widening to 8.6% at the longer prediction horizon (

H=32

). Ablation analysis confirms that each exogenous-related component contributes positively (PGVS +1.84%, ECRR +2.86%), and interpretability analysis reveals that PGVS learns physically meaningful, site-specific variable selection patterns, while ECRR converges to well-separated calibration strategies consistent across sites.

Cao Yuan, Junjun Wang

Wuhan Polytechnic University, Wuhan, 430048, Hubei, China

Time Series Forecasting Non-Stationary Time Series Forecasting Feature Selection Wind Power Forecasting Power Systems

May 12, 2026q-fin.ST

From Index to Equity: Pre-Training Transformers for Stock Return Prediction

This research aims to leverage machine learning to improve stock price prediction and support informed investment decisions related to buying, selling, and holding assets. Specifically, this work investigates transformer-based models for stock prediction and examines the impact of pre-training strategies on forecasting performance. A transformer model was first pre-trained on the Toronto Stock Exchange Index (TSX) to predict intra-day return direction and subsequently fine-tuned on individual TSX stocks. The model was further adapted for return-value regression tasks. Performance was benchmarked against Long Short-Term Memory (LSTM) and XGBoost models. Pre-training on the market index improved the binary cross-entropy loss for individual stock prediction from 0.69 to 0.64. The fine-tuned transformer regression model achieved lower mean squared error than the benchmark models, although the ensemble and XGBoost models achieved higher average daily returns. In addition, a practical application was developed to deliver real-time stock predictions for trading support. Future work will focus on increasing transformer model capacity, incorporating broader global technical indicators, and filtering out stocks with low predictability.

Marie Soehl Coolsaet, Roberto Gallardo, Zhen Gao

Faculty of Engineering, McMaster University · Department* of Economics, Universidad Veracruzana, Mexico

Time Series Forecasting Transfer Learning Time Series Transformers

May 12, 2026cs.AI

Dual-Temporal LSTM with Hybrid Attention for Airline Passenger Load Factor Forecasting: Integrating Intra-Flight and Inter-Flight Booking Dynamics

Accurate short-term demand forecasting is crucial to airline revenue management, yet most existing systems fail to meet this need because current models treat booking data as a single temporal dimension, either the accumulation of bookings for a specific flight or the historical booking profile of the same route. This unidimensional view discards information carried by the other temporal stream and forecasting absolute passenger counts introduces a further operational fragility when change in planned aircraft type alters total seat capacity. This study addresses both limitations. A dual-stream Long Short-Term Memory (LSTM) integrated with attention framework is proposed that simultaneously processes two complementary input sequences: a horizontal sequence capturing intra-flight booking accumulation over the days preceding departure, and a vertical sequence capturing inter-flight booking patterns at fixed days-before-departure offsets across historical flights. Multiple dual-stream architectural variants, combining self-attention, cross-attention, and hybrid attention with concatenation, residual, and gated fusion strategies, are developed and evaluated. Experiments on real-world reservation data from the national airline of Bangladesh, Biman Bangladesh Airlines (BBA), demonstrate that the proposed hybrid model achieves a Mean Absolute Error of 2.8167 and a coefficient of determination (

R^{2}

) of 0.9495, outperforming single-stream baselines, tree-based models, and three prior dual-LSTM architectures applied to the same data. Validation across four flight category pairs; domestic versus international, direct versus transit, high versus low frequency, and short versus mid versus long haul confirms that the model generalizes across operationally diverse route types. Biman Bangladesh Airlines (BBA) has officially integrated this methodology into its operations.

ASM Nazrul Islam, Md. Hasanul Kabir, Md. Liakot Ali +1

Institute of Information and Communication Technology, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh · Islamic University of Technology, Dhaka, Bangladesh

Time Series Forecasting Long Short-Term Memory Networks Attention Mechanisms

May 11, 2026cs.LG

Beyond Similarity: Temporal Operator Attention for Time Series Analysis

A persistent paradox in time-series forecasting is that structurally simple MLP and linear models often outperform high-capacity Transformers. We argue that this gap arises from a mismatch in the sequence-modeling primitive: while many time-series dynamics are governed by global temporal operators (e.g., filtering and harmonic structure), standard attention forms each output as a convex combination of inputs. This restricts its ability to represent signed and oscillatory transformations that are fundamental to temporal signal processing. We formalize this limitation as a simplex-constrained mixing bottleneck in softmax attention, which becomes especially restrictive for operator-driven time-series tasks. To address this, we propose

\textbf{Temporal Operator Attention (TOA)}

, a framework that augments attention with explicit, learnable sequence-space operators, enabling direct signed mixing across time while preserving input-dependent adaptivity. To make dense

N \times N

operators practical, we introduce Stochastic Operator Regularization, a high-variance dropout mechanism that stabilizes training and prevents trivial memorization. Across forecasting, anomaly detection, and classification benchmarks, TOA consistently improves performance when integrated into standard backbones such as PatchTST and iTransformer, with particularly strong gains in reconstruction-heavy tasks. These results suggest that explicit operator learning is a key ingredient for effective time-series modeling.

Jevon Twitty, Vinh Pham, Nitiwith Rotchanarak +4

Georgia Institute of Technology1

Time Series Classification Time Series Forecasting Temporal Attention

May 11, 2026cs.LG

Latent Chain-of-Thought Improves Structured-Data Transformers

Chain-of-thought and more broadly test-time compute are known to augment the expressive capabilities of language models and have led to major innovations in reasoning. Motivated by this success, this paper explores latent chain-of-thought as well as the impact of depth and looping for time-series and tabular data. We propose a recurrent scheme in which a structured-data transformer, after an initial forward pass, compresses its query-position hidden states into feedback tokens that are appended to the input and processed again, allowing multiple rounds of latent computation before prediction. We compare CoT models against a same-depth no-CoT baseline, a deeper baseline matched to the CoT model in effective depth, and a looped transformer with weight-tied recurrence but no additional chain-of-thought tokens. Across 36 datasets in time-series forecasting and tabular prediction, latent chain-of-thought improves over the baseline on 7/9 time-series datasets (+12.63% average gain) and 23/27 tabular datasets (+3.25% average gain), with CoT models performing best on average in both settings. We also show that the benefit of CoT extends to pretrained foundation models: applying latent CoT to nanoTabPFN, a small open-source tabular foundation model, improves its performance above the much larger TabPFN-v2 on TabArena. Together, these results demonstrate that chain-of-thought is a useful axis for scaling test-time compute for structured data.

Carson Dudley, Samet Oymak

CoT Reasoning Time Series Forecasting Recurrent Transformers Tabular Prediction Time Series Transformers Latent CoT Reasoning

May 11, 2026cs.LG

NoRIN: Backbone-Adaptive Reversible Normalization for Time-Series Forecasting

Reversible instance normalization (RevIN) and its successors (Dish-TS, SAN, FAN) have become the de facto plug-in for time-series forecasting, yet the map they apply to each data point is strictly affine,

x \mapsto ax+b

, so they cannot reshape the underlying distribution -- heavy tails remain heavy and skewness remains uncorrected. We propose NoRIN, a non-linear reversible normalization based on the arcsinh-form Johnson

S_U

transform with two shape parameters

(δ,\varepsilon)

that control tailedness and skewness; the linear

Z

-score used by RevIN is recovered only in the limit

δ\to \infty

. Training

(δ,\varepsilon)

jointly with the backbone via gradient descent reliably pushes them toward this linear limit within a few epochs -- a phenomenon we name the degeneration problem: the forecasting loss is locally indifferent to shape, and the high-capacity backbone compensates for any monotone reparameterization of its input. NoRIN escapes the degeneration by decoupling shape selection from gradient training:

(δ,\varepsilon)

are initialized by a closed-form Slifker-Shapiro quantile fit and refined by Bayesian optimization on the validation objective, while the inner training loop is identical to standard RevIN-style training. Across six representative backbones x five real-world datasets x three prediction horizons (90 configurations), decoupled shape optimization recovers

(δ^\star,\varepsilon^\star)

that sit systematically far from the linear limit, with values that vary in a backbone-dependent way. This empirically supports the central thesis: different backbones genuinely require different normalization parameters to reach their best performance.

Shun Zhang, Yuyang Xiao

Graduate School of China Academy of Engineering Physics, Beijing 100193, China · Institute of Applied Physics and Computational Mathematics, Beijing 100094, China

Time Series Forecasting

May 11, 2026cs.LG

Benchmarking Sensor-Fault Robustness in Forecasting

Cyber-physical system (CPS) forecasting models depend on sensor streams with noisy, biased, missing, or temporally misaligned readings, yet standard forecasting evaluation often selects models by nominal error without showing whether they remain robust under such faults. We introduce SensorFault-Bench, a shared CPS-grounded sensor-fault stress-test protocol for evaluating forecasting architectures and robustness-improvement methods, and an operational taxonomy organizing the method comparison. Across four real-world datasets and eight scored scenarios governed by a standardized severity model, it reports worst-scenario degradation, clean mean squared error (MSE), and worst-scenario fault-time MSE, separating relative robustness from absolute error. A disjoint fault-transfer split lets explicit fault-training methods train on adjacent fault families while evaluation uses separate benchmark scenarios. Empirically, forecasting architectures favored by clean MSE can degrade sharply under faults, and clean-MSE rankings can disagree with worst-scenario fault-time error rankings. Chronos-2, the evaluated zero-shot foundation-model representative, matches or trails the last-value naive forecaster in clean MSE on the two single-target datasets and has the largest worst-scenario degradation on ETTh1 and Traffic, where all channels are forecast targets. For the evaluated robustness-improvement method set, paired deltas show selective degradation reductions: projected gradient descent adversarial training and randomized training lead where value faults dominate observed degradation, while fault augmentation leads where availability faults dominate. SensorFault-Bench provides open-source code, documented data access, and reproduction and extension guides, so new datasets, architectures, and robustness-improvement methods can be evaluated under the same CPS sensor-fault robustness protocol.

Alexander Windmann, Philipp Wittenberg, Gianluca Manca +3

1Helmut Schmidt University · 2Ruhr University Bochum · 3ABB Corporate Research +2

Cyber-Physical Systems Time Series Forecasting Forecasting Benchmarks

May 11, 2026cs.LG

DeepLévy: Learning Heavy-Tailed Uncertainty in Highly Volatile Time Series

Modeling uncertainty in heavy-tailed time series remains a critical challenge for deep probabilistic forecasting models, which often struggle to capture abrupt, extreme events. While Lévy stable distributions offer a natural framework for modeling such non-Gaussian behaviors, the intractability of their probability density functions severely limits conventional likelihood-based inference. To address this, we introduce DeepLévy, a neural framework that learns mixtures of Lévy stable distributions by minimizing the discrepancy between empirical and parametric characteristic functions. DeepLévy incorporates a mixture mechanism that adaptively learns context-dependent weights and parameters over multiple Lévy components, enabling flexible multi-horizon uncertainty modeling. Evaluations on both real and synthetic datasets demonstrate that DeepLévy outperforms state-of-the-art deep probabilistic forecasting approaches in tail risk metrics, especially under extreme volatility.

Yang Yang, Du Yin, Hao Xue +1

University of New South Wales Australia NSW Sydney · The Hong Kong University of Science and Technology (Guangzhou)

Time Series Forecasting Distribution Matching Heavy-Tailed Distributions Probabilistic Time Series Forecasting

May 11, 2026stat.ML

Fast Training of Mixture-of-Experts for Time Series Forecasting via Expert Loss Integration

We propose a novel adaptive Mixture-of-Experts (MoE) framework for time series forecasting that addresses the optimization problem arising from small gating weights by incorporating expert-specific losses, which provide each expert with a direct learning signal independent of the gate-assigned weight. Specifically, the overall objective comprises the base forecasting loss and expert-specific losses, allowing individual expert prediction errors to directly influence parameter updates alongside the aggregate forecasting error. The framework also encourages different experts to learn from different temporal segments of the data. The proposed framework is further combined with a partial online learning strategy that enables efficient incremental updates of model parameters. By integrating expert-level loss information with partial online optimization, the proposed method improves forecasting performance while retaining computational efficiency. Empirical results across economic, tourism, and energy datasets with different sampling frequencies show that the proposed approach generally outperforms state-of-the-art supervised neural forecasting models, including Transformer-based architectures such as PatchTST, as well as zero-shot time-series foundation models such as TimeMoE. Furthermore, ablation studies confirm the effectiveness of the expert-specific loss integration strategy, highlighting its contribution to enhancing predictive performance.

Btissame El Mahtout, Florian Ziel

Chair of Data Science in Energy and Environment, University of Duisburg-Essen, Germany · Chair of Econometrics and Statistics, Technical University of Dortmund, Germany

Time Series Forecasting Mixture-of-Experts Models

May 11, 2026cs.LG

LeapTS: Rethinking Time Series Forecasting as Adaptive Multi-Horizon Scheduling

Time series forecasting serves as an essential tool for many real-world applications, supporting tasks such as resource optimization and decision-making. Despite significant architectural advancements, most modern models still treat forecasting task as a fixed mapping from history to target horizons. This induces temporal decoupling across future time points and limits the model's ability to adapt to the evolving context as forecasting progresses. In this work, we present LeapTS, a novel framework that reformulates time series forecasting as a dynamic scheduling process over the prediction horizon. Specifically, LeapTS organizes the forecasting process into multi-level decisions using: (1) the hierarchical controller to dynamically select the optimal prediction scale and advancement length at each step, and (2) continuous-time state evolution driven by neural controlled differential equations. Within this process, the controlled update mechanism explicitly couples the irregular temporal dynamics with discrete scheduling feedback. Extensive evaluations on both real-world and synthetic datasets demonstrate that LeapTS improves overall forecasting performance by at least 7.4% while achieving a 2.6

\times

to 5.3

\times

inference speedup over representative Transformer-based models. Furthermore, by explicitly tracing the scheduling trajectories, we reveal how the model autonomously adapts its forecasting behavior to capture non-stationary dynamics.

Sheng Pan, Ming Jin, Bo Du +1

Griffith University

Neural Controlled Differential Equations Time Series Forecasting Non-Stationary Time Series Forecasting Multiscale Time-Series Modeling

May 11, 2026q-fin.TR

Game-Theoretic Modeling of Heterogeneous Investor Interactions for Stock Price Forecasting

Accurate stock price forecasting has consistently remained a pivotal yet challenging FinTech task that underpins quantitative trading and investment decision making. Recent efforts have been dedicated to modeling various complex relationships among stocks in the stock market toward more reliable stock price forecasting.These methods depend heavily on strong static prior assumptions by modeling either temporal dependencies within individual stocks or spatial dependencies across different stocks based on predefined structures, while the complex market dynamics that drive stock price movements remain unexplored. To alleviate this issue, we propose a novel game-theoretic modeling method that captures heterogeneous investor interactions for stock price forecasting. The core idea is to embed game-theoretic mechanisms into the heterogeneous graph structure to finely model the dynamic strategic interactions among heterogeneous investors with respect to target stocks. Additionally, temporal positional encoding is adopted to reflect the differentiated influences of each game event at different time steps within the time window on future stock price movements. Leveraging heterogeneous graph networks, we proxy the intricate dynamics of the stock market through investor games and enable real-time information propagation and node updates among all nodes. Extensive experiments conducted on two real-world benchmark dataset demonstrate that our method effectively outperforms state-of-the-art stock price forecasting methods.

Yong Zhang, Xinxiao Wu, Yunde Jia +1

School of Computer Science, Beijing Institute of Technology · Faculty of Engineering, Shenzhen MSU-BIT University

Quantitative Finance Time Series Forecasting

May 11, 2026cs.AI

Yield Curve Forecasting using Machine Learning and Econometrics: A Comparative Analysis

While machine learning has revolutionized many fields such as natural language processing (NLP) and computer vision, its impact on time-series forecasting is still widely disputed, especially in the finance domain. This paper compares forecasting performance on U.S. Treasury yield curve data across econometrics/time-series analysis, classical machine learning, and deep learning methods, using daily data over 47 years. The Treasury yield curve is important because it is widely used by every participant in the bond markets, which are larger than equity markets. We examine a variety of methods that have not been tested on yield curve forecasting, especially deep learning algorithms. The algorithms include the Autoregressive Integrated Moving Average (ARIMA) model and its extensions, naive benchmarks, ensemble methods, Recurrent Neural Networks (RNNs), and multiple transformers built for forecasting. ARIMA and naive econometric models outperform other models overall, except in one time block. Of the machine learning methods, TimeGPT, LGBM and RNNs perform the best. Furthermore, the paper explores whether stationary or nonstationary data are more appropriate as input to deep learning models.

Aman Singh, Tokunbo Ogunfunmi, Sanjiv Das

Department of Electrical and Computer Engineering, Santa Clara University, USA · School of Business, Santa Clara University, USA

Quantitative Finance Time Series Forecasting Forecasting Benchmarks Non-Stationary Time Series Forecasting Financial Time Series

May 10, 2026cs.LG

Benchmarking Transformer and xLSTM for Time-Series Forecasting of Heat Consumption

Obtaining an accurate short-term forecasting for heat demand is an essential part of operating district heating networks cost-efficient and reliable. Heat consumption time series at the building level are highly dependent on exogenous variables such as outdoor temperature and individual usage patterns, making forecasting in this context a challenging task. Thus, this paper benchmarks novel Transformer-based and xLSTM architectures for short-term heat-demand forecasting. Using hourly data from 25 German buildings (2017-2025), we compare three-hour and 24-hour forecasting horizons relevant for intraday control and day-ahead scheduling. We establish a multi-building benchmark that tests whether models trained on pooled, heterogeneous building data are able to generalize across diverse building stock. The results show that the xLSTM achieves the lowest RMSE (19.88 kWh for three-hour, 21.47 kWh for 24-hour forecasts), while the Temporal Fusion Transformer attains the best MAE (9.16 kWh for three-hour forecasts). As xLSTMs and Transformers require long training times and have a huge number of trainable parameters, their sustainability remains questionable. Therefore, this paper further investigates the trade-off between predictive accuracy and computational resource demand of the evaluated forecasting models. The findings indicate that also low-parameter models like a traditional fully-connected network achieve good predictive results, highlighting that marginal accuracy gains of the novel prediction models come at substantial resource expense for this use case.

Marja Wahl, Daniel R. Bayer, Sven Rausch +1

RAUSCH Technology GmbH, Würzburg, Germany · Modeling and Simulation, University of Würzburg, Würzburg, Germany

Energy-Efficient ML Time Series Forecasting Forecasting Benchmarks Time Series Transformers

May 10, 2026cs.LG

Spectral Transformer Neural Processes

Time series, spatial data, and images are natural applications of Neural Processes. However, when such data exhibit strong periodicity and quasi-periodicity, existing methods often suffer from underfitting and generalise poorly beyond the training distribution. In this work, we propose Spectral Transformer Neural Processes (STNPs), a frequency-aware extension of Transformer Neural Processes (TNPs). STNPs introduce a Spectral Aggregator that estimates an empirical context spectrum, compresses it into a spectral mixture, samples task-adaptive spectral features, and concatenates them with time-domain embeddings, thereby injecting a spectral-mixture-kernel bias into TNPs. This design reshapes the similarity geometry, allowing inputs that are distant in Euclidean space to remain close in an induced periodic manifold while enhancing time-frequency interactions. Extensive experiments on synthetic regression tasks, real-world time-series datasets, and an image dataset demonstrate that STNPs consistently improve predictive performance over existing baselines, extending Neural Processes beyond translation equivariance towards effective modelling of periodicity and quasi-periodicity.

Xianhe Chen, Hao Chen, Yingzhen Li

University of Cambridge · Tencent · Imperial College London

Transformer Neural Processes Frequency-Domain Feature Learning Time Series Forecasting Time Series Transformers

May 10, 2026cs.CV

SSDA: Bridging Spectral and Structural Gaps via Dual Adaptation for Vision-Based Time Series Forecasting

Large vision models (LVMs) have recently proven to be surprisingly effective time series forecasters, simply by rendering temporal data as images. This success, how ever, rests on a largely unexamined premise: the rendered time series images are sufficiently close to natural images for knowledge in pre-trained models to transfer effectively. We argue that two gaps still remain, i.e., spectral and structural gaps, fundamentally limiting the potential of LVMs for time series forecasting. Spectrally, we systematically reveal that rendered time series images exhibit a markedly shallower power spectrum than the natural images LVMs are pre-trained to recognize. Structurally, reshaping 1D temporal sequences into 2D grids fabricates spurious spatial adjacencies while severing genuine temporal continuities, misleading the spatial inductive biases of pre-trained LVMs. To bridge these gaps, we propose SSDA, a dual-branch network that spectrally and structurally adapts to unlock the full potential of LVMs for time series forecasting. At the data level, a Spectral Magnitude Aligner (SMA) applies 2D FFT to selectively enhance the magnitude spectrum toward natural-image statistics while preserving phase. At the model level, a Structural-Guided Low-Rank Adaptation (SG-LoRA) injects position-aware temporal encodings into patch embeddings and adapts at tention via low-rank updates. The two branches are further adaptively fused to produce the final forecast. Extensive experiments on seven real-world benchmarks demonstrate that SSDA consistently outperforms strong LVM- and LLM-based baselines under both full-shot and few-shot settings. Code is publicly available at https://anonymous.4open.science/r/SSDA-8C5B.

Mingrui Zhang, Hanchen Yang, Wengen Li +4

Domain Adaptation Time Series Forecasting Vision Foundation Model Adaptation Low-Rank Adaptation

May 9, 2026cs.LG

TSNN: A Non-parametric and Interpretable Framework for Traffic Time Series Forecasting

Although many complex models were proposed to analyze time series data, some studies have demonstrated remarkable performance with simpler structures. A recent study proposed a non-parametric framework for 3D point cloud classification, which has the potential to be adapted for time series forecasting and enable interpretability. Inspired by the previous works, we present TSNN, a non-parametric and interpretable framework for traffic time series forecasting. TSNN consists of multiple layers that decouple the time series by matching the entries in a memory bank, where the memory bank is constructed using a similar matching process within the training set. It leverages the periodicity in traffic data to enhance forecasting accuracy while maintaining a simple model architecture. The proposed model operates without trainable parameters, preserving its inherent interpretability. In the experiments, TSNN achieves competitive performance compared to the typical deep learning models in four real-world traffic flow datasets. We also visualize the decoupling process to show the effectiveness of the components. Finally, we demonstrate the interpretability of the model and illustrate the contribution of each time step within the memory bank.

Bowen Liu, Haijian Lai, Chan-Tong Lam +4

Faculty of Applied Sciences, Macao Polytechnic University, Macao SAR, China

Time Series Forecasting Traffic Forecasting

May 9, 2026q-fin.CP

A Market-Rule-Informed Neural Network for Efficient Imbalance Electricity Price Forecasting

Accurate and efficient imbalance electricity price forecasting is critical for industrial energy trading systems, especially as battery assets and automated bidding pipelines increasingly participate in balancing markets. However, real-time forecasting is complicated by nonlinear market-rule-based price formation, heterogeneous input signals, and incomplete data availability caused by communication delays, publication lags, and measurement outages. This paper proposes a market-rule-informed neural forecasting framework that embeds imbalance price formation rules into the latent space of an expressive neural network. The proposed framework preserves raw signal information while exploiting transparent market-rule priors. We further analyze operational robustness by removing price-component information and characterize how forecasting performance scales with input length and forecasting horizon. Experimental results show that the proposed model achieves competitive forecasting performance with substantially fewer trainable parameters and shorter training time than generic deep learning baselines. Experimental results show that the proposed model achieves competitive forecasting performance with substantially fewer trainable parameters and shorter training time than generic deep learning baselines, demonstrating that market-rule priors and expressive neural networks should be jointly used for accurate and computationally sustainable forecasting in industrial energy trading applications. The implementation is publicly available at https://runyao-yu.github.io/MRINN/.

Runyao Yu, Julia Lin, Derek W. Bunn +6

Delft University of Technology · Austrian Institute of Technology · London Business School +2

Electricity Price Forecasting Time Series Forecasting Power Systems

May 9, 2026physics.ao-ph

Visibility nowcasting in South Korea: a machine learning approach to class imbalance and distribution shift

Atmospheric visibility is a critical variable for transportation safety and air quality management, however, accurate prediction remains challenging due to the complex interactions between meteorological conditions and air pollutants, as well as the rarity of low-visibility events. This study introduces a machine learning framework to nowcast visibility in six major South Korean cities. To handle the imbalance in the 2018-2020 training data, we applied the Synthetic Minority Over-sampling Technique with Nominal and Continuous (SMOTENC) and Conditional Tabular Generative Adversarial Network (CTGAN). An ensemble approach combining machine learning and deep learning models was then used and evaluated on a 2021 test dataset. The results revealed a marked decline in predictive performance in the test set compared to the cross-validation phase. This degradation was attributed to a distributional shift between training and testing periods, which was quantitatively confirmed by measuring the Wasserstein distance of the most influential feature identified by SHAP analysis. In general, this study presents a methodology that aims to simultaneously address the dual challenges of data imbalance and temporal distributional shifts, and emphasizes the necessity of accounting for evolving external environmental factors when implementing nowcasting models on time-series data.

Bong Gyun Shin, Chan Sik Lee, Hyesun Suh

Department of AI Big Data, Daejin University, 1007 Hoguk-ro,2026 Pocheon-si, Gyeonggi-do, 11159, Republic of Korea. · Department of Statistics and Actuarial Science, Soongsil University, 50 Sadang-ro, Dongjak-gu, Seoul, 06978, Republic of Korea. · College of Artificial Intelligence Convergence, Daejin University, 1007 Hoguk-ro, Pocheon-si, Gyeonggi-do, 11159, Republic of Korea.

Distribution Shift Robustness Time Series Forecasting

May 9, 2026cs.CL

A Quantum Inspired Variational Kernel and Explainable AI Framework for Cross Region Solar and Wind Energy Forecasting

Reliable short horizon forecasting of solar and wind generation is a structural prerequisite of any modern power system yet most published forecasters are tuned and evaluated on a single climatic regime and most algorithmic novelty has been concentrated either on classical recurrent networks or on monolithic foundation models that combine forecasting and explanation We develop a four stage hybrid framework that separates these concerns The first stage acquires hourly generation irradiance and surface weather records through public application programming interfaces The second stage trains three classical baselines autoregressive integrated moving average gradient boosted regression trees and a two layer long short term memory network and produces a strong point forecast together with a residual error series The third stage corrects the residual through a quantum inspired variational kernel built on a six qubit hardware efficient ansatz with three repeated entangling layers The fourth stage uses generative artificial intelligence strictly as an explainability layer that reads the measured benchmark numbers and produces a structured natural language interpretation Across three regions drawn from open public archives Iberian solar North Sea wind and a mixed Texas trace the proposed configuration stays within one percentage point of the strongest classical baseline on the in domain forecasting task and the quantum inspired kernel separates calm and stormy weather regimes with a Fisher discriminant ratio approximately fifteen fold higher than a tuned radial basis kernel

Pavan Manjunath, Thomas Prufer

Independent Research Scholar, Germany

Time Series Forecasting Quantum-Inspired ML Solar Power Forecasting Quantum Kernel Methods Spatiotemporal Forecasting Wind Power Forecasting+1

May 9, 2026cs.LG

TailedTS: Benchmark Dataset for Heavy-Tailed Time Series Prediction and Periodicity Quantification

We present TailedTS, a large-scale benchmark dataset derived from Wikipedia hourly page view observations throughout 2024, specifically designed to test time series forecasting models under heavy-tailed, zero-inflated, and non-Gaussian conditions. The dataset comprises approximately 24.69 billion data points spanning roughly 3 million unique Wikipedia pages per month, stored in high-efficiency Apache Parquet format. Wikipedia traffic follows a pronounced power-law distribution where roughly 5% of pages account for over 70% of total page views, creating a natural and rigorous testbed for model robustness against extreme volatility that are absent from or underrepresented in existing benchmarks such as M4, M5, and UCI electricity datasets. TailedTS enables several research tasks. First, we introduce a periodicity quantification framework based on sparse autoregression with sparsity and non-negativity constraints, revealing that frequently-viewed pages exhibit significantly weaker periodic structure than their less-viewed counterparts, showing direct implications for server allocation and traffic forecasting on large digital platforms. Second, we provide standardized prediction benchmarks evaluated under a suite of non-Gaussian loss functions, including

\ell_1

-norm, Huber, quantile, and

\ell_p

-norm losses, demonstrating that standard Gaussian-based estimators degrade substantially on high-volume page categories, while robust alternatives provide consistent gains across all traffic scales. TailedTS is publicly available at https://doi.org/10.5281/zenodo.17070469.

Xinyu Chen, HanQin Cai, Lijun Ding +1

University of Central Florida Orlando, FL 32816 · Massachusetts Institute of Technology Cambridge, MA 02139

Time Series Forecasting Heavy-Tailed Noise Forecasting Benchmarks Heavy-Tailed Distributions

May 9, 2026cs.LG

RareCP: Regime-Aware Retrieval for Efficient Conformal Prediction

Recent advances in uncertainty quantification for time series forecasting show that conformal prediction can provide reliable prediction intervals, yet standard conformal methods are often inefficient under temporal dependence, drift, and heterogeneous error behavior. Existing methods typically either update miscoverage rates over time or learn unconstrained calibration weights, without explicitly separating two central sources of nonstationarity: smoothly drifting error distributions and co-existing distinct error regimes. We introduce RareCP, a regime-aware retrieval method for adaptive conformal time series prediction. RareCP learns local calibration representations through a mixture of cosine-attention experts that each capture distinct error regimes, while a compact hypernetwork adapts the kernel parameters to track temporal drift. Given a new forecasting context, RareCP retrieves the top-k most relevant calibration examples, assigns similarity weights, and forms a weighted conformal quantile over their signed residuals, yielding asymmetric prediction intervals. The adaptive kernel is trained using a smooth interval score objective, with a parameter-space anchor to a lightweight teacher kernel to preserve stable local representations. On the GIFT-Eval benchmark, RareCP improves interval efficiency over recent conformal baselines and foundation model uncertainty estimates while maintaining empirical coverage. Ablations confirm that regime-specific experts, drift-adaptive kernels, sparse retrieval, and teacher anchoring each contribute to the final performance.

Manuel Heurich, Maximilian Granz, Tim Landgraf

Institute for Computer Science Freie Universität Berlin Arnimallee 7 14195 Berlin

Weighted Conformal Prediction Time Series Forecasting Conformal Prediction Adaptive Conformal Inference Regression Prediction Intervals

May 9, 2026cs.LG

LEAF: A Living Benchmark for Event-Augmented Forecasting

Large Language Models (LLMs) are increasingly applied to forecasting. To evaluate this capability while mitigating pre-training data contamination, several living benchmarks have been proposed. However, existing benchmarks either lack the multidimensional events essential for accurate forecasting due to data scarcity, or focus on relatively closed environments. To assess the predictive capabilities of LLMs in complex, real-world scenarios, we propose LEAF, the first living benchmark for event-augmented forecasting tasks, including future event probabilities, trend and time series forecasting. LEAF utilizes a recursive retrieval agent system paired with dual-agent cross-validation to provide comprehensive and relevant auxiliary text for forecasting. Evaluating state-of-the-art proprietary and open-weight LLMs, we find that these models can leverage signals extracted from complex events to enhance predictive performance. In the stock domain, we find that LLMs achieve better performance on equities they confidently identify as more predictable. Furthermore, the events demonstrate a strong correlation with the target equities. To this end, LEAF provides a necessary, dynamically updating testbed to continuously track and drive progress in event-driven forecasting tasks.

Mingtian Tan, Mihir Parmar, Palash Goyal +5

Google · University of Virginia

Financial Forecasting Time Series Forecasting Forecasting Benchmarks Probabilistic Forecasting LLM-Based Time Series Forecasting

May 9, 2026cs.LG

Reasoning-Aware Training for Time Series Forecasting

Time Series Foundation Models (TSFMs) excel at numerical forecasting but operate as black boxes lacking qualitative reasoning. Conversely, applying LLMs directly to temporal data introduces a modality gap: text tokenizers fragment continuous numerical values, degrading mathematical relationships and exploding sequence lengths, leading to computational overhead. To resolve this, we introduce STRIDE (Strategic Time-series Reasoning Injected via Distilled Embeddings), a novel framework natively integrating LLM reasoning into the continuous embedding space of TSFMs. Instead of discrete tokens, STRIDE distills reasoning traces into a lightweight LLM, dynamically projecting its mean-pooled hidden states as a cross-modal prior into the target numerical encoder. The architecture is jointly optimized using cross-entropy and quantile losses. Evaluations demonstrate STRIDE establishes state-of-the-art numerical forecasting on GIFT-Eval (0.674 MASE, 0.454 CRPS) compared to TSFMs and exhibits superior in-domain and out-of-domain numerical as well as reasoning performance on TFRBench. Specifically, STRIDE acts as a plug-and-play enhancement, consistently improving diverse TSFMs (e.g., Chronos-2, Timer-S1) across various LLM configurations. Thus, injecting semantic reasoning as a continuous prior equips TSFMs with human-interpretable reasoning while fundamentally improving predictive accuracy.

Md Atik Ahamed, Mihir Parmar, Palash Goyal +4

1Google · University of Kentucky

Time Series Reasoning Time Series Forecasting LLM-Based Time Series Forecasting Time-Series Foundation Models Probabilistic Time Series Forecasting

May 8, 2026cs.LG

STEPS: A Temporal Smooth Error Propagation Solver on the Manifolds for Test-Time Adaptation in Time Series Forecasting

Test-Time Adaptation (TTA) aims to improve time series forecasting under distribution shifts by using limited observations revealed during inference. However, forecasting TTA must operate in a source-free online setting, where the adaptation signal is short, temporally correlated, and potentially noisy. Existing methods can therefore suffer from weak identifiability, error accumulation, and unstable long-horizon corrections when the revealed prefix is sparse or contaminated. To address these issues, we propose STEPS, a Smooth Temporal Error Propagation Solver for TTA in time-series forecasting. STEPS reformulates forecasting TTA as a Dirichlet Boundary Value Problem on a temporal manifold, where the revealed prefix error serves as the boundary condition for the unknown future error field. Then, STEPS solves a smooth and bounded correction field in prediction space: a Local Solver propagates prefix errors under temporal smoothness, a Global Solver retrieves stable cross-window error memory and Spatiotemporal Manifold Fusion (SMF) integrates both solutions into the final correction. Across six standard benchmarks and four frozen backbones, STEPS achieves an average relative MSE reduction of 26.82% over the zero-shot backbone, exceeding the strongest compared TTA baseline by 12.77%. Additional sparse prefix and contamination tests confirm the robustness of STEPS under limited and noisy prefixes.

Jiaqi Liu, Yifan Ouyang, Zhifei Song +2

School of Artificial Intelligence and Robotics, Xiamen University Malaysia · S.M.A.R.T. NEXUS Centre of Excellence, Xiamen University Malaysia Sepang, Selangor 43900, Malaysia

Source-Free Domain Adaptation Test-Time Adaptation Time Series Forecasting Non-Stationary Time Series Forecasting Temporal Distribution Shift

May 8, 2026cs.LG

NPMixer: Hierarchical Neighboring Patch Mixing for Time Series Forecasting

Multivariate time series forecasting remains a challenge due to the complexity of local temporal dynamics and global dependencies across multiple variables. In this paper, we propose \textbf{N}eighboring \textbf{P}atching \textbf{Mixer} (\textbf{NPMixer}), a hierarchical architecture featuring a Learnable Stationary Wavelet Transform that adaptively learns filter coefficients to decompose signals into trend and detail components in a data-dependent manner. Our framework introduces a Neighboring Mixer Block that captures local temporal dynamics through a series of hierarchical MLP layers operating on non-overlapping patches. Specifically, the mixer block utilizes MLPs to learn temporal patterns within and across these patches, expanding the receptive field to capture multi-scale dependencies. A Channel-Mixing Encoder is applied to high-frequency components to learn channel correlations while preserving the stability of the underlying global trend. Extensive experiments on seven benchmark datasets demonstrate that NPMixer consistently outperforms state-of-the-art models, achieving better performance in 20 out of 28 (

71.4\%

) evaluated experimental setups for MSE.

Jung Min Choi, Vijaya Krishna Yalavarthi, Lars Schmidt-Thieme

1ISMLL, University of Hildesheim, VWFS Data Analytics Research Center (VWFS-DARC), Hildesheim, Germany.

Multivariate Time Series Forecasting Time Series Forecasting Wavelet Methods Time Series Decomposition Multiscale Time-Series Modeling

May 8, 2026cs.LG

What If We Let Forecasting Forget? A Sparse Bottleneck for Cross-Variable Dependencies

Multivariate time series forecasting is critical in many real-world systems, and thus modeling cross-channel dependencies is essential. Although existing methods improve overall accuracy by enhancing representations and cross-channel interactions, it remains challenging to reliably capture inter-variable dependencies under specific conditions. We observe that dependencies in real data are often state-dependent and noisy; in such cases, dense interactions can amplify spurious correlations and lead to representation over-smoothing, which may yield unreliable predictions in certain scenarios. Motivated by this, we propose MS-FLOW, a sparse-bottleneck framework that explicitly models inter-variable interaction as capacity-limited information flow. Specifically, MS-FLOW replaces fully connected communication with selective sparse routing, retaining only a few critical dependency paths and injecting cross-variable signals under a strict communication budget, thereby suppressing redundant connections and spurious-correlation propagation. Extensive experiments demonstrate that MS-FLOW learns more reliable multivariate correlations, achieving state-of-the-art forecasting accuracy on 12 real-world benchmarks while producing fewer yet more reliable dependencies, shifting multivariate forecasting from "more interaction" to "more effective interaction".

Fan Zhang, Shiming Fan, Hua Wang

Shandong Technology and Business University, Yantai, Shandong, China · Ludong University, Yantai, Shandong, China

Multivariate Time Series Forecasting Feature Interaction Modeling Time Series Forecasting Spurious Correlation Robustness

May 8, 2026cs.LG

Exactness Matters for Physical Rule Enforcement

Autoregressive scientific forecasters often enforce physical or structural constraints by repairing each predicted state before feeding it back into the model. However, it remains unclear when stronger physical rule enforcement becomes reliable and when it becomes a source of distribution shift. We study this question through operator exactness, meaning whether the repair map is the identity on the target manifold and is aligned with the target geometry. We compare raw forecasting, post hoc repair, and in-loop repair across periodic incompressible Navier--Stokes, non-periodic CFDBench flows, and a hierarchical-forecasting support task. In the exact periodic regime, Fourier projection substantially improves rollout accuracy. On the NS-128 benchmark, a strong Raw-FNO has a final-step rollout MSE at horizon 100 of

(9.390 \pm 6.290)\times 10^{-5}

, and post hoc and in-loop projection reduce it to

(1.130 \pm 0.165)\times 10^{-6}

and

(5.370 \pm 0.113)\times 10^{-7}

. However, once an exact projection is unavailable and only approximate boundary-preserving cleanup is available, the ordering changes. Across cavity, tube, dam, and cylinder flow, stronger Poisson-based cleanup can reduce divergence while worsening rollout error; target-distortion MSE predicts this harm far better than a linear-system residual. Controlled mismatch, screened cleanup, adaptive gating, and external-backbone checks show that the best approximate-regime operating point can be raw or near-identity. Hierarchical forecasting gives the same broader pattern. Exact forecast reconciliation is a stable baseline, whereas blended top-down repair, a validation-tuned interpolation toward historical-proportion top-down reconciliation, is dataset-dependent. Thus, constraint enforcement should be benchmarked by operator--data alignment before enforcement strength.

Bum Jun Kim

The University of Tokyo, Japan

Time Series Forecasting Spatiotemporal Forecasting Computational Fluid Dynamics

May 8, 2026cs.LG

Don't Learn the Shape: Forecasting Periodic Time Series by Rank-1 Decomposition

How few parameters do we really need to forecast a periodic time series? An hourly electricity series, reshaped as a 24-row matrix with one column per day, is approximately rank-1: a daily shape modulated by a daily level (median centered rank-1 energy 0.82 on GIFT-Eval). Should we learn the shape? Smoothing, shrinkage, and low-rank fits all seem like obvious upgrades over the simple average of the last K=2 cycles. On all 97 GIFT-Eval configurations, we tested 8 such alternatives (e.g., Fourier, EWMA, James-Stein, rank-r SVD): none significantly beats the frozen baseline under Holm correction; two are significantly worse. The resulting method, FLAIR, is (a) Effective: matches PatchTST on aggregate GIFT-Eval (relMASE 0.838 vs 0.849); (b) Compact: 28 scalars for hourly, 57 for weekly; (c) Fast: 22 minutes on one CPU core of a MacBook Pro; (d) Closed-form & Hands-Off: one SVD per period candidate, GCV-averaged Ridge, no GPU, no pre-training, no per-task tuning. In the high-rank-1, many-cycle regime, extra flexibility is estimation noise.

Takato Honda

Mellon Inc.

Low-Rank Matrix Decomposition Time Series Forecasting Low-Rank Approximation Time Series Decomposition

May 7, 2026cs.LG

Dual-Scale Temporal Fusion Reveals Structured Predictability in Subseasonal-to-Seasonal Temperature Prediction

Subseasonal-to-seasonal (S2S) temperature forecasts, spanning several weeks to a few months, are critically needed in agriculture practice, energy planning, and extreme-weather induced risk management, yet their reliability varies substantially across seasons and regions. Forecast skill is often attributed primarily to lead time, but this perspective does not fully explain the spatiotemporal patterns of predictability. Here we show that S2S predictability is organized across interacting temporal components, spatial heterogeneity, and large-scale pattern coherence, and that this structure can be explicitly characterized and exploited. We develop a dual-scale learning framework that separates calendar-aligned historical climate context from lead-time matched recent weather evolution, combining them through spatially adaptive fusion to enable stable temperature forecasts across the 30 to 90-day window. The learned fusion weights reveal that the balance between these two temporal scales shifts systematically with season and geography: during winter, interannual context dominates over high latitudes and complex terrain where forecast is the most difficult, while summer predictions reflect a more balanced temporal contribution across the domain. This spatially explicit reorganization of predictability, rather than simple lead-time decay, emerges as the primary determinant of forecast skill within the subseasonal window. Topology-aware structural constraints further improve spatial coherence of predicted temperature fields, stabilizing large-scale pattern organization particularly over complex terrain. These results reframe S2S predictability as a structured, multi-scale phenomenon, providing a more interpretable foundation for improving forecast systems and informing their use in practice.

Elnaz Bashir, Jiali Wang, Lin Yan

Department of Computer Science, Iowa State University, Ames, IA 50011, USA · Environmental Science Division, Argonne National Laboratory, Lemont, IL 60439, USA

Time Series Forecasting Multi-Scale Feature Fusion Multiscale Time-Series Modeling Weather Forecasting