Non-Stationary Time Series Forecasting

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4 papers in the last four weeks, up 33% on the four weeks before. 0.0% of all new papers.

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Latest papers 63

Jun 4, 2026cs.LG

Adaptive Oscillatory-State Alignment for Time Series Forecasting

Long-term time series forecasting benefits from inductive biases that expose recurring temporal structure. Existing periodic forecasting methods typically model recurrence through predefined periods, global spectral components, or fixed learnable templates. However, real-world temporal dynamics are rarely rigidly periodic: around a nominal cycle, oscillatory behavior often exhibits \emph{non-rigid periodicity} (NRP), where cycle magnitude, cycle alignment, and local cycle duration vary over time. Under these conditions, fixed-template periodic modeling can become fundamentally mismatched to the underlying temporal states. We propose AOSNet, a Hilbert-guided forecasting framework that reformulates periodic forecasting from fixed template matching to adaptive oscillatory-state alignment. AOSNet extracts analytic-signal descriptors from both the observed sequence and a learnable global oscillatory prior, then adaptively aligns local states through a descriptor-conditioned gate that selectively preserves reliable observations while softly correcting mismatched regions. The learned prior serves not as a rigid repeated template but as a flexible oscillatory reference interpreted through local state dynamics. Experiments on eight public benchmarks and two cloud workload traces demonstrate leading or highly competitive accuracy with a compact model size and low inference latency, supporting repeated forecasting settings such as capacity planning and autoscaling. Controlled synthetic studies that isolate cycle-magnitude and cycle-alignment variation and combine them with cycle-duration changes show that the advantage of oscillatory-state alignment increases as NRP intensifies.

Zhangyao Song, Chaofeng Qu, Chao Zha +3

School of Cyber Science and Engineering, Southeast University, Nanjing, China · State Key Laboratory of Blockchain and Data Security, Zhejiang University, Hangzhou, China · School of Information Science and Engineering, Southeast University, Nanjing, China

Long-Term Time Series Forecasting Time Series Forecasting Non-Stationary Time Series Forecasting

Jun 3, 2026cs.AI

EpiEvolve: Self-Evolving Agents for Streaming Pandemic Forecasting under Regime Shifts

Epidemic LLM forecasters are usually trained and evaluated as static supervised models, whereas operational pandemic forecasting is a streaming process in which labels arrive after predictions and disease regimes shift over time. We study this mismatch in weekly COVID-19 hospitalization trend forecasting across five variant regimes. We introduce EpiEvolve, a self-evolving agent that wraps an LLM forecaster trained on the warm-start period and keeps its weights fixed during streaming. EpiEvolve adapts by storing forecast outcomes in a hierarchical episodic memory, reflecting on delayed labels, retrieving cases relevant to the current regime, and distilling recurring errors into strategic rules. The resulting context lets the forecaster reuse its own past predictions and outcomes in later weeks while following a chronological protocol that prevents future leakage. On the streaming dataset, EpiEvolve reaches

0.629

average accuracy, compared with

0.561

for the static backbone and

0.325

for the external CDC ensemble, and reduces recovery lag after regime shifts from

5

to

2

weeks. Ablations show that reflection, strategic memory, and regime-aware retrieval each contribute to the gains.

Yiming Lu, Sihang Zeng, Zhengxu Tang +3

Emory University · University of Washington

Epidemic Forecasting Time Series Forecasting LLM-Based Time Series Forecasting Non-Stationary Time Series Forecasting Spatiotemporal Forecasting Retrieval-Augmented Time Series Forecasting+1

Jun 3, 2026cs.LG

AdaKoop: Efficient Modeling of Nonlinear Dynamics from Nonstationary Data Streams with Koopman Operator Regression

Real-time data analysis requires the ability to accurately and adaptively address nonlinear dynamics in a nonstationary data stream while preserving computational efficiency. However, nonlinear dynamics are so complex that capturing dynamically changing nonlinear patterns and utilizing them for downstream tasks under strict time constraints is nontrivial. To bridge the gap between nonlinear complexity and computational tractability, this study applies Koopman operator theory, which states that nonlinear dynamics can be represented as linear transitions in an infinite-dimensional space. Building upon finite-dimensional approximations of this operator, we present AdaKoop, an efficient streaming algorithm for modeling nonlinear dynamics over nonstationary data streams. Our approach utilizes a probabilistic framework grounded in Koopman operator theory, treating both raw observations and reproducing kernel Hilbert space (RKHS) features as emissions from latent vectors. This dual-view formulation allows nonlinear dynamics to be expressed as a tractable linear system. Therefore, AdaKoop enables the efficient and stable modeling of nonlinear dynamics in a streaming fashion, avoiding the prohibitive computational costs of iterative nonlinear optimization. Furthermore, to address nonstationarity in data streams, AdaKoop adaptively detects the switching of patterns via statistical hypothesis testing for abrupt pattern shifts and incrementally updates model parameters to handle continuous changes. Extensive experiments on a total of 71 practical benchmark datasets across various domains demonstrate that AdaKoop outperforms state-of-the-art methods in terms of real-time forecasting accuracy and computational efficiency.

Naoki Chihara, Ren Fujiwara, Yasuko Matsubara +1

SANKEN, The University of Osaka Osaka, Japan

Koopman Operator Learning Nonlinear System Identification Non-Stationary Time Series Forecasting Online Learning

Jun 2, 2026cs.LG

Stationarity-Aware Retrieval-Augmented Time Series Forecasting

Time series forecasting relies on historical patterns, but real-world series often exhibit non-stationarity and regime shifts that challenge fully parametric forecasters. Inspired by Retrieval-Augmented Generation (RAG), recent work augments forecasters by retrieving relevant historical segments and using them as external evidence at inference time. However, due to the intrinsic non-stationarity of real-world time series, a highly similar past segment does not necessarily imply a similar future, rendering similarity-only retrieval brittle and prone to redundancy. We propose Stationarity-Aware Retrieval-Augmented Time Series Forecasting (SARAF), a framework that adaptively balances relevance and diversity in retrieval. SARAF first forms a candidate pool via temporal similarity with time-aligned enhancement, then applies a diversity-aware selection strategy to cover heterogeneous historical regimes, with the diversification strength automatically modulated by dataset-level stationarity. Moreover, SARAF uses stationarity-aware aggregation to fuse the retrieved futures. Extensive experiments on eight real-world datasets show that SARAF achieves competitive forecasting performance and improves average accuracy and robustness over strong baselines, with particularly clear benefits under challenging non-stationary settings. Code: https://github.com/ShiqiaoZhou/SARAF.

Shiqiao Zhou, Holger Schöner, Zipeng Wu +3

University of Birmingham Birmingham, United Kingdom · Siemens AG Munich, Germany

Time Series Forecasting Non-Stationary Time Series Forecasting Retrieval-Augmented Time Series Forecasting

May 31, 2026cs.LG

FreqLite: A Lightweight Frequency-Decomposed Linear Model with Adaptive Reversible Normalization for Robust Long-Term Time-Series Forecasting

Long-term time-series forecasting needs models that are accurate yet efficient enough for commodity hardware. Lightweight linear forecasters are remarkably strong in this regime, yet they leave two openings: reversible instance normalization (RevIN) de-normalizes the entire horizon with a single lookback statistic, which is inaccurate under non-stationarity, and time-domain trend/seasonal decomposition relies on a fixed, non-adaptive filter. We present FreqLite, an ultra-lightweight, channel-independent frequency-decomposed linear forecaster: a learnable, lossless, partition-of-unity spectral filter splits the input into bands that are forecast by per-band linear heads and, unlike low-pass-truncation approaches, the high-frequency band is retained and modeled. FreqLite is the best lightweight model on the standard long-term forecasting benchmarks and, at long lookback (L=336), attains a lower average error than a PatchTST Transformer (0.3244 vs. 0.3587 MSE) while using 4x fewer parameters, 2.2x less memory, and 2.2x less time per epoch on a single 4 GB laptop GPU; although modest in magnitude, its improvements are statistically significant under paired Wilcoxon tests across all matched cells (p < 1e-5). We further introduce Adaptive Reversible Instance Normalization (A-RevIN), a regime-adaptive reversible normalization that strictly generalizes RevIN (recovered exactly when its gate is closed), engages under non-stationarity, and reduces to RevIN without harm on stationary data. We validate this on both a real strongly non-stationary dataset (ILI, up to ~5% MSE reduction) and a controlled synthetic drift sweep in which A-RevIN's benefit and its learned gate both rise monotonically with injected non-stationarity. Every component is independently ablatable (Linear and RLinear are special cases of FreqLite), and all results are reproducible on commodity hardware.

Mirza Samad Ahmed Baig, Syeda Anshrah Gillani

Fandaqah, Al Khobar, Saudi Arabia · Hamdard University, Karachi, Pakistan

Long-Term Time Series Forecasting Frequency-Domain Feature Learning Time Series Forecasting Non-Stationary Time Series Forecasting

May 25, 2026cs.LG

STaT: Resolving Shape Distortion in Non-Stationary Time Series via Tri-Modal Synergy

Recent research in time series forecasting frequently investigates the integration of textual and visual modalities with numerical models to better navigate non-stationary environments. Despite delivering solid numerical results, existing multi-modal approaches usually encounter a dilemma: prioritizing the minimization of average errors can result in excessively smooth forecasts that overlook essential fluctuations. To resolve this limitation, we introduce STaT, an innovative multimodal architecture for Symbolic-Temporal-Textual Alignment, which seamlessly unites three synergistic modalities. Specifically, the symbolic modality converts continuous time series into discrete tokens, facilitating the accurate identification of structural patterns and turning points; the temporal modality extracts inherent sequential dependencies; and the textual modality leverages domain semantics to steer the macroscopic forecasting trends. Comprehensive evaluations on eight real-world benchmarks indicate that STaT delivers exceptional performance, enhancing conventional magnitude indicators by up to 8.9% while simultaneously decreasing shape distortion by up to 8.5%.

Hui Cheng, Jinsheng Guo, Zhenhao Weng +2

Hefei University of Technology Hefei, China

Non-Stationary Time Series Forecasting Multimodal Fusion Time Series Representation Learning

May 25, 2026cs.LG

Modeling Dynamic Mixtures of Time-Delay Systems from Streaming Time Series

This research addresses the problem of adaptive modeling in time-series data streams with clear input-output relationships. This problem is challenging because rapid system changes (regime shifts) caused by environmental factors or input delay changes degrade model performance, and the trade-off among accuracy, robustness, and memory usage arises when using multiple small models for each time-series pattern. To address these issues, this paper presents an online framework/method that treats streaming time series as dynamic mixtures of time-delay systems. This framework maintains robustness of model tracking and reduces memory usage by summarizing past regimes using a fixed-length representation that captures both the system dynamics and input-output delays. Concretely, this approach constructs a summary system tensor using the system's Markov parameter series, capturing both dynamic behavior and delay characteristics. If necessary, a tensor decomposition algorithm extracts relevant past models from the tensor and helps select the system that best fits the current regime. This method enables rapid adaptation to environmental changes and is computationally efficient. Tests on real datasets show that DelayMix consistently outperforms other methods, achieving superior forecast accuracy and faster adaptation to delays, especially for highly non-stationary data.

Ren Fujiwara, Yasuko Matsubara, Yasushi Sakurai

SANKEN, The University of Osaka, Japan

Dynamical Systems Online System Identification Non-Stationary 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 20, 2026cs.LG

Dynamic TMoE: A Drift-Aware Dynamic Mixture of Experts Framework for Non-Stationary Time Series Forecasting

Non-stationary time series forecasting is challenged by evolving distribution shifts that static models struggle to capture. While Mixture-of-Experts (MoE) architectures offer a promising paradigm for decoupling complex drift patterns, existing approaches are limited by fixed expert pools and memoryless routing, hampering their ability to adapt to abrupt regime shifts. To address this, we propose Dynamic TMoE, a framework that unifies architectural evolution with temporal continuity during learning phase. By detecting distribution shifts via Maximum Mean Discrepancy (MMD), we dynamically instantiate heterogeneous experts and prune redundant ones to optimize capacity. Additionally, a temporal memory router leverages recurrent states and an anomaly repository to ensure stable, context-aware expert selection without requiring test-time updates. Experiments on nine benchmarks demonstrate state-of-the-art performance, reducing MSE by 10.4% and MAE by 7.8%. Code is available at https://github.com/andone-07/Dynamic-TMoE.

Jiawen Zhu, Shuhan Liu, Di Weng +1

School of Software Technology, Zhejiang University, Ningbo, China · State Key Lab of CAD&CG, Zhejiang University, Hangzhou, China

Concept Drift Mixture of Experts Non-Stationary Time Series Forecasting Mixture-of-Experts Models Temporal Distribution Shift

May 20, 2026cs.LG

Deep Learning Surrogates for Emulating Stochastic Climate Tipping Dynamics

This work explores a dynamics-informed Temporal Fusion Transformer (TFT) as a data-driven surrogate for computationally intensive Earth system simulations. Focusing on multivariate time series describing global ocean transport, we demonstrate the surrogate's ability to forecast tip events across thousands of time steps. The data involve up to 21 non-stationary time series in addition to static covariates describing free parameters and initial conditions. Modifications to the architecture and objective function yield a surrogate that anticipates the timing of Atlantic and Pacific collapses to high fidelity and captures the stochastic uncertainty in transition timing across ensemble predictions. The learned surrogate achieves a 465x computational speedup over the numerical simulator while maintaining differentiability with respect to parameters and initial conditions.

Adeline Hillier, Jennifer Sleeman, Jay Brett +3

Johns Hopkins Applied Physics Laboratory Hopkins University · Johns

Neural Surrogate Modeling Multivariate Time Series Forecasting Climate Science Probabilistic Forecasting Non-Stationary Time Series Forecasting Climate Modeling+1

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

L-Drive: Beyond a Single Mapping-Latent Context Drives Time Series Forecasting

Mainstream methods for multivariate time-series forecasting largely follow the Direct-Mapping paradigm. They learn a unified mapping from history to the future in the observation space to fit value-level dependencies. However, real-world systems often undergo distribution shifts and regime changes. In such cases, a unified mapping can exhibit response lag around turning points, causing error accumulation within the switching window and reducing forecasting reliability. To address this issue, we propose L-Drive, a change-aware forecasting framework. L-Drive introduces a Latent-Context, to explicitly characterize high-level dynamics evolving over time, and uses gating to modulate increment representations. This provides more timely change cues and improves adaptation to changing segments. In addition, it incorporates patch-shared relative positional basis functions to strengthen intra-segment structural modeling and reduce overfitting caused by absolute-position memorization. Extensive experiments validate the effectiveness of L-Drive and show a better overall trade-off between forecasting accuracy and computational efficiency.

Fan Zhang, Shijun Chen, Hua Wang

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

Multivariate Time Series Forecasting Latent Dynamics Modeling Time Series Forecasting Non-Stationary Time Series Forecasting Temporal Distribution Shift

May 16, 2026cs.LG

Mechanism Learning: Prototype-Anchored Mechanism Inference for Scientific Forecasting

Scientific forecasting typically relies on direct state prediction, an approach that grows brittle under data scarcity, extended horizons, non-stationary dynamics, or high-dimensional complexity. While raw state trajectories are highly sensitive in these regimes, underlying local evolution rules often exhibit robust reusability. We introduce mechanism learning, a framework that forecasts future states by estimating the currently active local mechanism. Our method compresses local spatiotemporal fragments into mechanism descriptors, forming a data-driven, structured mechanism space where proximity reflects similar local evolution rules. To ground these estimates in observed data, we utilize prototype anchors, a set of representative mechanisms that sparsely cover the space of local rules. We evaluate this approach on Burgers dynamics, WeatherBench2, and Lorenz96. Empirically, the learned mechanism spaces resist collapse and maintain strong local consistency. Compared to direct prediction and other models including FNO, NODE, LSTM, and reservoir-family methods, our framework demonstrates predictive gains in fragile regimes: it significantly improves switching stability in Burgers dynamics and achieves state-of-the-art performance both under the scarce-data fixed-horizon WeatherBench2 protocol and in intermediate-complexity Lorenz96. Ablation studies and drift diagnostics confirm that these improvements are driven by finite prototype anchoring rather than sheer latent capacity. Together, these results establish mechanism learning as a principled, robust alternative to direct state prediction in forecasting complex systems.

Qian Jiang, Liping Sun

School of Computing · The Australian National University · Canberra, ACT 2601, Australia +3

Prototype-Based Learning Non-Stationary Time Series Forecasting Scientific ML Spatiotemporal Forecasting

May 16, 2026cs.LG

PULSE: Generative Phase Evolution for Non-Stationary Time Series Forecasting

Time series forecasting under non-stationarity faces a fundamental tension between capturing stable representations and adapting to distribution shifts. Existing methods implicitly rely on static historical assumptions, leading to a critical failure mode we term Phase Amnesia, where models become blind to the evolving global context. To resolve this, we formalize non-stationary dynamics through three physical hypotheses: wold decomposition, dynamical phase evolution, and heteroscedastic manifold generation. These principles inspire PULSE, a physics-informed, plug-and-play framework adopting a Disentangle--Evolve--Simulate design philosophy. Specifically, PULSE utilizes phase-anchored disentanglement to resolve optimization interference caused by dominant trends, employs a Phase Router to actively generate future trajectories, and introduces Statistic-Aware Mixup (SAM) to ensure robustness against out-of-distribution volatility. Empirically, PULSE enables a simple MLP backbone to achieve state-of-the-art or highly competitive performance across 12 real-world benchmarks. This validates that a correct physics-informed inductive bias is far more critical than raw architectural complexity for non-stationary forecasting. The code is available at: https://github.com/Gemost/PULSE.

Yangyou Liu, Zezhi Shao, Xinyu Chen +3

College of Computer Science, Sichuan University, Chengdu, China · Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China · Institute of Artificial Intelligence, University of Central Florida, Orlando, USA +1

OOD Generalization Time Series Generation Non-Stationary Time Series Forecasting Physics-Informed ML

May 15, 2026cs.LG

Nested Spatio-Temporal Time Series Forecasting

Spatiotemporal forecasting is critical for real-world applications like traffic management, yet capturing reliable interactions remains challenging under noisy and non-stationary conditions. Existing methods primarily rely on historical spatial priors, often failing to account for evolving temporal correlations and suffering from systematic errors. In this work, we propose a nested forecasting framework that couples future macro-level regional trends with micro-level historical observations, enabling top-down guidance from abstract future representations for fine-grained forecasting. Specifically, we employ a spectral clustering-based approach to construct semantically coherent regions, providing both theoretical and empirical evidence that this representation effectively filters systematic noise while preserving essential trends. Building on this, we develop a progressive coarse-to-fine predictor to integrate these representative features into the inference process. This enables the model to leverage trend predictions to anticipate dynamic anomalies, such as periodic offsets, in advance. Furthermore, extensive experiments on multiple high-dimensional datasets demonstrate that our method consistently outperforms state-of-the-art baselines, validating the effectiveness of future macro-guided nested forecasting.

Yinghao Ai, Yukai Zhou, Ruoxi Jiang +8

National Key Laboratory for Novel Software Technology, Nanjing University, China · Shanghai Academy of AI for Science, Shanghai · Department of Computer Science and Technology, Nanjing University +3

Non-Stationary Time Series Forecasting Spatiotemporal Forecasting Multiscale Time-Series Modeling

May 14, 2026cs.LG

SeesawNet: Towards Non-stationary Time Series Forecasting with Balanced Modeling of Common and Specific Dependencies

Instance normalization (IN) is widely used in non-stationary multivariate time series forecasting to reduce distribution shifts and highlight common patterns across samples. However, IN can over-smooth instance-specific structural information that is essential for modeling temporal and cross-channel heterogeneity. While prior methods further suppress distribution discrepancies or attempt to recover temporal specific dependencies, they often ignore a central tension: how to adaptively model common and instance-specific dependency based on each instance's non-stationary structures. To address this dilemma, we propose SeesawNet, a unified architecture that dynamically balances common and instance-specific dependency modeling in both temporal and channel dimensions. At its core is Adaptive Stationary-Nonstationary Attention (ASNA), which captures common dependencies from normalized sequences and specific dependencies from raw sequences, and adaptively fuses them according to instance-level non-stationarity. Built upon ASNA, SeesawNet alternates dedicated temporal and channel relationship modeling to jointly capture long-range and cross-variable dependencies. Extensive experiments on multiple real-world benchmarks demonstrate that SeesawNet consistently outperforms state-of-the-art methods.

Hao Li, Lu Zhang, Liu Chong +3

1Sichuan University · 2Chengdu University of Information Technology · 3McGill University +1

Multivariate Time Series Forecasting Non-Stationary Time Series Forecasting Temporal Attention

May 12, 2026cs.LG

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

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

H=32

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

Cao Yuan, Junjun Wang

Wuhan Polytechnic University, Wuhan, 430048, Hubei, China

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

May 11, 2026cs.LG

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

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

\times

to 5.3

\times

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

Sheng Pan, Ming Jin, Bo Du +1

Griffith University

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

May 11, 2026cs.AI

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

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

Aman Singh, Tokunbo Ogunfunmi, Sanjiv Das

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

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

May 8, 2026cs.LG

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

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

Jiaqi Liu, Yifan Ouyang, Zhifei Song +2

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

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

May 7, 2026cs.LG

Hedging Memory Horizons for Non-Stationary Prediction via Online Aggregation

We study online prediction under distribution shift, where inputs arrive chronologically and outcomes are revealed only after prediction. In this setting, predictors must remain stable in quiet regimes yet adapt when regimes shift, and the right adaptation memory is unknown in advance. We propose MELO (Memory-hedged Exponentially Weighted Least-Squares Online aggregation), a model-agnostic method that hedges across adaptation scales: it wraps any non-anticipating base-predictor pool with exponentially weighted least-squares (EWLS) adaptation experts at multiple forgetting factors, and aggregates raw and EWLS-adapted forecasts with MLpol, a parameter-free online aggregation rule. Under boundedness conditions, we establish deterministic oracle inequalities showing that it competes with both the best raw predictor and the best bounded, time-varying affine combinations of the base predictions, up to a path-length-dependent tracking cost and a sublinear aggregation overhead. We evaluate MELO on French national electricity-load forecasting through the COVID-19 lockdown using no regime indicators, lockdown dates, or policy covariates. MELO reduces overall RMSE by 34.7% relative to base-only MLpol and achieves lower overall RMSE than a TabICL reference supplied with an external COVID policy-response covariate. Moreover, MELO requires only lightweight per-step recursive updates without model retraining.

Yutong Wang, Yannig Goude, Qiwei Yao

Department of Statistics, LSE · Électricité de France R&D

Ensemble Learning Time Series Forecasting Non-Stationary Time Series Forecasting Electricity Load Forecasting Adaptive Learning Temporal Distribution Shift

May 7, 2026cs.LG

Perceive, Route and Modulate: Dynamic Pattern Recalibration for Time Series Forecasting

Local temporal patterns in real-world time series continuously shift, rendering globally shared transformations suboptimal. Current deep forecasting models, despite their scale and complexity, rely on fixed weight matrices applied uniformly to all temporal tokens. This creates a static pattern response: models settle into a compromised average, unable to adapt to changing local dynamics. We introduce Dynamic Pattern Recalibration (DPR), a backbone-agnostic mechanism that resolves this via token-level recalibration. Through a lightweight "Perceive-Route-Modulate" pipeline, DPR computes a soft-routing distribution over a learned basis of adaptive response patterns, generating a time-aware modulation vector that recalibrates hidden states via a residual Hadamard product. As a backbone-agnostic adapter, DPR enhances forecasting across diverse architectures with minimal overhead, confirming it addresses a general bottleneck. As a minimalist standalone model, DPRNet achieves competitive performance across 12 benchmarks, validating dynamic recalibration against macroscopic parameter scaling.

Siru Zhong, Zhao Meng, Haohuan Fu +3

The Hong Kong University of Science and Technology (Guangzhou) · Tsinghua University · Squirrel Ai Learning

Dynamic Neural Networks Time Series Forecasting Non-Stationary Time Series Forecasting

May 1, 2026cs.LG

PAMod: Modeling Cyclical Shifts via Phase-Amplitude Modulation for Non-stationary Time Series Forecasting

Real-world time series forecasting faces the fundamental challenge of non-stationary statistical properties, including shifts in mean and variance over time. While reversible instance normalization (RevIN) has shown promise by stationarizing inputs and denormalizing outputs, it relies on the strong assumption that historical and future distributions remain identical. We observe that in many practical applications, distribution shifts follow cyclical patterns that correlate with periodic positions (e.g., seasonal and holiday volatility). To this end, we propose PAMod, a lightweight yet powerful framework that models cyclical distribution shifts via Phase-Amplitude Modulation in the normalized feature space. PAMod learns periodic embeddings to modulate representations: phase modulation captures mean shifts, while amplitude modulation adapts to variance changes. Crucially, we prove mathematically that modulating in normalized space is equivalent to applying dynamic denormalization, offering an elegant unification of distribution adaptation and representation learning. Extensive experiments on twelve real-world benchmarks demonstrate that PAMod achieves state-of-the-art performance with fewer computational resources. Furthermore, our modulation mechanism, as a novel plug-and-play technique, can improve existing time-series forecasting methods with simple integration.

Yingbo Zhou, Yutong Ye, Shuhao Li +5

Fudan University · Beihang University · Beijing University of Posts and Telecommunications

Distribution Shift Time Series Forecasting Non-Stationary Time Series Forecasting Non-Stationary Time Series Temporal Distribution Shift

Apr 29, 2026cs.LG

Electricity price forecasting across Norway's five bidding zones in the post-crisis era

Norway's electricity market is heavily dominated by hydropower, but the 2021-2022 energy crisis and stronger integration with Continental Europe have fundamentally altered price formation, reducing the reliability of forecasting models calibrated on historical data. Despite the critical need for updated models, a unified benchmark evaluating feature contributions across all structurally diverse Norwegian bidding zones remains lacking. Here we present a comprehensive evaluation of one-step-ahead forecasting of the Nord Pool market across all five Norwegian bidding zones. We constructed a multimodal hourly dataset spanning 2019-2025 and evaluated eight forecasting model families, including Light Gradient Boosting Machine (LightGBM), autoregressive models with exogenous variables, and advanced deep learning architectures, using a strictly causal test set. We implemented robust rolling-origin backtesting, leave-one-group-out feature ablation, and conditional regime analysis to dissect model performance and feature utility. Our results show that LightGBM achieves the best performance in every zone, with mean absolute error ranging from 1.60 to 5.58 euros per megawatt-hour, while a ridge-regularized autoregressive model with exogenous variables remains a highly competitive linear benchmark in northern zones. Feature ablation reveals that models relying solely on lagged prices and calendar variables achieve high accuracy and often match or closely approach the performance of the full multimodal model. However, conditional regime analysis demonstrates that external features like reservoir levels and gas prices remain crucial to stratify forecast errors, which consistently increase under stressed market regimes. This highlights the practical value of model interpretability and regime awareness for decision makers facing structural changes in market dynamics.

My Thi Diem Phan, Trung Tuyen Truong, Hoai Phuong Ha +1

Independent researcher · Department of Mathematics, University of Oslo · Department of Computer Science, The Arctic University of Norway +1

Electricity Price Forecasting Time Series Forecasting Forecasting Benchmarks Non-Stationary Time Series Forecasting

Apr 24, 2026cs.LG

Liquid Neural Network Models for Natural Gas Spot Price Time-Series Forecasting

Natural gas is undoubtedly an essential component of the global energy system. Accurate short-term forecasting of natural gas price is challenging due to pronounced volatility driven by seasonal demand patterns, geopolitical developments, and shifting macroeconomic conditions. The nonlinear dynamics and frequent regime changes can limit the effectiveness of traditional time-series models. In this study, we explore the use of Liquid Neural Networks (LNNs) for short-horizon forecasting of the Henry Hub spot price, a primary benchmark for pricing. LNNs are designed to adapt continuously to evolving temporal patterns through dynamic internal state updates, making them well suited for nonstationary price behavior. By improving forecast accuracy in volatile market conditions, this work aims to reduce uncertainty and enhance decision support across energy trading and power market applications.

Yiqian Liu, Jiayi Niu, Adam Kelleher +1

Department of Data Science, Columbia University New York, NY, USA

Liquid Neural Networks Time Series Forecasting Non-Stationary Time Series Forecasting

Apr 20, 2026cs.LG

CAARL: In-Context Learning for Interpretable Co-Evolving Time Series Forecasting

In this paper we investigate forecasting coevolving time series that feature intricate dependencies and nonstationary dynamics by using an LLM Large Language Models approach We propose a novel modeling approach named ContextAware ARLLM CAARL that provides an interpretable framework to decode the contextual dynamics influencing changes in coevolving series CAARL decomposes time series into autoregressive segments constructs a temporal dependency graph and serializes this graph into a narrative to allow processing by LLM This design yields a chainofthoughtlike reasoning path where intermediate steps capture contextual dynamics and guide forecasts in a transparent manner By linking prediction to explicit reasoning traces CAARL enhances interpretability while maintaining accuracy Experiments on realworld datasets validate its effectiveness positioning CAARL as a competitive and interpretable alternative to stateoftheart forecasting methods

Etienne Tajeuna, Patrick Asante Owusu, Armelle Brun +1

Explainable Time Series Forecasting Time Series Forecasting LLM-Based Time Series Forecasting Non-Stationary Time Series Forecasting In-Context Learning

Apr 18, 2026cs.LG

In-Context Learning Under Regime Change

Non-stationary sequences arise naturally in control, forecasting, and decision-making. The data-generating process shifts at unknown times, and models must detect the change, discard or downweight obsolete evidence, and adapt to new dynamics on the fly. Transformer-based foundation models increasingly rely on in-context learning for time series forecasting, tabular prediction, and continuous control. As these models are deployed in non-stationary environments, understanding their ability to detect and adapt to regime shifts is important. We formalize this as an in-context change-point detection problem and formally establish the existence of transformer models that solve this problem. Our construction demonstrates that model complexity, in layers and parameters, depends on the level of information available about the change-point location, from no knowledge to knowing exact timing. We validate our results with experiments on synthetic linear regression and linear dynamical systems, where trained transformers match the performance of optimal baselines across information levels. We also show that encoding and incorporating changepoint knowledge indeed improves the real-world performance of a pretrained foundation models on infectious disease forecasting and on financial volatility forecasting around Federal Open Market Committee (FOMC) announcements without retraining, demonstrating practical applicability to real-world regime changes.

Carson Dudley, Yutong Bi, Xiaofeng Liu +1

Department of Mathematics, University of Michigan · Department of Electrical Engineering and Computer Science, University of Michigan · Michigan Institute for AI and Data in Society, University of Michigan

Transformer Distribution Shift Detection Non-Stationary Time Series Forecasting Change-Point Detection Time-Series Foundation Models

Apr 18, 2026eess.SP

TimeRFT: Stimulating Generalizable Time Series Forecasting for TSFMs via Reinforcement Finetuning

Time Series Foundation Models (TSFMs) advance generalization and data efficiency in time series forecasting by unified large-scale pretraining. But TSFMs remain lacking when adapting to specific downstream forecasting tasks for two reasons. First, the non-stationary and uncertain nature of time series data lead to inevitable temporal distribution shifts between historical training and future testing data, while current Supervised FineTuning (SFT)-based methods are prone to overfitting and may degrade generalization. Second, training data availability varies across forecasting tasks, requiring TSFMs to generalize well under diverse data regimes. To address these challenges, we introduce the Time series Reinforcement Finetuning (TimeRFT) paradigm for TSFM downstream adaptation, which consists of two task-specific training recipes: i) A forecasting quality-based temporal reward mechanism that conducts a multi-faceted evaluation of the contribution of each prediction step to overall forecasting accuracy. ii) A forecasting difficulty-based data selection strategy to identify time series samples with generalizable predictive patterns and informative training signals. Extensive experiments demonstrate TimeRFT can consistently outperform SFT-based adaptation methods across various real-world forecasting tasks and training data regimes, enhancing prediction accuracy and generalization against unforeseen distribution shifts.

Siyang Li, Yize Chen, Zijie Zhu +4

HKUST(GZ) Guangzhou, China · University of Alberta Edmonton, Canada · Alibaba Cloud Guangzhou, China +3

Time Series Forecasting OOD Generalization Non-Stationary Time Series Forecasting RL Fine-Tuning Time-Series Foundation Models

Apr 17, 2026cs.CV

TriTS: Time Series Forecasting from a Multimodal Perspective

Time series forecasting plays a pivotal role in critical sectors such as finance, energy, transportation, and meteorology. However, Long-term Time Series Forecasting (LTSF) remains a significant challenge because real-world signals contain highly entangled temporal dynamics that are difficult to fully capture from a purely 1D perspective. To break this representation bottleneck, we propose TriTS, a novel cross-modal disentanglement framework that projects 1D time series into orthogonal time, frequency, and 2D-vision spaces.To seamlessly bridge the 1D-to-2D modality gap without the prohibitive

O(N^2)

computational overhead of Vision Transformers (ViTs), we introduce a Period-Aware Reshaping strategy and incorporate Visual Mamba (Vim). This approach efficiently models cross-period dependencies as global visual textures while maintaining linear computational complexity. Complementing this, we design a Multi-Resolution Wavelet Mixing (MR-WM) module for the frequency modality, which explicitly decouples non-stationary signals into trend and noise components to achieve fine-grained time-frequency localization. Finally, a streaming linear branch is retained in the time domain to anchor numerical stability. By dynamically fusing these three complementary representations, TriTS effectively adapts to diverse data contexts. Extensive experiments across multiple benchmark datasets demonstrate that TriTS achieves state-of-the-art (SOTA) performance, fundamentally outperforming existing vision-based forecasters by drastically reducing both parameter count and inference latency.

Xiang Ao

School of Software Engineering, Beijing Jiaotong University Beijing 100044, China

Long-Term Time Series Forecasting Cross-Modal Representation Learning Non-Stationary Time Series Forecasting Multimodal Fusion Multiscale Time-Series Modeling

Feb 6, 2026cs.LG

How (Not) to Hybridize Neural and Mechanistic Models for Epidemiological Forecasting

Epidemiological forecasting from surveillance data is a hard problem and hybridizing mechanistic compartmental models with neural models is a natural direction. The mechanistic structure helps keep trajectories epidemiologically plausible, while neural components can capture non-stationary, data-adaptive effects. In practice, however, many seemingly straightforward couplings fail under partial observability and continually shifting transmission dynamics driven by behavior, waning immunity, seasonality, and interventions. We catalog these failure modes and show that robust performance requires making non-stationarity explicit: we extract and extrapolate multi-scale structure from the observed infection series and use it as an interpretable control signal for a controlled neural ODE coupled to an epidemiological model. Concretely, we decompose infections into trend, seasonal, and residual components and use these signals to drive continuous-time latent dynamics while jointly forecasting and inferring time-varying transmission, recovery, and immunity-loss rates. Across early outbreak and multi-wave regimes, our approach attains the lowest RMSE on all five datasets (27-70% reduction over the strongest baseline), achieves the best peak detection accuracy, and recovers time-varying epidemiological rates within ground-truth ranges, without relying on auxiliary covariates.

Yiqi Su, Ray Lee, Jiaming Cui +1

Department of Computer Science, Virginia Tech, Alexandria, USA.

Epidemic Forecasting Non-Stationary Time Series Forecasting Neural ODEs Multiscale Time-Series Modeling