Time Series Modeling

Follow this topic Ask about this topic

Latest papers

48 papers12 papers in the last four weeks, up 71% on the four weeks before. 0.1% of all new papers.

Oct 16, 2026

Towards a GraphNARX model for structural dynamics

The current paper introduces the GraphNARX model, a graph-based nonlinear autoregressive exogenous model for structural dynamics. The model is built to account for the geometry of structures and to model dynamic behaviour as the interaction between elements of the structure. Similar to other types of NARX models, GraphNARX is used for system identification. Nodal attributes of the graph encode past displacements and nodal forces, and the output of the model is the next-timestep displacement. The graph formulation of the model allows it to generalise to structures of different dimensions and degrees of freedom. Moreover, because graph-learning is performed locally between the nodes, the GraphNARX model can also learn to infer displacements of nodes for which data are not available, i.e.\ to perform virtual sensing. The proposed model's performance is evaluated in a system-identification framework and a virtual-sensing framework, and achieves good accuracy and exhibits generalisation capabilities to structures of different sizes.

George Tsialiamanis, Keith Worden

Dynamics Research Group, School of Mechanical, Aerospace, and Civil Engineering, University of Sheffield, Sheffield, Mappin St, Sheffield, United Kingdom

Nonlinear System Identification Time Series Modeling Spatiotemporal GNNs Structural Mechanics Virtual Sensing

Oct 14, 2026

Time-partitioning Gaussian Process Mixture Model

Nonstationarity and heterogeneous dynamics are common in financial and macroeconomic time series. Volatility alternates between calm and turbulent regimes, interest rates follow monetary-policy cycles, and major events trigger persistent structural shifts. We propose the Time-partitioning Gaussian Process Mixture Model (TPGPMM), a Bayesian nonparametric framework for regime identification and nonstationary prediction that infers such regimes and their within-regime dependence from data, without Markovian assumptions. It combines (i) an adaptive Pitman-Yor process prior on ordered compositions, mapped to block lengths with contiguity enforced by construction, and (ii) regime-specific Gaussian processes for temporal dependence, yielding a nonstationary predictive distribution. By inferring its discount parameter, the prior adapts to homogeneous and highly heterogeneous regime lengths. Unlike sequential or Markov-switching methods, it flags persistent structural shifts as change points rather than reacting to transient shocks. A split-merge Metropolis-within-Gibbs sampler with exact Gibbs updates of regime boundaries jointly learns change points and hyperparameters in batch, quantifying uncertainty over the partition and within-regime dynamics. With an RBF kernel and a fixed, data-informed noise level, TPGPMM produces a sparse, confident segmentation. On simulated data it recovers the true regimes, and on the CBOE Volatility Index and the 10-year US Treasury yield it identifies regimes aligned with documented market and monetary-policy events. For prediction, variants estimating the noise level fit better than change-point baselines and fit and forecast better than the main specification, at the cost of a less sparse or less event-aligned segmentation; with a regime mean, they fit better than a fitted stationary Gaussian process and have lower forecast RMSE except at the shortest horizons.

Guilherme Piantino, Hedibert F. Lopes

Insper Institute of Education and Research, São Paulo

Time Series Modeling Non-Stationary Time Series Change-Point Detection Gaussian Processes Bayesian Inference

Oct 14, 2026

CTIA-ODE: Continuous-Time Inter-Variable Attention for Long-Term Time Series Forecasting

Although multivariate time series forecasting has broad application prospects, effectively incorporating exogenous variables remains challenging. Prevailing discrete-time architectures often impose rigid temporal alignment across heterogeneous variables, which may limit their ability to capture continuously evolving external effects. To address this limitation, we introduce CTIA-ODE, a continuous-time forecasting framework centered on Continuous-Time Inter-Variable Attention (CTIA). Specifically, CTIA is embedded within an ordinary differential equation (ODE) solver, enabling the continuously evolving endogenous trajectory to dynamically query a static exogenous context along the integration path without requiring explicit temporal alignment. To improve the stability of the continuous latent dynamics, we further introduce a dual-stabilization strategy: architecturally, a Linear Residual Augmentation (LRA) module provides a macroscopic trend anchor, while an Outlier-Robust Hybrid Loss (ORHL) mitigates the influence of heavy-tailed anomalies during optimization. Extensive experiments across eight real-world datasets demonstrate that CTIA-ODE achieves state-of-the-art forecasting performance across diverse datasets and prediction horizons, while maintaining a favorable accuracy-efficiency trade-off with a compact memory footprint and low inference latency, particularly under long-horizon forecasting settings. Anonymous code is available at https://anonymous.4open.science/r/CTIA-ODE-15A6/.

Chengyi Pan, Huangqimei Zheng, Hao Xue

UGOD, HKUST-GZ · School of Software, Yunnan University · UGOD, The Hong Kong University of Science and Technology (Guangzhou)

Time Series Modeling Exogenous Time Series Forecasting Time Series Forecasting Multivariate Time Series Forecasting Long-Term Time Series Forecasting Neural ODEs

Oct 12, 2026

ChronoScribe: Semantic-Numerical Specialization for Instruction-Driven Time Series Forecasting

Recent advances in instruction-driven time series forecasting highlight a fundamental tension: systems must simultaneously master natural-language instruction following and precise numerical prediction. Current approaches often force a compromise. Large language models (LLMs) can interpret unstructured requests but may be inaccurate when asked to produce forecast values directly, whereas time series foundation models (TSFMs) provide numerical forecasts but typically require structured inputs specifying the target series, context window, and horizon. We present ChronoScribe, which applies semantic-numerical specialization to this workflow. A LoRA-adapted LLM proposes an execution path and context length; deterministic rules resolve the executable configuration. On the specialist path, a frozen TSFM produces quantile trajectories for the task-specified horizon. Deterministic trajectory summaries condition the response, while the LLM neither generates nor revises predicted values. We evaluate a Qwen3.5-9B--Chronos-2 implementation across 23 evaluation dimensions and 30 public datasets against eleven proprietary direct LLMs and three open TSFMs. ChronoScribe has the lowest error on sMAPE, MASE, WAPE, RMSE, and MAE among all evaluated systems, including fixed-context controls. Across these metrics, even the lowest direct-LLM error remains 2.0--2.7 times the corresponding ChronoScribe error. At the system level, ChronoScribe achieves a Task-Level Score (TLS) of 65.5, 10.6 points above the strongest direct-LLM baseline. The results support ChronoScribe's division of labor, in which the LLM handles interpretation, configuration, and communication while the TSFM handles numerical forecasting.

Yuchen Jiao, Miao Zhang, Yuxuan Liu +1

Beijing University of Posts and Telecommunications

Time Series Forecasting LLM-Based Time Series Forecasting Time Series Modeling Time-Series Foundation Models

Oct 7, 2026

Temporal Predictive Multiplicity: Equally Accurate Time Series Models Yield Different Forecast Trajectories

Models with near-identical predictive performance can yield substantially different predictions, a phenomenon known as predictive multiplicity. Prior work has mostly studied this at the level of individual scalar outputs. In time-series forecasting, however, predictions across horizons jointly define a trajectory, and horizon-wise comparisons can hide important differences in predictive behavior. To address this problem, we introduce temporal predictive multiplicity, a framework that characterizes disagreement over complete forecast trajectories among models with near-identical predictive performance. We show that constraining predictive performance alone can still admit a broad range of different trajectories. We further show that constraining multiplicity at individual horizons partially reduces, but does not eliminate, trajectory-level multiplicity. Experiments with 19 neural forecasting architectures on 11 datasets confirm that near-optimal models can exhibit substantial variability in the forecast trajectories they produce, and trajectory-level disagreement is largely unrelated to horizon-wise disagreement. Our framework, therefore, exposes a gap in existing multiplicity studies: models with indistinguishable predictive performance imply fundamentally different temporal trajectories, with consequential downstream effects.

Emanuele Albini, Francesca Toni, Saumitra Mishra +1

J.P. Morgan AI Research Imperial College London London, UK · Imperial College London London, UK · J.P. Morgan AI Research London, UK

Time Series Forecasting Time Series Modeling

Oct 5, 2026

StaFIR: Convex Learning of Stationarity-Aware Causal Filters

Reducing nonstationarity in a persistent time series entails deciding how much of its temporal dependence to remove. In finance, fractional differencing is often tuned using the Augmented Dickey--Fuller (ADF) test, limiting the search to a one-parameter family of lag profiles and addressing input preservation only indirectly. We propose StaFIR, a causal finite-impulse-response filter with a learned nonnegative mixture of exponential lag profiles. Its convex learning objective balances empirical stationarity with similarity to the input. We evaluate StaFIR on ARFIMA--GARCH controlled settings and rolling financial series, including a realized-volatility forecasting task. The experiments show that StaFIR adjusts its filtering strength to persistence while limiting unnecessary transformation in stationary regimes. In downstream forecasting, there is no clear accuracy difference from fixed half-order differencing, while StaFIR achieves higher measured similarity to the raw signal. A complementary direct forecasting experiment finds that greater input similarity is associated with smaller forecasting penalties, although the raw representation remains stronger.

Lorena Egger, Mathis Linger

Drakai Capital Paris

Time Series Forecasting Financial Time Series Non-Stationary Time Series Time Series Modeling

Sep 30, 2026

OpenTSLM TeeMoE: A Unified Time-Series Language Model for Forecasting, Contextual Prediction, and Reasoning

Real-world time-series applications increasingly require models that can handle time series forecasting, context-conditioned prediction, and language-based temporal reasoning. Yet current time-series foundation models remain fragmented across these capabilities: numerical specialists often provide the strongest forecasts, while language-based models offer broader contextual understanding and analysis. A central challenge is to unify these heterogeneous capabilities without reducing their individual performance. We introduce OpenTSLM TeeMoE, a generalist time-series language model that can forecast directly from observed time series, reason over textual context and temporal patterns, and synthesize and refine predictions from external numerical forecasting specialists. We independently train three low-rank experts for forecast aggregation, native forecasting, and temporal analysis over a shared backbone. A learned LoRA mixture-of-experts controller then weights their frozen parameter updates for each request. Our proposed model achieves strong performance on widely used benchmarks for time series forecasting, context-conditioned prediction, and language-based temporal reasoning, ranking among the top three on GIFT-Eval by mean MASE rank, Context is Key by RCRPS, and TimeSeriesExam by accuracy.

Tony Chen, Timo Stoffregen, Maxwell Xu +8

Columbia University, USA · Stanford University, USA · Aionic Labs, Switzerland +4

Temporal Reasoning in Language Models LLM-Based Time Series Forecasting Mixture-of-Experts Models Time-Series Foundation Models Time Series Forecasting Time Series Modeling+2

Sep 29, 2026

ZeroDiff: Zero-Shot Time Series Reconstruction via Informed-Prior Diffusion

Time series modeling increasingly demands high-quality supervision, yet target observations remain scarce - exogenous inputs are broadly available, but target measurements are often unavailable due to cost, infrastructure, or accessibility constraints. Can models trained on observed locations reconstruct target time series where measurements have never been collected? We term this zero-shot time series reconstruction. A naive approach - directly mapping exogenous inputs to targets - can yield predictions at unobserved locations, but without target signals, such models fail to capture the intrinsic dynamics of the target variable, producing overly smooth outputs that underestimate extremes. This reveals systematic errors that call for explicit modeling and calibration. We propose ZeroDiff, which constructs an informed prior from exogenous variables alone, then learns to calibrate reconstruction errors through diffusion - training on observed locations and generalizing to unobserved ones. Experiments across diverse real-world datasets demonstrate significant improvements over existing approaches. Our code is available at https://github.com/YingdaFan/ZeroDiff-ICML2026.

Yingda Fan, Dan Lu, Xiaowei Jia

Department of Computer Science, University of Pittsburgh, Pittsburgh, PA, USA · Oak Ridge National Laboratory, Oak Ridge, TN, USA

Time Series Modeling Diffusion Models

Sep 28, 2026

Dynamical Parameters: An Interpretability Framework for Time-Series Foundation Models

This work studies a central gap in interpreting time-series foundation models (TSFMs): a dynamical property may be accessible in a hidden state even when the forecast fails to respond correctly as that property changes. We formalize these properties as Dynamical Parameters, including trend slope, oscillation frequency, and autoregressive dependence. We compare their representation accessibility, measured by recovery from hidden states, with their forecast response, measured by agreement with the expected forecast change. Across nine frozen TSFMs and thirteen laws, 42 of 63 model-parameter cells achieve accessibility above 0.95, whereas their median reference-aligned response relative to the conditional reference is only 0.46. To explain this gap, causal geometry compares the hidden-state change required to produce the reference response with the change induced by the parameter intervention. Directly modifying the hidden state recovers the reference response, but the parameter intervention often moves the state in a different direction. These results show that accessible parameter information need not be expressed in forecasts when input changes miss the required hidden-state direction.

Kang Yang, Gaofeng Dong, Liying Han +1

Department of Electrical and Computer Engineering University of California, Los Angeles

Explainable Time Series Forecasting Representation Probing Time Series Representation Learning Time-Series Foundation Models Time Series Modeling

Sep 27, 2026

Correct then Forecast: Observer State-Space Models for Time Series Forecasting

Time series forecasting requires extrapolating the dynamics of an observed process beyond the last available measurement. Yet recurrent forecasting models typically treat observations as inputs that directly control their latent dynamics. It leads to a regime change when these observations become unavailable at prediction time. Following a state-estimation perspective, we introduce Observer State-Space Models (OSSMs), a class of recurrent models that interprets the observed input time series as measurements of an underlying autonomous dynamical system. OSSMs explicitly separate latent-state propagation from measurement assimilation: a single transition governs the dynamics across both context and forecasting intervals, while available observations correct the estimated state through an observer. This formulation naturally exposes classical control-theoretic properties, including observability and convergence of the state estimation error. We further show that conventional and recent SSMs can be recovered as particular instances of our OSSM framework, thereby providing a unified interpretation of their recurrent dynamics and revealing modeling inconsistencies. We perform experiments across several benchmarks showing that OSSM achieves substantial improvements while maintaining the same parameter count and training setup as the corresponding SSM baseline. These results support a simple principle for recurrent forecasting: observations should correct the estimated latent state, rather than control the dynamics used to propagate it.

Alexis-Raja Brachet, Guillaume Clavier--Frémond, Abdelhakim Ziani +2

MICS, CentraleSup´elec, Universit´e Paris-Saclay, France · CentraleSup´elec, IETR UMR CNRS 6164, France · Universit`a di Torino, Torino, Italy.

Latent Dynamics Modeling Time Series Forecasting State Space Models Time Series Modeling

Sep 27, 2026

DrafTS: Time-Aware Decomposition with Residual Correction for Time Series Modeling

Real-world time series contain evolving underlying dynamics with irregular variations that lack stable temporal patterns and are often referred to as noise. Existing methods address this mixture by filtering frequencies or suppressing noisy observations. They either miss temporal evolution or risk suppressing useful dynamics. We propose DrafTS, a model-agnostic framework that aims to reduce noise while preserving evolving dynamics through time-aware Decomposition with ResiduAl correction For Time Series. DrafTS uses features derived from instantaneous amplitude and frequency to guide decomposition into a primary component intended to capture underlying dynamics. A task-specific backbone models the primary component, while a lightweight correction module uses residual information to correct the backbone output. Across four time series modeling tasks, DrafTS improves six diverse backbones, demonstrating its effectiveness. Code is at https://github.com/Autumn61q/DrafTS

Yiqiu Liu, Siru Zhong, Zhiguang Wang +2

The Hong Kong University of Science and Technology (Guangzhou), China · Abel AI Lab, USA · Squirrel Ai Learning, USA

Time Series Decomposition Non-Stationary Time Series Time Series Modeling

Sep 25, 2026

EXAONE Demand 1.0: A Time Series Foundation Model for Demand Forecasting

Time series foundation models (TSFMs) are pretrained on series from diverse domains, where demand series make up only a small fraction. Demand data has properties that such corpora rarely contain: Short histories, frequent zeros, censoring by stock-outs, and exogenous events that the series does not record. To this end, we propose EXAONE Demand, built on 1) a demand-specific corpus and 2) a demand-aware adapter. For the corpus, we assemble 11.3M series and 48.4B observations from 73 sources, and a synthetic generator supplies the behaviour that open demand data under-represents. For the adapter, we attach low-rank branches to a frozen general-domain backbone, one for each of the four demand classes (smooth, intermittent, erratic, and lumpy), and a router that reads eight scale-free statistics of the input series decides how much each branch contributes. We build EXAONE Demand in two versions, one trained on real-world and synthetic demand together and one trained on the synthetic corpus alone. On 22 held-out datasets, both versions outperform 36 TSFMs, and real-world demand adds a gain over synthetic data alone.

Seunghan Lee, Sangjun Han, Jun Seo +9

LG AI Research

Time Series Forecasting Time Series Modeling Time-Series Foundation Models

Sep 23, 2026

Forecast Workflow Bench: Evaluating Language-Model Decisions with Budgeted Forecast Tools

Time-series foundation models (TSFMs) provide forecasts for operational decisions, but accuracy alone does not determine their value. Evaluating agents that use these models requires measuring decision quality and forecast cost. FWBench evaluates this capability on 1,251 electricity and cycle-hire cases using fixed forecast tools and simulated capacity contracts. Agents select models, histories and horizons, then submit capacities to minimize a stated loss-cost objective. We evaluated two hosted and eight local configurations, including small language models, and tested local models with and without TSFMs. GPT-6 Astra bought inexpensive short-horizon forecasts selectively, using 2.5% of the budget, and outperformed fixed policies when the saved decisions were scored with three loss-cost weightings. FWBench enables reproducible evaluation of how language models select and use time-series forecasts to make decisions under cost constraints.

Shunya Nagashima

Neurogica Inc.

Forecasting Benchmarks LLM Tool Use Time-Series Foundation Models Time Series Modeling

Sep 20, 2026

Leaky-integrator reconstruction: taming error accumulation in recursive differenced time-series forecasting

Recursive differenced forecasting, the standard remedy for non-stationarity, predicts one-step changes and integrates them by cumulative summation. We show that this reconstruction is a discrete integrator with a pole on the unit circle, so the biased increment errors of a learned nonlinear model are summed without bound and the rollout diverges: at 336 steps its normalised MAE reaches 1.6-3.8 for every neural architecture tested, against 0.80 for a stable linear recursion. We then introduce leaky-integrator reconstruction, a training-free fix that moves the pole inside the unit circle with H(z) = 1/(1 - gamma z^-1), gamma < 1, bounding the accumulation of the model's own increment errors. Applied post hoc with a single fixed gamma=0.9 (no retraining, a two-line change to any deployed one-step or foundation-model forecaster), it beats the traditional recursive integrator at every horizon, with the mean gain over seven diverging architectures and twenty datasets growing from ~3% at H=24 to 23% at H=96, 37% at H=192 and 51% at H=336 (43-75% across those architectures; 78% with an oracle pole), bringing all of them to 0.87-0.97. Based on these extensive empirical experiments, adding a leaky integrator thus improves recursive differenced time-series forecasting.

Zijiang Yang

New York University, Tandon School of Engineering, Brooklyn, NY 11201

Time Series Forecasting Time Series Modeling Non-Stationary Time Series Forecasting

Sep 15, 2026

SOTER: A Generative Time-Series Foundation Model for Wearable Human Physiological Signals

Time-series foundation models have demonstrated strong cross-domain transfer, yet their common architectural assumptions remain poorly aligned with wearable physiological signals, which are multichannel, irregularly sampled, noisy, and governed by coupled continuous-time dynamics spanning distinct spectral scales. We present SOTER, a generative foundation model for wearable physiological time series that unifies cross-channel coupling, spectrum-guided expert specialization, and continuous-time latent evolution within a single pre-training framework. SOTER combines a spatial feature-aware backbone that models inter-signal dependencies, a power spectral density (PSD)-guided mixture-of-experts layer that routes representations to experts associated with fixed spectral bands through an inspectable, non-learned rule, and a neural controlled differential equation decoder that supports prediction and imputation at arbitrary timestamps. We pre-train SOTER on 226 billion time points from five public physiological datasets and evaluate the same pre-trained model across out-of-distribution zero-shot forecasting, frozen-encoder linear-probe classification, and continuous-time imputation on wearable benchmarks. SOTER achieves the best RMSE on 4 of 6 datasets and the best MAE on 5 of 6 in zero-shot forecasting, the highest average Macro-AUROC in classification, and the lowest imputation error on all six datasets at 75% missingness. It further remains robust to additive acquisition noise, matching or surpassing baselines evaluated on clean inputs even under the strongest corruption. These results indicate that domain-specialized foundation models for wearable physiology benefit from jointly modeling channel structure, spectral scale, and continuous-time dynamics.

Fangke Chen, Sirry Chen, Wei Chen +1

School of Integrated Circuits, Zhejiang University Hangzhou, China · Shanghai Innovation Institute Shanghai, China · School of Data Science, Fudan University Shanghai, China +1

Irregular Time-Series Modeling Time Series Imputation Zero-Shot Time Series Forecasting Time Series Modeling Wearable Health Monitoring Time-Series Foundation Models

Sep 14, 2026

Parameter-Efficient Adaptation of Pretrained Language Models for Time-Series Forecasting

We study the adaptation of pretrained language models to univariate time-series forecasting through a parameter-efficient transfer learning framework, with the goal of understanding which design choices drive effective cross-modal transfer. While language models operate on discrete textual tokens, time series consist of continuous numerical observations with temporal dependencies. To bridge this modality gap, we project fixed-length time-series patches directly into the embedding space of a pretrained GPT-2 backbone, bypassing textual tokenization and treating the Transformer as a generic sequence encoder. Through controlled ablation studies on seven benchmark datasets spanning energy, weather, traffic, and finance, we analyze the effects of (i)~representation strategy (continuous embeddings versus textual serialisation), (ii)~adaptation regime (frozen backbone versus partial or full fine-tuning), (iii)~architectural components such as adapters, pooling strategies, and prediction heads, and (iv)~input context length. Continuous patch-based embeddings consistently outperform textual prompting and randomly initialised backbones. The adapted pipeline attains MASE within the range of specialised forecasting architectures while updating less than 1% of total model parameters. Results further indicate that freezing the pretrained backbone and training lightweight projection and adapter modules provides a favourable accuracy--efficiency trade-off with stable behaviour across varying context lengths.

Tamanna Kumavat, Georg Brunner, Kyriakos Flouris

University of Zurich, Switzerland · Computer Vision Laboratory, ETH Zurich, Switzerland · MRC Biostatistics Unit, University of Cambridge, United Kingdom

Time Series Forecasting LLM-Based Time Series Forecasting Parameter-Efficient Fine-Tuning Time Series Modeling

Sep 11, 2026

Rolling Day-Wise Mortality Prediction in Critically Ill Patients With AKI on CRRT Utilizing Machine Pressure Waveforms

Critically ill patients with acute kidney injury (AKI) on continuous renal replacement therapy (CRRT) face high mortality, yet current risk assessment relies primarily on clinical parameters from electronic health records (EHR) and ignores minute-level circuit pressure waveforms generated by CRRT machines that track the extracorporeal circuit's interaction with the patient. Clinicians therefore cannot see deterioration as it develops. Risk is reassessed only when labs are drawn, while this continuous record is discarded because it is contaminated by shared-device records, non-physiological minutes, and sensor artifacts. To make the stream usable, we aligned machine records to charted therapy intervals to prevent cross-patient leakage, removed priming and downtime minutes, tuned denoising on a synthetic spike-injection benchmark, and masked unobserved intervals rather than imputing them. On this cleaned stream, we define a rolling day-wise task and a transformer-based stacked ensemble that late-fuses a window-reduced sequence transformer with classical models using circuit-instability features and clinical EHR variables. In a leak-safe benchmark on the multi-center CRRTnet cohort (976 patients, 4,585 treatment days), the machine-only model had the lowest standalone prognostic value (AUROC 0.625), followed by the EHR-only model (0.717). Integrating EHR and machine streams reached a one-day mortality AUROC of 0.766. SHAP attribution showed that circuit-instability descriptors raised the machine share of the top 15 combined-model features from 3 to 7 (20.0% to 46.7%), highlighting filter pressure, transmembrane pressure (TMP), and access-to-return difference (ARD). To our knowledge, this is the first patient-level mortality prediction incorporating CRRT machine data, turning a discarded bedside stream into a continuous risk signal.

Shehan Irteza Pranto, Joanna Yang, Joshua Lambert +6

Department of Biomedical Informatics and Data Science, University of Alabama at Birmingham, AL, USA · Windreich Department of Artificial Intelligence and Human Health at the Icahn School of Medicine at Mount Sinai, New York, NY, USA · College of Nursing, University of Cincinnati, OH, USA +4

Time Series Modeling Mortality Prediction Healthcare

Sep 11, 2026

Explaining Time Series Forecasting with Horizon-Resolved Attribution

Recent advances in explaining time series (TS) models have produced methods that identify which past values a prediction depends on. However, most existing methods return a single importance vector, assuming that every predicted step depends on the same past values. In this paper, we show that this assumption does not hold, as different forecast steps depend on different past values. Motivated by this observation, we propose Horizon-Resolved eXplanation (HRX), which adds a horizon axis to the explanation, so that every forecast step receives its own importance map. HRX is a simple yet effective plug-in framework with three components: 1) an estimator that reads these maps out of any differentiable forecaster without modifying the TS backbone, 2) an evaluation protocol that validates the horizon axis by measuring how much a single forecast step changes when the inputs an importance map ranks highest are removed, and 3) a rank criterion that predicts in advance whether the axis is worth resolving on a given TS. We further show that this step-wise dependence is low-dimensional, as the explanations of all steps are built from a few shared maps whose number does not grow with the forecast length. Extensive experiments across various backbones and datasets show that the improvement comes from the horizon axis and holds for estimators of previous explanation methods. Code is available at https://github.com/seunghan96/HRX.

Seunghan Lee, Jun Seo, Jaehoon Lee +9

LG AI Research

Explainable Time Series Forecasting Feature Attribution Explainable Artificial Intelligence Time Series Forecasting Time Series Modeling

Sep 5, 2026

Cadence: Error-Bounded Lossy Compression of Demand Time Series with a Time-Series Foundation Model

We present Cadence, an error-bounded lossy compressor for numeric time series pairing a 330M-parameter time-series foundation model (Google TimesFM-3) with an adaptive arithmetic coder, guaranteeing

|\hat{x}_t-x_t|\leτ

on every sample. One negative result constrains the design space: for lossless coding a foundation model is worth nothing, because bits saved are logarithmic in predictor accuracy,

Δb=\log_2(\mathrm{MAE_{old}}/\mathrm{MAE_{new}})

. So the

1.51\times

advantage TimesFM-3 holds over a 32-tap linear predictor buys 0.60 bits of 20.28, a median gain of +0.03%. Error-bounded coding escapes this at one point: once a forecast lands inside the band the residual index is zero and the sample nearly free. Cadence contributes: (1) an adaptive range coder with context-modelled binarization, beating xz/zstd on real indices by 9.7% (15/15) and reversing a finding from a general-purpose back end; (2) a determinism result -- predictions are not bit-identical across batch sizes, and no PyTorch configuration repairs this, forcing group size and execution device into the container format; and (3) domain localization on corpora postdating any plausible training cutoff. On 49 EIA-930 balancing-authority demand series (2026) Cadence gains 13.3% over the best of six classical predictors, and 28.3% on 50 MTA ridership series (2026): 21.4% median over 297 series-tolerance pairs, winning all 297. Against downsampling, what time-series databases deploy for retention, its guaranteed worst-case error is

28

--

56\times

tighter at equal size. End-to-end, once the context bootstrap is paid for, gains run from 6.8% at six months of hourly data to 15.1% asymptotically. Attempting to falsify the domain claim on SDRBench, theory predicts failure and delivers: -0.8% median, 0 of 27 pairs gaining. Three further negative results and eight retracted claims are reported in full.

Roberto Tacconelli

Independent Researcher

Predictive Coding Time Series Modeling Entropy Coding Time-Series Foundation Models

Aug 31, 2026

Liquid Gated Attention

Real-world time series often exhibit irregular sampling and extended temporal horizons, requiring models to capture continuous-time dynamics across arbitrary intervals without prohibitive scaling costs. Discrete-time methods collapse variable time intervals into static positional steps; solver-dependent continuous-time models preserve temporal structure but rely on sequential integration, precluding parallelization; and solver-free approximations avoid this cost yet none couples observed time intervals with input-driven state modulation. We propose Liquid Gated Attention (LGA), a solver-free parallel temporal operator. By parameterizing an input-driven gating mechanism with observed time intervals, LGA introduces a continuous-time inductive bias and formulates hidden state evolution as a fast-weight associative memory, enabling parallel computation across the temporal dimension. Using matrix associativity in non-causal encoding and a prefix scan in causal encoding, LGA attains linear temporal complexity in sequence length in both modes. A sequence-level normalization bounds cumulative temporal decay for stable long-horizon optimization. Building on LGA, we instantiate LFormer, a modular backbone for continuous-time representation learning. Across six tasks and sixteen datasets spanning up to 17,984 steps, LFormer demonstrates long-range dependency modeling, fine-grained state tracking, and trajectory reconstruction from sparse and noisy observations, while delivering competitive performance against state-of-the-art discrete-time and continuous-time baselines with linear scaling efficiency.

Yiheng Jiang, Yuanbo Xu, Yongjian Yang

Mobile Intelligent Computing Laboratory, College of Computer Science and Technology, Jilin University, China

Gated Attention Time Series Modeling Linear Attention Temporal Attention Time Series Representation Learning

Aug 28, 2026

Learning to Difference: Adaptive Reversible Differencing (AdaRDiff) for Time Series Forecasting

Reliable long-horizon time series forecasting is an important yet difficult problem. Trends and seasonality introduce complex temporal structure that challenges learning-based forecasting models. Differencing, which subtracts nearby past values to remove such structure, is the classical remedy, but its reliance on hand-picked orders and periods has kept it largely absent from recent deep architectures. We propose Adaptive Reversible Differencing (AdaRDiff), a generalized differencing approach that uses learnable weights to simplify the series through weighted differencing with previous time instants. This yields stabilized residuals on which forecasting is performed, after which the removed components are restored autoregressively to reconstruct the forecast, capturing trend and seasonality jointly through a single operator. This reconstruction admits a closed-form convolutional expression, which parallelizes on GPU and yields up to

33.7\times

speedup over the naive recurrence. We furthermore rely on a two-phase training schedule that separates temporal structure discovery from reconstruction learning, as suggested by a theoretical analysis of the gradient when using a linear forecasting model. AdaRDiff attains state-of-the-art forecast accuracy across eight benchmarks spanning electricity, weather, traffic, and energy, at negligible parameter cost. Furthermore, it is designed as a plug-and-play module: integrating AdaRDiff improves eight diverse backbones, from linear models to Transformers, in the large majority of cases, by up to

25.9\%

with a linear backbone and

18.3\%

with iTransformer.

Morad Laglil, Younes Hlal, Marouane El Hadari +2

Univ. Grenoble Alpes, CNRS, Grenoble INP, LIG, 38000 Grenoble, France · Savoye, 21600 Longvic, France

Time Series Forecasting Long-Term Time Series Forecasting Time Series Modeling Multivariate Time Series Forecasting

Aug 25, 2026

Causal Analysis for Time Series Foundation Models

Transitioning from bespoke time series models towards time series foundation models changes the relationship of model and application from one-to-one to one-to-many. This shift introduces concentration risk as many, potentially high-risk, forecasting applications are exposed to the same biases and failure modes of a single time series foundation model. At the same time, this centralization allows for economies of scale in model development and validation. In this study we investigate how biases and failure modes of time series foundation models can be identified before deployment. We propose a causal analysis framework to investigate the ability of a time series foundation model to preserve time series patterns. To achieve this, we intervene on parameterized synthetic time series generators and measure the corresponding change in model output under ceteris paribus conditions. We apply our causal analysis framework to Chronos-2 and TimesFM-2.5 and test them across six distinct time series patterns. We find safe configurations for trend and harmonic oscillation patterns. The results also indicate a bias in both models towards overestimating persistence, sudden failures for both models against the regime switch pattern and failure for TimesFM-2.5 against the energy-release pattern. Our review of the original works for both models indicates that the findings might be explained by the data used for pretraining. We conclude our study with suggestions for further model development, recommendations for application-specific model selection, and a discussion of limitations and further research directions.

Mathis Jander, Wouter van Heeswijk, Martijn Mes

Faculty of Behavioral, Management and Social Sciences, University of Twente, Enschede, Netherlands · European Central Bank, Frankfurt am Main, Germany

Time-Series Foundation Models Time Series Modeling Time Series Forecasting

Aug 19, 2026

Lévy Attention: Single-Pass Predictive Uncertainty for Continuous-Time Attention

Deep models for irregularly-sampled time series answer queries at arbitrary continuous timestamps, yet report nothing about how far each answer should be trusted. We show the attention layer itself can close that gap: with the right stochastic formulation, the pass that makes each prediction also reports, in closed form and at no extra cost, how far it should be trusted. We introduce Lévy Attention, a cross-attention operator whose output is a stochastic integral against an inhomogeneous Poisson random measure: query-key compatibilities assemble an intensity over a continuous (time x channel) index space, the measure scatters atoms under it, and the output averages an interpolated value field at those atoms. In expectation it reduces to a mollified cosine-kernel attention, so it replaces a softmax layer and trains with exact gradients. What softmax discards, the Poisson construction preserves in closed form: the evidence

Λ_q

(total compatibility mass) and the disagreement

\mathrm{tr}\,Σ_V(q)

(value spread). An exact variance identity makes their combination

\hatσ(q)=\sqrt{\mathrm{tr}\,Σ_V(q)\,\varphi(Λ_q)}

the root-mean-square deviation of the sampled operator, emitted by the deterministic pass with no trained head. Empirically, disagreement carries the signal, while the evidence factor swings from uninformative on dense data to strongly informative on sparse. On t-PatchGNN the operator swap costs at most 5.6% accuracy against a matched control and nothing on the sparsest dataset. The free disagreement signal improves on 20-pass MC dropout across matched five-seed suites, and

\hatσ

scales a calibrated Gaussian whose zero-sample CRPS beats a fifty-draw sampler; a split-conformal wrapper reaches nominal coverage at every level, and one pass ranks 3,383 unseen patients by trust in 1.4 seconds.

Sotirios P. Chatzis, Loukas Papadoulas

GenML Laboratory, Department of Electrical Engineering and Computer Science and Engineering, Cyprus University of Technology, Limassol, Cyprus · Ethical AI Novelties, Cyprus

Time Series Modeling Uncertainty Quantification Cross-Attention

Aug 6, 2026

Scalable estimation of VARMA models

Vector autoregressive moving-average (VARMA) models have long been considered impractical beyond moderate dimensions: the likelihood is non-convex, the parametrization is identified only up to equivalence, and every evaluation costs a pass over the entire series. Yet their moving-average term captures with a few parameters what a pure autoregression matches only with many lags. We introduce an estimation framework that removes this computational barrier: each optimization iteration is independent of the series length

T

. The framework combines a partial-autocorrelation reparametrization that guarantees stationarity and invertibility by construction, Gaussian priors on the reparametrized coefficients with separate scales for diagonal and off-diagonal entries, and losses that depend on the data only through fixed-size sufficient statistics, evaluated by a Parseval (Fourier) identity at near-linear cost in the truncation length. This yields two point estimators: a regularized least-squares fit and a covariance-marginalized maximum-a-posteriori estimator. We prove that both recover the infinite-autoregressive representation of the true process at a near-parametric rate in fixed dimension, so the truncation introduces no asymptotic bias. The same machinery extends, at the same leading cost, to seasonal dynamics, exogenous regressors (VARMAX), and rolling-window refits. Empirically, the estimators stay close to the oracle forecast error from

d=10

to

d=40

(where classical conditional MLE returns non-invertible fits whose forecasts diverge) and match or beat VAR, Bayesian-VAR, component-wise ARMA, and sparse-VARMA baselines on retail-demand, meteorological, and air-quality data. This brings likelihood-based VARMA estimation, at a per-iteration cost independent of the series length, to the problem sizes where practitioners have so far relied on VAR models.

Daniel Paulin, Victor Elvira

College of Computing & Data Science Nanyang Technological University Singapore · School of Mathematics University of Edinburgh Edinburgh, UK

Multivariate Time Series Forecasting Parameter Estimation Time Series Modeling

Aug 3, 2026

ReasonCast: Towards Explainable Time Series Forecasting with Reasoning

Most time series (TS) models are specialized for a single task, either understanding (i.e., returning text answers about a TS) or generation (i.e., returning a numeric forecast). Only recently have unified models begun to handle the two within a single architecture. Even these models, however, produce the two outputs as task-separated paths and cannot predict a series and explain why that prediction arises within a single coherent response. In this paper, we argue for a task-fused model that jointly produces 1) prediction (generation) and 2) selfexplanation (understanding), thereby integrating 1) numerical TS forecasting and 2) interpretable text reasoning within a single response. To enable the systematic study of this capability, we present both a benchmark and a recipe that jointly address the two tasks. The benchmark, ReasonTS-Bench, identifies five fundamental patterns underlying TS and enables the joint evaluation of both tasks. ReasonCast, our recipe for finetuning any LLM to perform both tasks jointly, yields a model that generates a reasoning chain and a forecast together in a single autoregressive pass. Extensive experiments show that ReasonCast outperforms both LLMs and TS models on prediction accuracy while producing verifiable, causal reasoning. Code is available at: https://github.com/seunghan96/reasoncast.

Seunghan Lee, Jun Seo, Jaehoon Lee +9

LG AI Research

Explainable Time Series Forecasting Time Series Reasoning Time Series Forecasting Forecasting Benchmarks LLM-Based Time Series Forecasting Time Series Modeling

Jul 30, 2026

Enhancing Irregular Time Series Forecasting with Continuous-Time Modeling Framework

Irregular multivariate time series are widely encountered in applications such as healthcare monitoring, human activity recognition, and environmental sensing. Their core challenges stem from asynchronous observations, non-uniform sampling intervals, and the fact that temporal patterns themselves carry critical dynamic information. Existing approaches either rely on discretization-based preprocessing (e.g., interpolation, imputation, or aggregation), which disrupts the underlying continuous-time semantics, or adopt continuous-time modeling via ODE-based frameworks, which typically require specialized architectures and incur substantial computational overhead due to numerical solvers. To address these limitations, we propose WrapFlow, a continuous-time modeling framework for irregular time series forecasting. On the input side, WrapFlow introduces Continuous-Time Tokenization, which directly encodes raw observation events and explicitly models long unobserved intervals via gap-aware tokens. The resulting continuous-time tokens are then processed by a standard Transformer backbone to capture long-range temporal dependencies. On the output side, we develop a simulation-free training paradigm for Residual Flow Matching, which learns conditional residual vector fields around base predictions while avoiding numerical-solver simulation and backpropagation during training. This design enables high-quality continuous forecasting using only a small number of fixed rollout steps at inference. Extensive experiments on multiple real-world datasets demonstrate that WrapFlow achieves state-of-the-art performance.

Tianen Shen, Zhengyu Li, Yutong Li +4

Irregular Time-Series Modeling Multivariate Time Series Forecasting Flow Matching Time Series Modeling Time Series Transformers

Jul 14, 2026

The Spectrum Is Not Enough: When Context Helps Time-Series Forecasting

A growing family of indices scores how predictable a series is from its spectrum. Practitioners increasingly read these scores as answering a different question: whether adding context, a longer lookback, a retrieval plug-in, or a pretrained model, will help. These are not the same question. The value of context is a property of the operating point, not of the series. Any index built from the power spectrum is invariant under phase randomization, whereas the beyond-second-order value that retrieval and foundation models supply is not, because a phase-randomized series is asymptotically Gaussian. We state this as an impossibility result and isolate it with surrogate pairs that fix the spectrum and the marginal by construction. We then give a label-free, configuration-level diagnostic, the coverage deficit, whose principal term measures beyond-spectrum structure as the gain of analog over linear prediction. On seven benchmarks the prediction holds: window-keyed retrieval's value collapses across surrogate pairs (ECL median

+33\%\!\to\!-35\%

,

p{<}10^{-40}

) while every spectral index stays frozen; a foundation model's value splits into a surviving second-order part and a small beyond-linear margin that collapses; a longer linear window's value survives. Leave-one-dataset-out, the structure term predicts the sign of beyond-spectrum value where the spectral indices trail it, and the reverse holds for the second-order mechanism. We introduce no new forecaster; the contribution is the distinction, a controlled comparison, and a diagnostic for the deployment decision. Code: https://github.com/KurbanIntelligenceLab/SINE

Mert Onur Cakiroglu, Mehmet Dalkilic, Hasan Kurban

Luddy School of Informatics, Computing, and Engineering, Indiana University Bloomington, Bloomington, IN, USA · College of Science and Engineering, Hamad Bin Khalifa University, Doha, Qatar

Time Series Forecasting Retrieval-Augmented Time Series Forecasting Time-Series Foundation Models Time Series Modeling

Jul 8, 2026

Rethinking Multimodal Time-Series Forecasting Evaluation

We introduce a new context-enriched, multimodal time series forecasting benchmark, TimesX. TimesX contains a wide selection of high-quality real-world time series with diverse domains and textual contexts obtained from an automated data generation pipeline, which helps address three main issues of existing multimodal forecasting benchmarks: (1) poor generalization due to the small scale and synthetic nature of benchmark data, (2) very limited types of textual contexts in the benchmarks, and (3) an inability to mitigate data leakage in evaluation. We conduct a thorough empirical study of zero-shot multimodal forecasting approaches on TimesX. Our results suggest that many approaches that perform well on existing benchmarks may fail on TimesX. In contrast, simple ensemble methods that leverage rich textual context accompanying time-series can outperform strong baselines on TimesX.

Haoxin Liu, Yichen Zhou, Rajat Sen +2

Georgia Institute of Technology · Google Research

Multivariate Time Series Forecasting Zero-Shot Time Series Forecasting Forecasting Benchmarks Multimodal Model Evaluation Time Series Modeling Multimodal Dataset

Jul 6, 2026

When Do Foundation Models Pay Off? A Break-Even Analysis of Pretrained Time Series Forecasters

Deploying a time series foundation model requires GPU infrastructure, engineering overhead, and carries no guarantee of improvement over XGBoost. We provide the first systematic break-even analysis answering when this investment pays off. Across 30 benchmark datasets, we compare zero-shot and LoRA fine-tuned foundation models (Chronos, Moirai, Lag-Llama) against classical baselines (Naive, ETS, ARIMA, XGBoost) at six training set sizes from 2% to 100% of available data. Foundation models outperform classical methods at every evaluated training fraction on 15 of 30 datasets -- GPU deployment is unconditionally justified on these regardless of data volume. On 6 datasets, classical methods surpass zero-shot foundation models with as little as 2% of training data (21-2,768 samples); on the remaining 9, break-even ranges from 24 to 8,361 samples. One robust deployment rule requires no model training: if n_train < 700 and seasonality is non-negligible, use FM zero-shot and skip fine-tuning -- this resolves 10 of 30 deployment decisions immediately. Contrary to common practice, LoRA fine-tuning can actively degrade performance on short series. We operationalise these findings as a two-step decision framework -- compute dataset length and seasonality strength, run a brief 5-10% pilot only if needed -- enabling practitioners to make the FM-versus-classical decision before committing to full infrastructure. Four dataset features motivate mechanistic hypotheses for the remaining cases, though reliable automated prediction at this benchmark scale remains an open problem. Code, benchmark, and decision tools are available at https://github.com/nicolaisi/fm-breakeven.

Nicholas Tan Jerome, Frank Simon

Karlsruhe Institute of Technology (KIT) Eggenstein-Leopoldshafen, Germany

Zero-Shot Time Series Forecasting Time Series Forecasting Forecasting Benchmarks Time-Series Foundation Models Time Series Modeling

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 Time Series Modeling