Time Series Forecasting

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Latest papers 667

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

Jun 27, 2026

MACROCAST: A Vintage-Consistent Time Series Foundation Model for Real-Time Macroeconomic Forecasting

We introduce MACROCAST, a lightweight Time Series Foundation Model (TSFM) for real-time macroeconomic forecasting. Existing TSFMs suffer from data leakage in two forms: temporal contamination, as the model may have seen the realized values of the series it forecasts, and revision bias, as training on fully revised data diverges from the preliminary, vintage-specific releases available to real-time forecasters. MACROCAST is, to our knowledge, the first TSFM that rules out both forms of leakage entirely: at no stage of training is the model exposed to information that would not have been available to a forecaster in real time. We train MACROCAST first on purely synthetic time series in approximately one GPU-day and then fine-tune it on synthetic time series drawn from Bayesian VARs, dynamic factor models, and ARIMA specifications estimated on vintage-specific ALFRED data. Because pretraining uses only simulated data and fine-tuning uses only real-time vintages, no observed future or revised value ever enters the model; each fine-tuning run takes nine minutes. Evaluated on the FRED-MD database in a genuine real-time out-of-sample exercise, MACROCAST improves on the AR(1) benchmark for roughly 80% of series-horizon pairs, matches or surpasses Chronos-2 -- the strongest currently available TSFM -- and outperforms the Bayesian VAR and dynamic factor model benchmarks, all in a data-leakage-free manner.

Andrea Carriero, Davide Pettenuzzo, Shubhranshu Shekhar

School of Economics and Finance, Queen Mary University of London. · School of Business and Economics, Brandeis University.

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

Jun 26, 2026

Improving Coherence in Hierarchical Time Series Forecasting using Structured Temporal Fusion

In many real-world applications, such as retail sales, energy usage, and supply chain planning, forecasting is performed across hierarchical structures. These structures often represent aggregations (e.g., products to categories to regions), where forecasts must not only be accurate but also coherent, meaning that lower-level predictions sum correctly to higher-level forecasts. Traditional statistical methods, such as Bottom-Up and MinT, enforce coherence through post-processing but fail to model complex nonlinear temporal dependencies and covariate interactions. We propose Hierarchical Temporal Fusion (HTF), a novel extension of the Temporal Fusion Transformer (TFT) that integrates structured hierarchical embeddings with a coherence-aware loss function to ensure consistent forecasts across all levels of a hierarchy. Rather than applying reconciliation after forecasting, HTF embeds coherence directly into the training objective. The coherence loss penalizes the difference between aggregated child forecasts and their corresponding parent forecasts during training, enabling the model to learn both temporal dynamics and structural consistency simultaneously. We evaluate HTF on two publicly available benchmark datasets: the M5 Walmart forecasting dataset and a publicly available hierarchical energy consumption dataset. Results demonstrate that HTF substantially reduces forecast incoherence while improving forecasting accuracy compared with classical reconciliation methods and deep learning baselines. In addition, attention visualization and embedding analysis provide insight into how temporal and structural information contribute to hierarchical forecasting performance.

Ruchi Pakhle

Data and AI · Red Hat

Time Series Forecasting Time Series Transformers

Jun 26, 2026

NIVA: A Multimodal Foundation Model for Actionable Earth System Intelligence

Recent advances in AI-driven weather and climate modeling have improved forecast skill while reducing computational cost. However, existing data-driven approaches are limited in their ability to model coupled Earth system dynamics, which is required for extending predictability beyond the ~2-week horizon. To address this, we introduce NIVA, a multimodal foundation model designed to learn unified representations across Earth system components. While the full framework targets atmosphere, ocean, ice, and land interactions, we focus here on a two-modality setting (ocean and atmosphere) as a controlled proof of concept to evaluate whether foundation models can learn coupled dynamics. Trained on large-scale Earth system simulations, NIVA learns physically meaningful cross-modal structure, providing a foundation for subseasonal-to-seasonal prediction. As initial validation, we show that NIVA captures key modes of climate variability through accurate prediction of major climate indices.

Anisha Pal, Aodhan Sweeney, Kyle Heyblom +1

Independent Researcher · Work done while at Planette AI · Planette AI, USA.

Climate Science Multimodal Pretraining Time Series Forecasting Climate Modeling Time-Series Foundation Models

Jun 26, 2026

The Remittance Blueprint: Data-driven Intelligence for Sri Lanka

This study analyzes Sri Lankan migration and remittances over 32 years (1994-2025). Using a 384-month harmonized dataset, we apply exploratory data analysis, stationarity corrected time-series modeling (ADF, Johansen, VAR/VECM), and supervised learning. Results reveal remittance inflows are primarily driven by external macroeconomic variables, specifically exchange rate dynamics and global oil prices, rather than domestic indicators. Impulse response analysis confirms the asymmetric impact of currency depreciation and oil price shocks. Predictively, multivariate machine learning models outperform traditional univariate approaches; Ridge Regression achieves a 73.8% accuracy improvement over SARIMA (Annualized RMSE: USD 494.8 Mn). The optimized framework projects 2026 remittances at USD 9,001 million under stable conditions. These findings highlight the structural dependence of remittances on global economies, emphasizing the need for robust exchange rate policies, skilled migration, and formal financial channels to enhance long-term economic resilience.

Dhinanjaya Fernando, Dinura Ginige, Kalana Lakshan +6

Dept. of Computer Science & Engineering, University of Moratuwa, Sri Lanka.

Multivariate Time Series Forecasting Time Series Forecasting

Jun 26, 2026

GNBAN: Graph Neural Basis Attention Networks for Long-Horizon Forecasting over Large Entity Sets

Demand forecasting at the bottom of a retail hierarchy requires predicting tens of thousands of correlated long-horizon series across products, stores, and regions. Modern systems must scale across massive catalogs, capture shared demand dynamics, and remain interpretable enough to be trusted. Classical statistical methods need a separate model per series and are hard to manage at scale; deep autoregressive models struggle as the joint state grows to tens of thousands of dimensions; and recent graph-based forecasters, while capturing cross-entity dependencies, often produce opaque long-horizon forecasts. We propose GNBAN (Graph Neural Basis Attention Network), an end-to-end architecture combining heterogeneous graph representation learning with an interpretable basis-decomposition head. Retail data are represented directly as a heterogeneous graph derived from the relational schema, so a single model serves the entire catalog. Rather than predicting the horizon directly, GNBAN decomposes each forecast into trend, seasonal, and generic components. Its key innovation is a per-basis attention mechanism: each basis function keeps its own learnable query and retrieves information independently from the entity's historical neighborhood, letting different bases specialize to distinct temporal patterns while preserving interpretability. On two large-scale benchmarks, M5 Walmart and Favorita Grocery Sales, evaluated under matched protocols, GNBAN improves volume-weighted WRMSSE by roughly 4-5% over a matched graph baseline. Qualitative analysis shows the learned decomposition exposes trend, seasonal, and residual demand drivers without post-hoc explanation methods. These results demonstrate that scalable relational forecasting and interpretable forecast decomposition can be achieved together in a unified graph-based framework.

Janak M. Patel, Anirudh Deodhar, Dagnachew Birru

Phi Labs, Quantiphi Marlborough, MA 01752, USA

Multivariate Time Series Forecasting Long-Term Time Series Forecasting Heterogeneous GNNs Time Series Forecasting Time Series Decomposition

Jun 26, 2026

The Simulacrum: Decision-Theoretic Pretraining for Near-Optimal Time-Series Forecasting and Inference

We introduce a neural network-based framework for learning time series estimators through a process we term decision-theoretic pretraining. Analysts specify a generative world, a distribution over data-generating processes, and a target decision objective. A neural network trained on stratified simulations from this world approximates the corresponding optimal decision rule, yielding a neural estimator that provides forecasts, parameter estimates, predictive intervals, or model-selection for zero-shot inference on previously unseen time series. The joint specification of the generative world and objective enables the estimators to directly approximate process-level, finite-sample properties: near-optimal risk, bias control, minimax performance, and uniform calibration. Our experiments demonstrate that these neural estimators can outperform traditional baselines such as maximum likelihood estimation and model selection via AICc, for the same model structural model classes. Furthermore, even when trained purely on simulations of structural models, they achieve competitive or state-of-the-art forecasting accuracy on major real-world benchmarks, compared with statistical, neural or large pre-trained models. We illustrate the framework by addressing two longstanding challenges: finite-sample bias and miscalibration in AR(p) models, and the forecast combination puzzle. These applications highlight the approach's main advantage: its ability to approximate solutions to analytically intractable or computationally prohibitive time series problems, including complex structural equations or optimality criteria. Ultimately, by enabling explicit control over decision-theoretic trade-offs, the framework equips analysts with highly efficient estimation tools tailored to their specific analytical needs.

Pablo Montero-Manso, Marcel Scharth

University of Sydney Business School, Australia

Simulation-Based Inference Zero-Shot Time Series Forecasting Time Series Forecasting Probabilistic Time Series Forecasting

Jun 26, 2026

Deployment-Side Adaptiveness in Multi-Horizon Volatility Forecasting

In financial forecasting, predictive performance depends not only on which model is trained, but also on how the trained model is deployed. We study this issue in multi-horizon volatility forecasting. Our starting point is that a trained multi-output (MIMO) forecaster does not define a single deployable predictor: by changing the inference-time rollout rule, the same trained model induces a family of forecasts with different accuracy and cost profiles. Across 20 stock-volatility series, three forecast horizons, and architectures ranging from linear models to PatchTST, we find that non-default rollout rules often improve over standard MIMO deployment. However, the best fixed rule varies substantially across architectures and horizons, making any single static replacement unreliable. We therefore evaluate validation-based deployment policies over the induced rule family. Under the primary MSE objective, validation-selected singletons provide a low-cost improvement over default MIMO, while small rule subsets recover much of the benefit of larger ensembles at substantially lower inference cost. We also find that policy rankings are metric-sensitive: MSE-selected policies do not transfer uniformly to QLIKE, a finance-standard volatility loss. These results show that inference-time deployment is a meaningful source of adaptiveness in financial forecasting, and that trained volatility forecasters should be evaluated not only by their architecture, but also by their deployment policy.

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

The University of Bristol Bristol, UK

Financial Forecasting Time Series Forecasting Financial Time Series Finance

Jun 25, 2026

Global Explanations for Multivariate Time Series Forecasting Models via $K$ -Order Markov Approximations

While many explainable AI (XAI) methods have been proposed, most are not designed for time-series forecasting models and often rely on the implicit assumption that timestamp features are independent. This assumption ignores the fundamental property of temporal dependence and can lead to explanations that violate the sequential and causal structure of the data. We introduce \textsc{KARMA}, a method for explaining time-series predictors by constructing a Markov surrogate model that captures the temporal dependencies learned by the predictor. Our approach revolves around three main aspects: identifying the minimal history length

K

that is predictively sufficient for the model, estimating the best-fitting

K

-order Markov transition kernel from the discretized history space, and a five-level global explanation hierarchy that can be derived from the Markov transition kernel, which we illustrate using real-world weather data (Beijing PM 2.5). We also certify using complex synthetic data with known true causal edges that KARMA (i) recovers the data causal structure as learned by the model via a controlled experiment and (ii) identifies temporal dependencies better than established attribution methods such as TimeSHAP.

Amadeo Tunyi

XITASO GmbH Austraße 35, 86153 Augsburg, Germany

Multivariate Time Series Forecasting Surrogate Modeling Explainable Time Series Forecasting Markov Models Time Series Forecasting Causal Interpretability

Jun 25, 2026

How Good Can Linear Models Be for Time-Series Forecasting?

Time-series forecasting research has been moving steadily toward larger architectures, from specialized transformers to general-purpose foundation models, on the assumption that capacity is what unlocks accuracy. We take the opposite position: most of the gap can be closed at far lower cost by tuning preprocessing rather than scaling models. We use Ridge regression as the testbed, since it has a closed-form solution and interpretable weights, which let the optimal hyperparameters be read off the search directly. We search over context length, local normalization, regularization, and augmentation on eight standard benchmarks and find three patterns. (1) Optimal lookback is strongly series-specific and often non-monotonic in forecast horizon, with fitted power-law exponents ranging from

+0.46

on ETTm2 to

-0.19

on Exchange and Traffic, challenging the convention that longer horizons need longer history. (2) Normalizing over a learned trailing fraction of the context, rather than its entirety, is almost universally preferred. (3) Series within the same dataset often disagree on hyperparameters; the optimal degree of cross-series sharing varies from fully shared to fully per-series. The resulting models beat prior linear forecasters on most dataset-horizon entries and exceed Transformer, MLP, and CNN baselines on six of eight benchmarks. The optimized hyperparameters also serve as a diagnostic on the data itself, revealing structures that larger models absorb silently into their learned parameters. We provide an accompanying interactive online demonstration and the code at https://sakanaai.github.io/SearchCast/.

Lang Huang, Jinglue Xu, Luke Darlow

1Sakana AI, Tokyo, Japan · 2National Institute of Informatics, Japan

Time Series Forecasting Hyperparameter Optimization

Jun 25, 2026

PMDformer: Patch-Mean Decoupling Information Transformer for Long-term Forecasting

Long-term time series forecasting (LTSF) plays a crucial role in fields such as energy management, finance, and traffic prediction. Transformer-based models have adopted patch-based strategies to capture long-range dependencies, but accurately modeling shape similarities across patches and variables remains challenging due to scale differences. To address this, we introduce patch-mean decoupling (PMD), which separates the trend and residual shape information by subtracting the mean of each patch, preserving the original structure and ensuring that the attention mechanism captures true shape similarities. Futhermore, to more effectively model long-range dependencies and capture cross-variable relationships, we propose Trend Restoration Attention (TRA) and Proximal Variable Attention (PVA). The former module reintegrates the decoupled trend from PMD while calculating attention output. And the latter focuses cross-variable attention on the most relevant, recent time segments to avoid overfitting on outdated correlations. Combining these components, we propose PMDformer, a model designed to effectively capture shape similarity in long-term forecasting scenarios. Extensive experiments indicate that PMDformer outperforms existing state-of-the-art methods in stability and accuracy across multiple LTSF benchmarks. The code is available at https://github.com/aohu1105/PMDformer.

Ao Hu, Liangjian Wen, Jiang Duan +7

Southwestern University of Finance and Economics · Artificial Intelligence and Digital Finance Key Laboratory of Sichuan Province · Chengdu Everimaging Science and Technology Co., Ltd. +4

Multivariate Time Series Forecasting Long-Term Time Series Forecasting Cross-Attention Time Series Forecasting Time Series Transformers

Jun 25, 2026

Multipath Adaptive Gated Bottleneck Latent ODE with Raman Data Fusion for Cell Culture Process Forecasting

Mammalian cell-culture processes underpin the manufacture of many biopharmaceuticals, yet keeping a run on track is hard: critical process parameters drift over days, and an off-specification trend is often confirmed too late to intervene. Early-stage, multi-day forecasts could enable timely adjustment of feeding, sampling, and control, but bioprocess forecasting is challenging because measurements are sparse and irregularly sampled, operating conditions are heterogeneous across cell lines and media, and runs with near-identical early behaviour can diverge into different futures. We propose an adaptive framework combining a Gated Bottleneck Latent Ordinary Differential Equation (GB-Latent ODE) with Multi-Path Just-In-Time Fine Tuning (MP-JIT-FT). The GB-Latent ODE augments the stan dard Latent ODE with learnable variable-wise gating and a mask-aware bottleneck that compress high-dimensional sparse inputs, improving learning under limited data. Given a partially observed run, MP-JIT-FT retrieves similar historical trajectories, clusters the local neighbourhood into candidate regimes, and fine-tunes a separate model per regime to produce multiple plausible paths, each with a reconstruction-based confidence score, not a single averaged forecast. We further fuse Raman spectroscopy data: a machine-learning soft sensor turns dense Raman spectra into pseudo-observations that enrich the sparse offline measurements for more robust training. On 38 fed-batch 5L bioreactor runs spanning 14 conditions, MP-JIT-FT with Raman fusion achieves the best average rank and outperforms a global Latent ODE baseline on 8 of 9 target variables. Using local-divergence metrics, we show the multi-path gains are largest when locally similar prefixes diverge, whereas Raman fusion helps most when early dynamics are representative of later behaviour.

Johnny Peng, Thanh Tung Khuat, Ellen Otte +2

Complex Adaptive Systems Laboratory, The Data Science Institute, University of Technology Sydney, NSW 2007, Australia · CSL Innovation, Melbourne, VIC 3000, Australia

Irregular Time-Series Modeling Time Series Forecasting Neural ODEs Probabilistic Time Series Forecasting

Jun 25, 2026

Speaking Numbers to LLMs: Multi-Wavelet Number Embeddings for Time Series Forecasting

Large language models (LLMs) are attractive for context-aware time series forecasting because they can integrate heterogeneous textual signals, yet their discrete, language-oriented tokenization and embedding interfaces are misaligned with continuous numerical values, often harming numerical ordering and forecasting reliability. We propose TempoWave, a plug-and-play temporal wavelet digit interface that maps each scalar observation into digit-wise embeddings constructed from multi-wavelet, multi-scale coefficients. By directly overriding standard token representations, TempoWave seamlessly exposes both fine-grained local fluctuations and macro global structures in a transformer-compatible form, ensuring that precise numerical formatting, distinct digit identity, and robustness to common normalization operations are maintained throughout the LLM pipeline. Experiments across five context-enriched forecasting benchmarks demonstrate that TempoWave consistently improves LLM-based forecasters over standard numeric tokenization and alternative embedding interfaces, achieving a new state-of-the-art. These results highlight the numeric interface as a key bottleneck and suggest that principled multi-resolution embeddings can better couple LLMs' contextual reasoning with precise forecasting. Our code is available at https://github.com/DC-research/TempoWAVE and our model can be accessed at https://huggingface.co/Melady/TempoWAVE.

Defu Cao, Zijie Lei, Muyan Weng +2

University of Southern California · Meta · Google DeepMind

Time Series Forecasting LLM-Based Time Series Forecasting Wavelet Methods Multiscale Time-Series Modeling

Jun 24, 2026

Otter Weather: Skillful and Computationally Efficient Medium-Range Weather Forecasting

State-of-the-art medium-range AI weather models can outperform traditional Numerical Weather Prediction (NWP) but require massive training budgets. This restricts usage for under-resourced groups and severely limits fast model iteration. Here we develop Otter Weather, a highly efficient spatiotemporal forecasting model designed to democratise high-performance weather prediction with AI. Evaluated on ERA5 reanalysis data at 1.5° resolution using standard WeatherBench protocols, the Otter family significantly advances the skill-compute Pareto frontier. The deterministic version outperforms the best NWP baseline by 9.6% at a 24-hour lead time while requiring fewer than 3.5 A100-days for training. It provides a 2x efficiency gain over lightweight AI models and a 100-fold reduction in compute compared to resource-intensive frontier architectures. We extend these efficiency gains into probabilistic forecasting by training via the Continuous Ranked Probability Score (CRPS). Scaling to a larger architecture, Otter-XL achieves a 9.7% CRPS improvement over the IFS ENS baseline. This yields an almost two-fold increase in predictive skill over comparable lightweight models at similar compute budgets. Otter-XL also outperforms frontier architectures like GenCast by over 2%, while using an order of magnitude less compute. Finally, Otter is applied out-of-the-box to a complex acoustic scattering PDE task where it outperforms a state-of-the-art foundation modelling approach, suggesting that the advances made here might apply across a range of scientific domains.

Cristiana Diaconu, Jonas Scholz, Aliaksandra Shysheya +4

University of Cambridge

Time Series Forecasting Probabilistic Forecasting Spatiotemporal Forecasting Weather Forecasting

Jun 24, 2026

Sampling sea state using a diffusion model

Sea state prediction is essential for operational maritime applications and coupled earth system modeling, yet current spectral wave models remain computationally prohibitive for many use cases, including online coupling to climate simulations and making probabilistic (ensemble-based) predictions. While deep learning has recently demonstrated strong performance in weather forecasting, existing AI-based wave models are predominantly deterministic and largely limited to bulk variables such as significant wave height, leaving probabilistic sea state estimation largely unexplored. In this work, we propose a diffusion-based generative model for global sea state estimation that conditions on a relatively long history (5 days) of global wind forcing. This generative model directly samples the complex conditional distribution of sea state without autoregressive time-stepping. Unlike prior approaches, our framework naturally extends beyond bulk variables to estimate partition-related variables and derived quantities, such as Stokes drift and mean square slope. Trained on a 30-year global WAVEWATCH-III hindcast, the model achieves substantial computational acceleration compared with numerical spectral models while delivering skillful predictions and a calibrated ensemble spread for the bulk variables. Our results suggest that diffusion-based sea state sampling offers a promising path toward probabilistic wave forecasting and efficient coupling of sea state information into broader earth system models.

Jiarong Wu, Bertrand Chapron, Laure Zanna

Courant Institute School of Mathematics, Computing and Data Science, New York University, 251 Mercer Street, New York, 10012, NY, USA. · Laboratoire d’Oc´eanographie Physique et Spatiale (LOPS), Ifremer, 1625 route de Sainte-Anne, Plouzan´e, 29280, Bretagne, France.

Time Series Forecasting Probabilistic Forecasting Conditional Diffusion Models

Jun 24, 2026

Hierarchical Graph Learning for Calendar Spread Strategies in Commodity Futures Markets

Commodity futures can be represented hierarchically, with underlying assets at the upper level and individual futures contracts at the lower level. Entities at each level can be connected by edges reflecting inherent correlations, with cross-level edges capturing contract-to-underlying asset connections. Building on our observations of these structures, we propose a hierarchical graph learning approach for calendar spread (CS) strategies in commodity futures markets, addressing two significant gaps in the machine-learning literature: (i) the absence of learning-based methods for CS strategies in futures markets, and (ii) the lack of consideration of maturity-dependent interrelationships across commodity futures. We first establish the efficacy of CS strategies by analytically showing that CS strategies can possess higher risk-adjusted returns, measured by the information ratio, and lower risk, measured by variance and delta, than long-only strategies. We then introduce a method to convert learning-based predictions into CS positions. Next, we develop a hierarchical graph learning method that predicts futures price movements by utilizing the maturity-dependent interrelationships, thereby yielding a CS trading algorithm. Empirical results on commodity futures markets traded on the Chicago Mercantile Exchange Group demonstrate that our method outperforms benchmark models in both prediction and trading performance. We find that maturity-dependent interrelationships across commodity futures are instrumental in prediction and that CS trading based on hierarchical graph learning is effective for statistical arbitrage.

Yoonsik Hong, Diego Klabjan

Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, 60208, IL, USA

Quantitative Finance Time Series Forecasting Algorithmic Trading

Jun 24, 2026

Cellular Predictions on the Move: What about Data?

Mobile cellular load forecasting is native to network resource optimization and delivery of services with reliability, latency and quality guarantees. The mainstream of machine learning research in the area is focused primarily on developing powerful learning structures for improved prediction accuracy. The data used for forecasting traditionally belong to the cellular domain and at most contain exogenous information about the surroundings of the base stations. We approach the prediction task from the perspective of data as a vital component of any data learning process. We hypothesize that substantial improvements could be achieved when the data inform on the processes that create the cellular load. Specifically, we propose to characterize the population dynamics -- the potential number of cellular traffic sources and their mobility -- in addition to employing historical time series of mobile data traffic. We validate our hypothesis for the rarely examined highway scenario. Comprehensive experiments show forecasting improvements on the order of

60\%

due to the use of these data alone.

Natalia Vesselinova, Pauliina Ilmonen

Time Series Forecasting Traffic Forecasting

Jun 24, 2026

TopoCast: A Topological Fidelity Framework for Evaluating Transformer-Based Time Series Forecasting

Deep learning-based models have achieved state-of-the-art performance in Time Series Forecasting (TSF), yet their evaluation remains dominated by pointwise error metrics such as Mean Squared Error (MSE), which quantify numerical accuracy but overlook structural properties of the forecast signal, including recurrent dynamics, oscillatory behavior, and phase alignment. As a result, forecasts exhibiting over-smoothing, phase shifts, or frequency distortions may achieve favorable error scores despite substantial structural degradation. To address this limitation, we propose TopoCast, a topology-driven framework for evaluating structural fidelity in TSF. TopoCast reconstructs phase-space representations of forecast and ground-truth sequences using Takens delay embedding and applies persistent homology to characterize their intrinsic dynamics. We derive four complementary topological fidelity measures from persistence diagrams and aggregate them into a Topological Fidelity Score (TFS). We further introduce dominant cycle overlap, a novel metric that maps persistent topological features to the temporal domain to assess whether dominant oscillatory patterns occur at the correct time points. Combined with TFS, this yields the Localized Topological Fidelity Score (LTFS), a phase-aware measure that captures temporal localization errors invisible to existing evaluation metrics. Experiments on five Transformer architectures across three real-world benchmark datasets demonstrate that models with similar forecasting errors can exhibit markedly different structural fidelity profiles, revealing failure modes overlooked by conventional evaluation and highlighting the value of topology-aware forecast assessment.

Sandeepa Weerasekara, Sandareka Wickramanayake

Department of Computer Science and Engineering, University of Moratuwa, Katubedda, Moratuwa, 10400, Sri Lanka.

Time Series Forecasting Time Series Transformers

Jun 23, 2026

FDN: Interpretable Spatiotemporal Forecasting with Future Decomposition Networks

Spatiotemporal systems comprise a collection of spatially distributed yet interdependent entities each generating unique dynamic signals. Highly sophisticated methods have been proposed in recent years delivering state-of-the-art (SOTA) forecasts but few have focused on interpretability. To address this, we propose the Future Decomposition Network (FDN), a novel forecast model capable of (a) providing interpretable predictions through classification (b) revealing latent activity patterns in the target time-series and (c) delivering forecasts competitive with SOTA methods at a fraction of their memory and runtime cost. We conduct comprehensive analyses on FDN for multiple datasets from hydrologic, traffic, and energy systems, demonstrating its improved accuracy and interpretability.

Nicholas Majeske, Ariful Azad

Department of Intelligent Systems Engineering, Indiana University Bloomington, USA · Department of Computer Science and Engineering, Texas A&M University, USA

Explainable Time Series Forecasting Time Series Forecasting Time Series Decomposition Spatiotemporal Forecasting

Jun 23, 2026

Adapt Only When It Pays: Budgeted Decision-Loss Priority for Delayed Online Time-Series Adaptation

Online time-series forecasters receive labels only after horizon-dependent delays, while every adaptation step spends limited compute. We study when an online learner should update, not how to adapt at every opportunity, and introduce ADOWIP: a residual-adapter framework with sealed delay queues, exact budget accounting, and auditable update telemetry. Its main scheduler is an observed decision-loss priority gate that updates only after feedback is revealed, when downstream loss, optionally penalized by prediction MSE, exceeds a calibrated empirical quantile and budget remains. We prove hard-budget feasibility, projected-OGD regret for a convex linear accepted-update subproblem, and stability plus conditional finite-sample gate-selection statements. On public ETT capacity-planning tasks, a frozen calibration/evaluation split selects a gate that lowers held-out decision loss against always, fixed-period, and drift-triggered exact-update baselines under matched compute. Secondary threshold/load-index ETT suites are mixed: 33 of 41 selected contrasts clear the stricter cross-artifact Holm family, and the 8 nonpassing rows are explicitly excluded from primary claims. The same protocol improves an external UCI Bike capacity proxy with 20/0 held-out wins, and a fixed gate passes three full-year Capital Bikeshare station-rebalancing contrasts. Probe-based and finance experiments remain negative, delimiting the current scope of decision-prioritized adaptation.

Xibai Wang

NeuroQuant Labs Limited Hong Kong SAR, China

Test-Time Adaptation Continual Test-Time Adaptation Time Series Forecasting Online Learning

Jun 23, 2026

From Forecasting Leaderboards to Deployment Decisions: A Fail-Closed Certification Protocol

Forecasting leaderboards rank models by predictive quality, but their winners are often read as deployment-ready top-1 advice. That reading can fail when forecasts are passed through a fixed decision interface, such as an alert threshold, a top-k budget, or a switching-cost policy. We study when a forecast-side winner can be certified as deployment-actionable for a specified interface and deployed utility. We introduce a fail-closed certification protocol whose gates are sufficient evidential conditions for a strong claim: a friction-caused, non-tie, statistically supported, and recurrent deployment-side reversal. Traffic-Hourly provides a certified anchor: winners agree at zero friction, but positive switching friction makes the forecast winner deployed-suboptimal. A locked native audit tests overclaiming: across 22 verified candidates and 362 full-grid cells, 155 apparent forecast/deployment winner inversions are blocked before certification. The contribution is not a new forecaster, metric, or universal utility, but a conservative protocol for deciding when forecasting leaderboard winners should be read as deployment-actionable top-1 advice.

Geumyoung Kim

Chungbuk National University

Time Series Forecasting Forecasting Benchmarks

Jun 23, 2026

Model selection with proper scoring rules on data sets of time series: prefer the mean scaled score

We study the problem of model selection among probabilistic forecasting models evaluated on datasets of multiple time series. The performance of a model on a single time series is quantified by the average value (score) of a proper scoring rule over a test set, but extending model selection to data sets of time series requires aggregating these scores. Common approaches either rely on scaling scores and averaging them (mean scaled score) or avoid scaling by using alternative statistics such as mean ranks or win rates. However, these approaches can yield conflicting conclusions. We show that such discrepancies arise from the skewness of the distribution of the scores, which is particularly pronounced when test sets are short. The skewness can cause non-mean criteria (e.g., mean rank, median, win rate) to select misspecified models. In contrast, the mean score is immune from this problem. We further show that, as the size of the test sets increases, all aggregation criteria converge to the same model selection decision, mitigating these discrepancies. Our experiments on intermittent demand time series, including data from the M5 competition, highlight the importance of sufficiently large test sets; the mean scaled score appears to be the more reliable approach, also because empirically we found its decision to remain consistent when different scaling factors are adopted.

Giorgio Corani, Stefano Damato, Dario Azzimonti +1

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

Model Selection Time Series Forecasting Forecasting Benchmarks Probabilistic Forecasting Proper Scoring Rules Probabilistic Time Series Forecasting

Jun 23, 2026

Frequency Domain Reservoir Computing

While the quadratic sequence-length bottleneck of transformers has fueled a resurgence in recurrent models, effectively capturing complex dynamics requires architectures that balance efficient training with highly expressive latent states. Echo State Networks (ESNs) offer a compelling approach by utilizing fixed recurrent weights to circumvent backpropagation through time, enabling a closed-form training solution. However, achieving the expressivity needed for complex tasks demands large reservoirs, exposing an

\mathcal{O}(N^2)

state-update bottleneck that prevents ESNs from matching the scale of contemporary recurrent models. To address this limitation, we introduce Frequency Domain Reservoir Computing (FRESCO), an ESN architecture operating entirely in the frequency domain while avoiding domain-shift overheads to achieve

\mathcal{O}(N)

complexity for dense, non-linear recurrent updates. By employing a novel dimensional zero-padding input embedding, a packed \FDh readout, and a natively applied frequency-domain non-linearity, FRESCO drastically reduces computational costs and energy consumption of training and inference. Furthermore, FRESCO matches the state-of-the-art predictive performance on memory benchmarks, sequential classification, and multivariate long-horizon forecasting, offering a scalable path forward for dense recurrent architectures.

Klaus Schertler, Xiomara Runge, Andrea Ceni +2

Airbus Central Research & Technology Taufkirchen, Germany · Department of Computer Science University of Pisa, Italy · Faculty of Technology Bielefeld University, Germany

Time Series Forecasting Recurrent Neural Networks Reservoir Computing

Jun 23, 2026

Towards Continuous Power Forecasting: Practical Continual Learning for Real-World Energy Systems in Nonstationary Time Series

Power forecasting models deployed in real-world energy markets must operate under nonstationary conditions, where data distributions continually evolve due to weather variability, infrastructure upgrades, and changing consumption behaviors. In practice, these models face strict operational constraints: historical data may be limited or unavailable for repeated retraining, and uninterrupted long-term service is often required. This paper addresses these challenges by proposing the paradigm of Continuous Power Forecasting, which views power forecasting as a continual learning problem rather than a static offline task. Based on an adaptive continual learning framework for regression, we systematically investigate the practical effectiveness of six representative continual learning approaches from three methodological categories. These approaches are evaluated under different realistic assumptions regarding data accessibility and update policies. Experimental validation on real-world power datasets demonstrates that continual learning enables forecasting models to self-adapt to distributional drift, accumulate knowledge over time, and mitigate catastrophic forgetting without relying on large-scale historical data storage. Beyond performance gains, our study provides practical insights into the stability and adaptation behaviors of different continual learning approaches under realistic operational constraints. Overall, this work illustrates how continual learning can be pragmatically integrated into industrial power forecasting pipelines, offering a scalable and sustainable solution for long-term deployment in dynamic environments.

Yujiang He, Frederic Uhrweiller, Bernhard Sick

Intelligent Embedded Systems, University of Kassel, 34121 Kassel, Germany

Continual Learning Time Series Forecasting Non-Stationary Time Series Forecasting Catastrophic Forgetting

Jun 23, 2026

MacroLens: A Multi-Task Benchmark for Contextual Financial Reasoning under Macroeconomic Scenarios

Financial decision-making is contextual: forecasting prices, valuing companies, and assessing event exposure weigh price history, accounting fundamentals, macroeconomic regime, and contemporaneous text. A benchmark over these four signals is hard to build because finance violates four assumptions of time-series evaluation: text must be gated by its publication date to prevent look-ahead, quarterly fundamentals are reported with a one- to ninety-day lag, filing text is partly redundant with the numerical statement fields it accompanies, and macroeconomic regimes leak across calendar splits. No public benchmark addresses all four signals jointly. MacroLens covers 4,416 U.S. small- and micro-cap equities over 2021-2026. Seven tasks share one point-in-time panel of prices, 46.8M XBRL accounting facts, 53 macroeconomic series, 295,860 SEC filings, and 215,882 news articles, plus a scenario layer of 1,130 macroeconomic events across 49 types automatically detected and rendered as natural language. Tasks span contextual forecasting, public and private valuation, statement generation from fundamentals and descriptions, scenario-conditioned returns, and real-estate valuation. We evaluate 19 methods across six families spanning naive heuristics through time-series foundation models, fine-tuned LLM-based time-series models, and zero-shot large language models (LLMs), plus a five-step feature-context ablation on two frontier LLMs and a gradient-boosted baseline. MacroLens is released at https://huggingface.co/datasets/DeepAuto-AI/MacroLens.

Patara Trirat, Jin Myung Kwak, Jay Heo +2

KAIST

Quantitative Finance Financial Forecasting Time Series Forecasting Forecasting Benchmarks LLM-Based Time Series Forecasting Financial Time Series+2

Jun 23, 2026

RAVEN: A Regime-Aware Variable-context Expert Network for Financial Time Series Forecasting

Financial time series forecasting presents structural challenges absent from standard benchmarks. Log-returns are non-stationary, exhibit exceptionally low signal-to-noise (SNR) ratios, and are governed by regime-dependent temporal dependencies. We identify a key limitation of state-of-the-art (SOTA) time series models in financial settings. A fixed context window is mismatched to the time-varying optimal look-back of non-stationary price processes. We propose the Regime-Aware Variable-context Expert Network (RAVEN), a Mixture-of-Experts framework designed to adaptively determine the temporal context for each input sample. Instead of relying on a fixed look-back horizon, RAVEN constructs a hierarchy of nested contiguous windows whose lengths are determined by the data itself. Specifically, RAVEN scores patches by learned importance in reverse chronological order and applies the Cumulative Importance Thresholding (CIT) mechanism to derive nested prefix windows, each routed to a scale-specialized expert. A Global Compressed Representation (GCR) branch runs in parallel over the full context, preserving global temporal coherence that local experts cannot guarantee. Because the nested routing induces structured overlap among expert inputs, we introduce a Correlation-Aware Weighting (CAW) to align variable-length expert outputs and penalize pairwise cosine similarity prior to aggregation. Experiments on cumulative log-return prediction (HS300, S&P500) and fund sales forecasting demonstrate that RAVEN achieves SOTA performances, improves Pearson correlation by 9.2% on HS300 and 20.2% on S&P500, and reduces MSE by 18.2% on fund sales forecasting, while achieving the best results in 14 of 16 metrics on four PEMS traffic benchmarks.

Cheng He, Zhenyu Guan, Xijie Liang +6

University of Science and Technology of China, China · Shanghai Black Wing Asset Management Co., Ltd., China · College of Sciences, Shanghai University, China +2

Financial Forecasting Time Series Forecasting Non-Stationary Time Series Forecasting Financial Time Series Mixture-of-Experts Models Multiscale Time-Series Modeling+1

Jun 22, 2026

Selective Time Series Forecasting via Metalearning

Deep learning methods have achieved state-of-the-art in time series forecasting, yet their accuracy varies considerably across samples, as some instances remain inherently difficult to predict. Reject option mechanisms, which allow models to abstain from high-risk predictions, are well established in classification and regression but underexplored in forecasting. Existing abstention strategies typically rely on proxies, such as the width of the prediction interval or learned confidence scores derived from forecasts. However, these approaches are inherently tied to the training domain, limiting their ability to generalize. We propose a selective forecasting framework that addresses this limitation by modeling the empirical percentile of forecasting errors, that is, a scale-invariant statistic, based on structural characteristics extracted from recent lags via metalearning. By decoupling the rejection decision from the forecast itself and grounding it in domain-agnostic features, the framework enables effective abstention transfer across heterogeneous time series. Experiments in both in-domain and transfer learning settings show that rejecting samples predicted as challenging consistently improves forecasting accuracy across coverage levels.

Ricardo Inácio, Vitor Cerqueira, Marília Barandas +1

Faculdade de Engenharia da Universidade do Porto, Porto, Portugal · University of Coimbra, Portugal · Fraunhofer Portugal AICOS, Portugal

Selective Prediction Time Series Forecasting

Jun 22, 2026

Interpretable Kolmogorov-Arnold Network with Feature-Isolated Temporal Attention Mechanism for Electricity Load Forecasting

Accurate electricity load forecasting is a crucial prerequisite for stable power system operations. While prevalent deep learning models present competitive performance, they often operate as black boxes and lack interpretability. While the Kolmogorov-Arnold network (KAN) has emerged as a promising alternative because of its learnable activation function design, its direct application to time-series forecasting faces challenges in modeling complex temporal data patterns. Also, simple integration into existing architectures, such as serving as replacement of neural modules, cannot fully leverage KAN's interpretability strengths. To address these gaps, this study develops LoadKAN, a novel hybrid and interpretable framework for load forecasting that synergistically combines a specifically-designed feature-isolated temporal attention mechanism with a KAN module. The attention stage aims to extract temporal dynamics from each input feature independently, such as historical load and human mobility, providing distilled feature representations to the KAN module for interpretable predictions. When evaluated on datasets from three representative U.S. electricity markets, our LoadKAN remains highly competitive when compared to extensively-tuned, state-of-the-art, black-box deep learning benchmarks. More importantly, LoadKAN's interpretability enables a granular analysis of the learned non-linear relationships between six distinct mobility patterns and electricity load. Through KAN-learned activation functions, our quantitative sensitivity analyses on mobility features reveal complex and market-specific dependencies. These findings further demonstrate the ability of our LoadKAN to generate insights often obscured by opaque black-box neural forecasting models.

Jinhao Li, Hao Wang

Department of Data Science and AI, Faculty of Information Technology, Monash University, Melbourne, Victoria, Australia · Monash Energy Institute, Monash University, Melbourne, Victoria, Australia

Multivariate Time Series Forecasting Time Series Forecasting Neural Network Interpretability Kolmogorov-Arnold Networks Temporal Attention Electricity Load Forecasting

Jun 22, 2026

Self-Modulating Quantum Fast-Weight Programmers for Efficient Adaptive Sequential Learning

Recent advances in quantum machine learning have motivated efficient models for sequential data processing. In this paper, we propose Self-Modulating Quantum Fast Weight Programmers, or Self-Modulating QFWP, which extends Quantum Fast Weight Programmers by introducing adaptive modulation over both newly generated fast-weight updates and historical fast-weight memory. Numerical results show that the proposed mechanism improves convergence stability and prediction performance across varying model settings, including different numbers of qubits and input sequence lengths. We further provide theoretical arguments explaining how self-modulation balances new information injection with memory retention, thereby enhancing temporal information propagation. These results suggest that Self-Modulating QFWP is a compact and effective framework for quantum machine learning on time-series data.

Samuel Yen-Chi Chen, Yifeng Peng, Kuo-Chung Peng +8

Wells Fargo · Stevens Institute of Technology · National Taiwan University +3

Time Series Forecasting Quantum Machine Learning Adaptive Learning

Jun 22, 2026

A Novel Approach to Temporal QoS Estimation via Extended Kalman Filter-Incorporated Latent Feature Analysis

Predicting temporal Quality of Service (QoS) data is critical for optimizing network services and rationalizing resource allocation in cloud computing and service-oriented systems. Existing mainstream methods have achieved promising predictive performance. However, their purely data-driven manner limits their ability to capture non-stationary temporal patterns, thereby leading to accuracy degradation when temporal QoS data exhibits fluctuations. To tackle this limitation, we propose a novel Extended Kalman Filter-Enhanced Latent Feature Analysis (EKL) model to perform efficient and accurate temporal QoS prediction from the perspective of bidirectional model-data-driven learning. Its main idea is three-fold: a) designing a model-driven feature producer to obtain the temporal latent features to capture the intricate temporal pattern following the principle of an Extended Kalman Filter; b) building a data-driven feature producer based on the alternating least squares algorithm to identify time-invariant latent features describing intrinsic user-service characteristics; c) exploiting a density-oriented parallel strategy that achieves workload balancing by sorting users in accordance with their service invocation density, which effectively elevates computational efficiency. In addition, we provide a rigorous theoretical analysis to formally prove the convergence of the proposed EKL. Experimental evaluations conducted on real-world temporal QoS datasets reveal that our proposed EKL surpasses existing state-of-the-art models with respect to both computational efficiency and prediction accuracy for missing temporal QoS data.

Ye Yuan, Song Wang, Hongxun Zhou +2

College of Computer and Information Science, Southwest University, Chongqing 400715, China

Time Series Forecasting Cloud Computing Matrix Factorization

Jun 21, 2026

Federated Learning for Global Carbon Emission Forecasting: A Hybrid Time-Series Approach with Statistical and Neural Models

Climate change, primarily driven by carbon dioxide (CO2) emissions, requires accurate forecasting tools to support effective mitigation policies and sustainable development strategies. Existing forecasting approaches typically rely on centralized data collection, which is often restricted by privacy regulations and the distributed nature of emission data across countries and industrial sectors. This paper proposes a novel federated hybrid forecasting framework that integrates ARIMA-based trend modeling, GARCH-based volatility modeling, LSTM-Attention temporal representation learning, and XGBoost prediction within a privacy-preserving federated learning environment. The proposed framework enables collaborative learning among distributed clients without requiring the exchange of raw data. Experimental evaluation across 14 clients demonstrates strong forecasting performance, achieving client R2 values between 0.50 and 0.97 with an average of 0.73, RMSE values ranging from 0.06 to 2.35 with an average of 1.21, and MAPE values between 1.5% and 11.3% with an average of 6.5%. The results indicate that the proposed framework provides an accurate, scalable, and regulation-compliant solution for collaborative carbon-emission forecasting.

Attia Qammar, Qazi Haseeb Yousaf, Ali Azam +3

School of Computing and Artificial Intelligence, Southwest Jiaotong University, Chengdu, 610031, China · Department of Computer Science, Bahria University, Islamabad · School of Mechanical Engineering, Southwest Jiaotong University, Chengdu, 610031, PR China

Time Series Forecasting Federated Learning