Probabilistic Time Series Forecasting

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14 papers in the last four weeks, up 56% on the four weeks before. 0.1% of all new papers.

Jul 13Week of Sep 28

Latest papers 112

Jun 4, 2026cs.LG

TS-ICL: A Flexible Time-Indexed Foundation Model for Time Series via In-Context Learning

Foundation models mark a profound paradigm shift in time series modeling, with task-specific models being superseded by general-purpose zero-shot models. Yet, current approaches primarily focus on forecasting, while real-world time series are often irregularly and partially observed, requiring models that can jointly forecast, impute missing values, and handle degraded sampling conditions. To address these challenges, we introduce TS-ICL, a novel probabilistic In-Context Learning encoder--regressor Transformer that unifies forecasting and imputation. TS-ICL formulates time series tasks as timestamp-aligned regression and naturally incorporates covariates by training on synthetic dependency structures generated from a novel causal data prior. Empirically, TS-ICL achieves a new state-of-the-art in imputation, while remaining competitive with leading forecasting foundation models across both univariate and covariate-aware benchmarks. It shows particularly strong performance in forecasting with partially observed look-back windows.

Etienne Le Naour, Tahar Nabil, Adrien Petralia

1EDF R&D, Palaiseau, France

Irregular Time-Series Modeling Time Series Imputation Time Series Forecasting In-Context Learning Time-Series Foundation Models Probabilistic Time Series Forecasting

Jun 3, 2026cs.LG

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

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

\boldsymbol{\le 5\%}

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

\mathbf{17.3\%}

and gains exceeding

\mathbf{30\%}

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

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

The University of Bristol Bristol, UK

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

Jun 2, 2026q-fin.CP

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

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

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

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

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

Jun 1, 2026cs.LG

A Systematic Evaluation of Current Architectures in Wind Power Forecasting

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

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

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

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

Jun 1, 2026stat.ML

ProbRes: Volatility Learning for Probabilistic Time-Series Forecasting

Probabilistic time series forecasting has attracted increasing attention in financial applications due to the need to quantify risk and uncertainty in future observations. We propose ProbRes, a post-hoc probabilistic calibration method that explicitly learns and incorporates volatility dynamics into probabilistic forecasting, enabling effective handling of heteroskedastic data. During training, ProbRes employs two architecture-agnostic modules to separately model the conditional mean and conditional volatility. At the inference stage, it generates predictive distributions by resampling normalized residuals. ProbRes is applicable to both univariate and multivariate time series and remains robust under a wide range of error distributions, including non-Gaussian innovations with conditional heteroskedasticity. Theoretical results demonstrate ProbRes's validity and experiments on both synthetic and real-world datasets show that ProbRes accurately captures predictive distributions and produces well-calibrated prediction intervals.

Tingting Wang, Yunyi Zhang, Benyou Wang

School of Data Science, The Chinese University of Hong Kong, Shenzhen

Financial Time Series Uncertainty Calibration Probabilistic Time Series Forecasting

May 30, 2026stat.AP

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

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

R^2 = 0.9906

versus

0.8213

for Holt-Winters alone, with

94.2\%

of residuals within

\pm 2σ

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

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

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

May 28, 2026cs.AI

Uncertainty-Aware Transfer Learning for Cross-Building Energy Forecasting: Toward Robust and Scalable District-Level Energy Management

Scaling data-driven energy forecasting to district level requires models that can be re-used across buildings with minimal target-domain data and honest uncertainty estimates. We present an uncertainty-aware transfer learning (TL) framework for cross-building energy forecasting based on the Temporal Fusion Transformer (TFT), evaluated on a newly released high-resolution real sub-meter dataset: an educational building at Aalborg University, Denmark (source) and the multi-typology NEST building at EMPA, Switzerland (target). We introduce the Transfer Robustness Index (TRI), an architecture-agnostic metric for quantifying generalization quality across domain gaps. A four-strategy layer-freezing ablation shows that Probe-Only fine-tuning, updating only 455 output-layer parameters out of 806K, achieves the best transfer quality (TRI = 3,097), outperforming full fine-tuning and suggesting that TFT encoders learn transferable temporal representations. Monte Carlo Dropout yields a prediction interval coverage probability of 93.2%, close to the nominal 95% target. A data-scarcity analysis further shows monotonic improvement with increasing target-domain data, providing practical guidance for district energy deployment.

Shadmehr Zaregarizi, Khashayar Yavari

Politecnico di Torino · Turin, Italy

Uncertainty Quantification Time Series Forecasting Building Energy Management Cross-Domain Transfer Learning Time Series Transformers Probabilistic Time Series Forecasting

May 27, 2026cs.LG

Stabilizing distribution-free probabilistic forecasts

Multi-step-ahead forecasts are often updated as new observations become available, since shorter forecast horizons typically improve forecast quality. However, such improvements come at the cost of forecast instability, i.e., variability in forecasts for the same target period. This instability can trigger costly changes to plans formulated based on the forecasts and may erode trust in the forecasting system. In this work, we integrate forecast stability alongside forecast quality into the training of distribution-free probabilistic time-series forecasting models, allowing us to control this trade-off. We propose a method for generating stabilized forecasted conditional quantile functions using regression splines parameterized by a neural network. This approach enables joint optimization of quality and stability, as it allows us to directly penalize dissimilarities arising from forecast updates. Furthermore, it allows assigning varying importance to stabilizing different parts of the forecast distributions (e.g., central parts vs. tails) to focus on the parts most relevant for the intended downstream use (e.g., the upper tail for inventory management). We empirically evaluate the proposed method on two datasets with different statistical properties and show that it can effectively reduce forecast instability without a substantial loss in forecast quality, and that it can target stabilization effort toward specific parts of the forecast distributions.

Jente Van Belle, Honglin Wen, Wouter Verbeke +1

Faculty of Economics and Business, KU Leuven, Belgium · Department of Electrical Engineering, Shanghai Jiao Tong University, China · Dyson School of Design Engineering, Imperial College London, United Kingdom +3

Probabilistic Forecasting Probabilistic Time Series Forecasting

May 27, 2026cs.LG

Universal Time Series Generation with Neural Controlled Differential Equations

Recent work on the sequence universality of State Space Models (SSMs) has introduced efficient, maximally expressive continuous-time approaches for time-series modelling. While these works focus on discriminative settings, we extend this perspective to generative time-series modelling by proving that maximally expressive Structured Linear Controlled Differential Equations (SLiCEs) are universal time-series generators, in the sense that they can approximate the induced path laws of continuous causal pushforwards on compact latent sets in

W_\infty

. Building on these theoretical results, we propose Generative SLiCEs (G-SLiCEs), a maximally expressive continuous-time model for flow matching on path-space. Empirically, we show that expressivity improves performance in probabilistic forecasting and downstream tasks, while retaining the advantages of continuous-time models such as generalising to arbitrary observation grids. This is particularly beneficial for irregular grids, where fixed-grid models often struggle.

Torben Berndt, Elyes Farjallah, Leif Seute +3

Heidelberg Institute for Theoretical Studies, Heidelberg, Germany · IAR, Karlsruhe Institute of Technology, Karlsruhe, Germany · Max Planck Institute for Polymer Research, Mainz, Germany +4

Neural Controlled Differential Equations Time Series Generation Neural ODEs Probabilistic Time Series Forecasting

May 26, 2026cs.LG

Distribution-Aware Conformal Prediction: A Framework for generating efficient prediction intervals for time series

We present Distribution-aware Conformal Prediction (DCP), a unified framework integrating probabilistic predictors like Monte Carlo dropout, deep ensembles, and quantile regression with score-agnostic conformal calibration to produce valid and efficient prediction intervals. Leveraging a numerical inversion approach to construct interval bounds, DCP accommodates arbitrary combinations of distribution generating predictors and nonconformity scores. Benchmark analysis on synthetic and real-world time series data demonstrate DCP's ability to adaptively calibrate prediction intervals under varying uncertainty regimes. Crucially, DCP's modular design facilitates plug-and-play experimentation with different predictor-score pairings, quantitatively supported by a newly introduced modified Winkler score that balances validity and efficiency by explicitly penalizing undercoverage. While DCP generalizes and extends existing approaches like Conformalized Quantile Regression and Conformalized Monte Carlo, its modular design allows further extensions, setting a foundation for advancing uncertainty quantification in dynamic environments and high-risk applications.

Daniel Schweizer, Peter Kuhn, Jayant Sharma +3

Fraunhofer Institute for Highspeed Dynamics, Ernst-Mach-Institut, EMI Freiburg, Germany

Conformal Prediction Uncertainty Calibration Probabilistic Time Series Forecasting Regression Prediction Intervals

May 23, 2026cs.LG

Deep ZakaiJ: Structured Filtering for Jump-Diffusion Time Series Forecasting

Time series driven by unobserved latent states frequently exhibit abrupt jump discontinuities whose timing and magnitude cannot be predicted from observed history alone. Classical jump-diffusion models offer a principled mathematical framework but assume rigid parametric forms, while recent neural jump models operate on fully observed trajectories without inferring the hidden states that govern the dynamics. We propose \textit{Deep ZakaiJ}, a latent-state model for partially observed jump-diffusion systems that embeds the Zakai nonlinear filtering equation into a neural encoder--decoder architecture. The encoder recursively updates a belief over the latent state via Strang splitting into three interpretable substeps: prior propagation, diffusion innovation, and jump innovation, yielding a differentiable, first-order-accurate approximation of the exact filtering evolution. The decoder is a structured jump-diffusion model explicitly conditioned on the filtered belief, preserving the separation between continuous dynamics and discontinuous shocks. On synthetic, financial, and oceanographic datasets, \textit{Deep ZakaiJ} improves distributional forecasts while remaining competitive in point accuracy, achieving calibrated predictive intervals and recovering interpretable latent structure in synthetic and qualitative case studies.

Yan Leng, Thibaut Mastrolia, Hao Wang

University of Texas at Austin · University of California, Berkeley

Stochastic Differential Equations Latent Dynamics Modeling Time Series Forecasting Probabilistic Time Series Forecasting

May 22, 2026cs.LG

Valid and Expressive Copulas for Irregular Multivariate Time Series

We introduce CopFITi, a copula model for probabilistic forecasting of irregular multivariate time series (IMTS). Our model combines the expressivity of normalizing flows for univariate marginals with the consistency and flexibility of a Gaussian Mixture Copula for the joint dependency structure. Our experiments show that copula-based approaches, which decouple the marginals from the joint, yield better marginal models than architectures that directly fit the full joint. With CopFITi, we propose the first IMTS copula that is marginalization-consistent by construction and establish a new state of the art in joint IMTS density modeling.

Christian Klötergens, Tom Hanika, Lars Schmidt-Thieme +1

Institute of Computer Science University of Hildesheim Hildesheim, Germany

Irregular Time-Series Modeling Copula Models Generative Modeling Probabilistic Time Series Forecasting

May 22, 2026cs.LG

Parametric Prior Mapping Framework for Non-stationary Probabilistic Time Series Forecasting

Effectively modeling non-stationary dynamics in probabilistic multivariate time series(MTS) forecasting requires balancing expressiveness with robustness. Existing parametric approaches benefit from strong inductive biases but lack flexibility, whereas deep generative models struggle to capture complex temporal dependencies without extensive data and computation. We introduce Parametric Prior Mapping (PPM), a framework that injects parametric structural priors into a generative modeling process. Specifically, PPM utilizes a parametric estimator to derive a dynamic, adaptive prior that guides the learning of a complex predictive distribution via a learnable mapping. This design allows the model to retain the efficiency of parametric methods while exploiting the expressive power of generative models. Trained with a hybrid objective, PPM yields precise forecasts with well-calibrated uncertainty estimates. Empirical results show that PPM outperforms existing baselines in handling non-stationary data, offering a superior trade-off between accuracy and computational efficiency. The code is available at https://github.com/ljl8336/PPM.

Jinglin Li, Jun Tan, QI Fang +1

School of Computer Science and Engineering, Central South University, Changsha, China.

Multivariate Time Series Forecasting Non-Stationary Time Series Forecasting Conditional Generative Modeling Probabilistic Time Series Forecasting

May 22, 2026cs.LG

PaP-NF: Probabilistic Long-Term Time Series Forecasting via Prefix-as-Prompt Reprogramming and Normalizing Flows

Time series forecasting plays a central role in many real-world applications and has been extensively studied. Most existing approaches rely on deterministic models. However, real-world environments exhibit inherently uncertain and complex future behaviors, making single-point predictions insufficient. This highlights the need for probabilistic forecasting methods that can quantify and represent uncertainty. In this work, we propose PaP-NF, a probabilistic forecasting framework that aligns continuous time series representations with a frozen large language model (LLM) using a Prefix-as-Prompt mechanism, and conditions a normalizing flow decoder on the global context extracted by the LLM. The quality of the resulting predictive distributions is evaluated using the Continuous Ranked Probability Score (CRPS), a standard metric in probabilistic forecasting. Across a variety of long-term forecasting benchmarks, PaP-NF robustly captures multi-modal uncertainty while maintaining competitive point forecasting accuracy. The official implementation is available at: https://github.com/democracy04/PaP-NF

Minju Kim, Youngbum Hur

Department of Industrial Engineering, Inha University, Incheon, Republic of Korea

Long-Term Time Series Forecasting LLM-Based Time Series Forecasting Probabilistic Time Series Forecasting

May 21, 2026cs.AI

Is Capability a Liability? More Capable Language Models Make Worse Forecasts When It Matters Most

We document inverse scaling in LLMs on forecasting problems whose underlying time series exhibit superlinear growth and tail risk of regime change, a structure common in finance and epidemiology. On these tasks, more capable models produce worse distributional forecasts. The pattern appears on ForecastBench-Sim (FBSim), a contamination-free, simulated-world benchmark we release, in forecasting synthetic SIR epidemics with a matched linear control, and replicates in real-world datasets on COVID-19, measles, housing markets, and hyperinflation. A per-quantile decomposition shows the failure concentrates at the upper tail, which more capable models shift upward to track aggressive extrapolations of growth, while the lower tail stays put. A within-family study of Llama-3.1 shows that both model scale and post-training independently contribute to this effect. Domain knowledge does not reliably rescue calibration. This inverse scaling does not appear on single-threshold metrics common in LLM forecasting benchmarks, reversing the sign of the capability--accuracy relationship on identical outputs. Single-threshold scoring at conventional cutoffs misses the upper-tail cost; tail-inclusive scoring reverses the sign of the capability--accuracy relationship on the same outputs. We recommend that LLM forecasting evaluations use continuous (and unbounded) measures of accuracy alongside bounded binary threshold metrics.

Nick Merrill, Jaeho Lee, Ezra Karger

Forecasting Research Institute · UC Berkeley

Language Model Scaling Laws Forecasting Benchmarks Probabilistic Forecasting LLM-Based Time Series Forecasting Language Model Calibration Probabilistic Time Series Forecasting

May 21, 2026cs.LG

Reasoning through Verifiable Forecast Actions: Consistency-Grounded RL for Financial LLMs

Financial markets are characterized by extreme non-stationarity, low signal-to-noise ratios, and strong dependence on external information such as news, company fundamentals, and macroeconomic signals. Yet, existing approaches either abstract time-series into text or decouple forecasting from language-based reasoning, leading to a fundamental mismatch between qualitative reasoning and quantitative outcomes. To address this, we introduce StockR1, a time-series-enhanced LLM that unifies stock forecasting and financial reasoning through a verifiable forecast action. Based on a tool-call design, the model first emits a forecast action, which is a structured and interpretable representation of its qualitative market outlook. It then invokes a time-series decoder conditioned on this action to generate distributional future trajectories, leading to more informed question answering and financial reasoning. We optimize the full pipeline with reinforcement learning, where rewards jointly reflect answer validity, forecast accuracy, and consistency between generated actions and observed time-series dynamics. In addition, rewards are reweighted by a sample-level uncertainty scalar, encouraging the model to accommodate varying uncertainty in market dynamics. We evaluate StockR1 on financial question answering and stock forecasting over a large-scale 10-year benchmark. Our method consistently outperforms time-series baselines and general-purpose LLMs, improving reasoning accuracy by 17.7% (4B) and 25.9% (8B). These findings demonstrate that structuring the forecast actions establishes a powerful synergy between language reasoning and temporal prediction, enabling LLMs to reason through verifiable, interpretable, and numerically grounded decisions.

Jialin Chen, Aosong Feng, Harshit Verma +7

Yale University · Arizona State University · University of Texas Rio Grande Valley

Time Series Reasoning RL for Language Model Reasoning Financial QA Time Series Forecasting Probabilistic Time Series Forecasting

May 19, 2026stat.ML

Probabilistic Multivariate Time Series Forecasting with Diffusion Copulas

Accurately assessing financial risk requires capturing both individual asset volatility and the complex, asymmetric dependence structures that emerge during extreme market events. While modern diffusion-based models have advanced multivariate forecasting, they often suffer from a "normality bias" when trained end-to-end, sacrificing marginal calibration for joint coherence and consistently underestimating tail risk. To address this, we propose a Diffusion-Copula framework that explicitly decouples the learning of marginal distributions from their dependence structure. We employ deep Mixture Density Networks to capture heavy-tailed asset dynamics, followed by a Classification-Diffusion Copula to model the joint dependence. Applied to cryptocurrency markets, our approach demonstrates superior performance over state-of-the-art baselines in forecasting systemic extremes of both marginal and joint events. Crucially, we demonstrate that while baseline models classify simultaneous market crashes as statistically impossible "Black Swans" (high surprise), our framework identifies them as "Expected Crashes" (low surprise), successfully preserving the correlation structure necessary for robust risk management during contagion events.

David Huk, Dongshan Wang, Miha Bresar

Department of Statistics The University of Warwick · School of Data Science The Chinese University of Hong Kong, Shenzhen

Multivariate Time Series Forecasting Copula Models Quantitative Finance Probabilistic Forecasting Probabilistic Time Series Forecasting Diffusion Models

May 19, 2026cs.LG

DeRegiME: Deep Regime Mixtures for Probabilistic Forecasting under Distribution Shift

We introduce DeRegiME -- Deep Regime Mixture of Experts -- a direct multi-horizon probabilistic forecaster that separates latent uncertainty regimes from the underlying signal and softly assigns each forecast location to learned recurring regimes using a sparse variational Gaussian process (GP) whose nonstationary regime-mixing kernel and Student-t likelihood combine per-regime sub-kernels and noise processes via a shared gate. This yields a single sparse-GP posterior, not a mixture of GP experts. DeRegiME addresses a key limitation of neural forecasters: point forecasts discard residual uncertainty, and probabilistic heads -- whether single marginals, uninterpreted mixtures, quantile sets, or diffusion samples -- rarely expose the regime structure of the residual. Yet distribution shift in noisy heteroskedastic time series may be abrupt, gradual, or horizon-dependent and often appears in residual uncertainty rather than the conditional mean. DeRegiME yields an interpretable mean-residual-noise decomposition with a direct-sum feature-space representation that anchors regimes as clusters of residual similarity whose transitions surface as implicit changepoints. The effective number of regimes is pruned by the stick-breaking gate. We prove kernel validity and predictive-density propriety, and across ten benchmarks and three encoder grids DeRegiME improves negative log predictive density (NLPD) by 20.3% over the strongest encoder-matched baseline, a DeepAR/GluonTS-style dynamic Student-t head, with parallel gains on CRPS (3.0%) and MSE (4.7%). Improvements are consistent across all datasets, which span abrupt, gradual, and seasonal shifts.

Kieran Wood, Stefan Zohren, Stephen J. Roberts

Machine Learning Research Group, University of Oxford · Oxford-Man Institute, University of Oxford

Distribution Shift Robustness Time Series Forecasting Non-Stationary Time Series Forecasting Probabilistic Time Series Forecasting Temporal Distribution Shift Gaussian Process Regression

May 18, 2026cs.LG

SAGA: A Sequence-Adaptive Generative Architecture for Multi-Horizon Probabilistic Forecasting with Adaptive Temporal Conformal Prediction

Microsimulation models used by ministries of finance and central banks rely on parametric processes for lifetime earnings that capture only first and second moments of the conditional distribution and miss long-range nonlinear structure. We propose SAGA, a decoder-only transformer for irregular tabular panel sequences, paired with a split conformal calibration wrapper that delivers individual-level prediction intervals with finite-sample marginal coverage guarantees. Trained on the longitudinal Swedish LISA register over 1990 to 2022, comprising 2,143,817 individuals and 61,284,903 person-years, the model forecasts annual labor earnings at horizons of one to thirty years and aggregates them by Monte Carlo into present-discounted lifetime earnings distributions. Against the canonical Guvenen, Karahan, Ozkan, and Song parametric process and tabular and recurrent baselines, SAGA reduces continuous ranked probability score by 31.9 percent at the ten-year horizon and mean absolute error by 37.7 percent at the twenty-year horizon. Conformal intervals achieve nominal coverage to within 0.4 percentage points marginally and within 2.4 percentage points on the worst-case demographic subgroup. The reconstructed lifetime earnings Gini coefficient is 0.327 against the partially observed truth of 0.341 and the GKOS estimate of 0.378. Model weights, calibration tables, and a synthetic equivalent dataset are released for replication outside the protected SCB MONA environment.

Gustav Olaf Yunus Laitinen-Fredriksson Lundström-Imanov, Hafize Gonca Cömert

Department of Economics, Stockholm University, SE-106 91 Stockholm, Sweden

Irregular Time-Series Modeling Time Series Transformers Probabilistic Time Series Forecasting

May 18, 2026cs.LG

Improving Spatio-Temporal Residual Error Propagation by Mitigating Over-Squashing

Residual error propagation remains a fundamental problem in recurrent models, where small prediction inaccuracies compound over time and degrade long-horizon performance. Accurately modeling the correlation structure of such residuals is critical for reliable uncertainty quantification in probabilistic multivariate timeseries forecasting. While recent time-series deep models efficiently parametrize time-varying contemporaneous correlations, they often assume temporal independence of errors and neglect spatial correlation across the observed network. In this paper, we introduce Teger, a structured uncertainty module that overcomes the spa- tial and temporal limitations of error-correlated autoregressive forecasting. Teger proposes a spatial curvature-aware graph rewiring mechanism explicitly strengthening information-bottleneck edges identified by discrete Forman curvature. The component is integrated into a low-rank-plus-diagonal covariance head, preserving tractable inference via the Woodbury identity. Teger is backbone-agnostic, requiring only the latent state produced by any autoregressive encoder. We provide theoretical evidence of Teger, and experimentally evaluate it on LSTM, Transformer, and xLSTM backbones across four real-world spatio-temporal datasets, showing consistent improvement in Continuous Ranked Probability Score (CRPS). We further provide a formal theoretical analysis connecting curvature-aware rewiring to (i) oversquashing alleviation, (ii) improved spectral connectivity, (iii) reduced effective resistance, and (iv) improved covariance calibration bounds

Seyed Mohamad Moghadas, Esther Rodrigo Bonet, Bruno Cornelis +1

ETRO Department, Vrije Universiteit Brussel, B-1050 Brussels, Belgium · imec Kapeldreef 75, B-3001 Leuven, Belgium

Graph Rewiring Over-Squashing Spatiotemporal Forecasting Uncertainty Propagation Probabilistic Time Series Forecasting

May 17, 2026cs.LG

Scale-Equivariant Generative Forecasting: Weight-Tied Dilated Convolutions, Wavelet Scattering Inputs, and Spectral-Consistency Training for Self-Similar Time Series

Many natural and engineered time series -- equity returns, climate anomalies, turbulent velocities, neural recordings, packet-level network traffic -- are approximately self-similar: their horizon-

T

distribution is tied to the horizon-

1

distribution by one scaling exponent

H

. Standard deep generative sequence models (transformers, dilated TCNs, the WaveNet family) ignore this. Their receptive fields are wide, but kernel parameters live independently at every dilation level, yielding a multi-scale architecture, not a scale-equivariant one. We make three contributions. First, we give a precise definition of discrete scale equivariance for 1D causal networks and prove that dyadic dilation commutes (up to boundary effects) with any dilated-convolution stack whose kernel weights are shared across levels. Tying the kernel shrinks the convolutional parameter budget by an

L

-fold factor (where

L

is depth) and hard-wires self-similarity in as an inductive bias. Second, we wrap this Scale-Equivariant WaveNet (SE-WaveNet) backbone in three components that carry the same prior: a one-level Daubechies-4 wavelet input, a Hurst-FiLM block exposing the local scaling exponent, and a spectral-consistency training term targeting the

|f|^{-(2H+1)}

power-law spectrum. The head is a conditional normalising flow, chosen to preserve equivariance. Third, on 30 years of S&P 500 daily log-returns, SE-WaveNet samples reproduce the empirical scaling-collapse diagnostic on the Allan-Variance top-25 universe (median

\mathcal{C}^\star = 0.020

), while a vanilla WaveNet at matched capacity does not (

\geq 0.06

). NLL, KS-calibration, and tail energy distance tie or beat the baseline, with

L\times

fewer convolutional parameters.

Andrea Morandi

Cisco Systems, Inc.

Time Series Forecasting Equivariant Neural Networks Probabilistic Time Series Forecasting

May 15, 2026cs.AI

Prospective multi-pathogen disease forecasting using autonomous LLM-guided tree search

Probabilistic forecasting of infectious diseases is crucial for public health but relies on labor-intensive manual model curation by expert modeling teams. This bespoke development bottlenecks scalability to granular geographic resolutions or emerging pathogens. Here, we present an autonomous system using Large Language Model (LLM)-guided tree search to iteratively generate, evaluate, and optimize executable forecasting software. In a fully prospective, real-time evaluation during the 2025-2026 US respiratory season, the system autonomously discovered methodologically diverse models for influenza, COVID-19, and respiratory syncytial virus (RSV). Aggregating these machine-generated models yielded an ensemble that consistently matched or outperformed the gold-standard, human-curated Centers for Disease Control and Prevention (CDC) hub ensembles out-of-sample. The system successfully navigated data-scarce "cold start" scenarios for RSV. Moreover, controlled retrospective ablations revealed that optimizing log-scale distance metrics prevents reward hacking, while an automated judge-in-the-loop ensures structural fidelity to complex scientific theories. By autonomously translating epidemiological theory into accurate, transparent code, this framework overcomes the modeling labor bottleneck, enabling rapid deployment of expert-level disease forecasting at unprecedented scales.

Sarah Martinson, Michael P. Brenner, Martyna Plomecka +3

Google Research · School of Engineering and Applied Sciences, Harvard University · Google Deepmind +1

Epidemic Forecasting Large Language Model-Guided Optimization Spatiotemporal Forecasting Probabilistic Time Series Forecasting

May 14, 2026cs.LG

PRB-RUPFormer: A Recursive Unified Probabilistic Transformer for Residual PRB Forecasting

Accurate forecasting of residual Physical Resource Blocks (PRBs) is critical for proactive network slice provisioning, energy-efficient operation, and spectrum-aware decision making in cellular systems, where residual PRBs serve as a practical proxy for short- and medium-term spectrum availability. Existing PRB prediction methods typically rely only on historical PRB values and are trained independently per carrier or sector, limiting their ability to capture cross-carrier dependencies and providing no measure of forecast uncertainty. Moreover, point forecasts alone are insufficient for robust spectrum-aware control under highly variable traffic conditions. This paper proposes PRB-RUPFormer, a recursive unified probabilistic Transformer for residual PRB forecasting. The proposed model jointly processes multivariate KPI time series using temporal, seasonal, and carrier-aware embeddings, preserving inter-metric temporal coupling during recursive rollout and stabilizing long-horizon forecasting. A single shared model is trained across all carriers and sectors of an eNB, enabling efficient learning of joint traffic dynamics with low computational overhead. Forecast uncertainty is captured through quantile-based prediction intervals, providing confidence-aware estimates of future PRB availability. Evaluations on six months of commercial LTE network data from multiple U.S. locations demonstrate median MAE below 0.05 and hit probabilities above 0.80 for both one-day and seven-day recursive forecasts. These probabilistic predictions directly support spectrum-aware RAN functions such as dynamic carrier activation, congestion avoidance, and proactive spectrum sharing, making the proposed framework well-suited for dynamic spectrum access scenarios.

Saad Masrur, Yuxuan Jiang, Matti Hiltunen +2

AT&T RAN Technology, Bedminster, NJ · Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC

Multivariate Time Series Forecasting Wireless Communications Time Series Transformers Probabilistic Time Series Forecasting

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, 2026cs.CV

PixelFlowCast: Latent-Free Precipitation Nowcasting via Pixel Mean Flows

Precipitation nowcasting aims to forecast short-term radar echo sequences for extreme weather warning, where both prediction fidelity and inference efficiency are critical for real-world deployment. However, diffusion-based models, despite their strong generative capability, suffer from slow inference due to multi-step sampling trajectories, limiting their practical usability. Conditional Flow Matching (CFM) improves efficiency via straightened trajectories, but relies on latent space compression, which inevitably discards high-frequency physical details and degrades fine-grained prediction quality. To address these limitations, we propose PixelFlowCast, a two-stage probabilistic forecasting framework that achieves both high-efficiency and high-fidelity prediction without latent compression. Specifically, in the first stage, a deterministic model first produces coarse forecasts to capture global evolution trends. In the subsequent stage, the proposed KANCondNet extracts deep spatiotemporal evolution features to provide accurate conditional guidance. Based on this, a latent-free, few-step Pixel Mean Flows (PMF) predictor employs an

x

-prediction mechanism to generate high-quality predictions, effectively preserving fine-grained structures while maintaining fast inference. Experiments on the publicly available SEVIR dataset demonstrate that PixelFlowCast outperforms existing mainstream methods in both prediction accuracy and inference efficiency, particularly for long sequence forecasting, highlighting its strong potential for real-world operational deployment.

Yufeng Zhu, Chunlei Shi, Yongchao Feng +1

Precipitation Forecasting Efficient Inference Spatiotemporal Forecasting Precipitation Nowcasting Probabilistic 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 6, 2026stat.ML

Forecasting Oncology Demand Trends with Boosting-Based Bayesian Conjugate Models

Accurate trend forecasting in healthcare time series is essential for planning and resource allocation. This paper proposes a Bayesian framework for predicting oncology demand trends, modeling weekly appointments as a Poisson process with a Gamma prior to the demand rate. To enhance adaptability and capture persistent directional patterns, we incorporate a residual-based boosting mechanism grounded in a Gamma-Log-Normal conjugate structure. This boosting approach allows the model to track both short- and long-term trend shifts while maintaining the analytical tractability of conjugate Bayesian updating. The methodology was evaluated on real oncology service data from Cariri, Ceara, Brazil, and compared against established baselines, including linear regression, ARIMA, naive forecasting, LSTM neural networks, and XGBoost. Results showed that the proposed model outperforms competing methods in trend detection accuracy, with gains in terms of percentage of correct direction of 38.25% in relation to the second best approach in some cases.

Ademir Batista dos Santos Neto, Tiago Alessandro Espinola Ferreira, Paulo Renato Alves Firmino

Bayesian Inference Time Series Forecasting Oncology Probabilistic Time Series Forecasting

May 5, 2026cs.CV

Densification and forecasting of Sentinel-2 time series from multimodal SAR and Optical satellite data using deep generative models

Optical satellite image time series are extensively used in many Earth observation applications, including agriculture, climate monitoring, and land surface analysis. However, clouds and swath edges result in irregular sampling along the temporal dimension, limiting continuous monitoring. To address this issue, a growing body of work has focused on temporal densification and reconstruction of satellite image time series, with the objective of filling missing or cloud-contaminated observations within the temporal extent of the available data. While these approaches improve temporal continuity, they are inherently restricted to the reconstruction of the gaps within the observed time periods, and do not address the prediction of future observations. This work proposes a probabilistic deep learning framework for the densification and forecasting of Sentinel-2 time series by generating optical images at arbitrary past or future dates. The approach leverages multimodal satellite data by jointly exploiting Sentinel-2 optical and Sentinel-1 SAR observations. Unlike most existing works, we propose to focus on the uncertainty of the generated images. Experimental results demonstrate effective densification and forecasting, on sparse and temporally misaligned time series.

Véronique Defonte, Dawa Derksen, Alexandre Constantin +1

Thales Services Num´eriques 31670 Lab`ege, France · Centre National d’Etudes Spatiales 31400 Toulouse, France

Irregular Time-Series Modeling Remote Sensing Spatiotemporal Forecasting Probabilistic Time Series Forecasting

May 5, 2026stat.ML

Training-Free Probabilistic Time-Series Forecasting with Conformal Seasonal Pools

We propose Conformal Seasonal Pools (CSP), a training-free probabilistic time-series forecaster that mixes same-season empirical draws with signed residual draws around a seasonal naive forecast. In an audited rolling-origin benchmark on the six time-series datasets where DeepNPTS was originally evaluated (electricity, exchange_rate, solar_energy, taxi, traffic, wikipedia), CSP-Adaptive significantly outperforms DeepNPTS on every metric we report -- CRPS (per-window paired Wilcoxon

p \approx 4 \times 10^{-10}

), normalized mean quantile loss (

p \approx 7 \times 10^{-10}

), and empirical 95% coverage (

p \approx 8 \times 10^{-45}

, mean 0.89 vs 0.66) -- while running over 500x faster on CPU. Coverage is the most decision-critical of these: a 0.95 nominal interval that contains the truth in only ~66% of cases fails the basic calibration desideratum and would not survive deployment in safety- or decision-critical settings. The failure mode is also more severe than aggregate coverage suggests: in the worst 10% of windows, DeepNPTS's prediction interval covers none of the H forecast horizons -- the entire multi-step trajectory misses the truth at every step simultaneously. This poses serious risk in safety- and decision-critical applications such as healthcare, finance, energy operations, and autonomous systems, where prediction intervals that systematically miss the truth across the entire planning horizon translate directly into misclassified patients, regulatory capital failures, grid imbalances, and safety-case violations. CSP achieves all of this with no learned parameters and no training. We argue training-free conformal samplers should be mandatory baselines when evaluating learned non-parametric forecasters.

Valery Manokhin

Independent researcher.

Time Series Forecasting Conformal Prediction Probabilistic Time Series Forecasting

May 5, 2026cs.LG

Bi-Level Chaotic Fusion Based Graph Convolutional Network for Stock Market Prediction Interval

Financial market forecasting is inherently uncertain, yet most deep learning approaches rely on point predictions that provide only single-value estimates without quantifying uncertainty. Such predictions are insufficient for risk-aware decision-making, as they fail to capture the range of possible outcomes and the associated confidence of forecasts.The problem can be solved using prediction intervals, which allow obtaining an upper and lower bound for the prediction, thus enabling uncertainty representation in the model. Yet, the current methods tend to disregard relationships between assets or cannot simultaneously ensure good calibration and sharpness of the resulting intervals in dynamically changing market regimes. In our work, we propose a spatio-temporal graph-based approach with a bi-level chaotic fusion technique to solve this problem. Our model uses separate nonlinear transformation functions to estimate the interval center and width. Additionally, a volatility-aware gating mechanism is used to make predictions dependent on the regime in which the market operates. Temporal dependencies are considered by embedding graph structures and sequentially modeling them. Training is conducted according to a Lower-Upper Bound Estimation (LUBE) objective. Our experimental results show significant improvements compared to existing baselines (LSTM, GRU, GCN, HGNN) when applied to data from 2016 to 2026 with 43 leading companies in eight sectors of the NSE. It provides the lowest Winkler score (0.0778), tightest prediction intervals (PIAW = 0.1407), and highest coverage (PICP = 96.6%), with all differences statistically significant (p < 0.001) according to the Diebold-Mariano test.

Eshwar Sai Kandimalla, Sravan Chowdary Kankanala, Sumana Bhimineni +2

Department of Computer Science & Engineering, SRM University AP, India

Financial Forecasting Financial Time Series Finance Probabilistic Time Series Forecasting Spatiotemporal GNNs Regression Prediction Intervals