Multiscale Time-Series Modeling

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8 papers in the last four weeks, up 167% on the four weeks before. 0.1% of all new papers.

Jul 13Week of Sep 28

Latest papers 69

Oct 7, 2026cs.LG

HAN-Mamba: Hierarchical Selective State Space Networks for Multi-Scale Financial Volatility Forecasting

Short-horizon realized volatility forecasting requires the integration of market information that evolves at incompatible temporal resolutions, from second-level order book dynamics to weekly regime drift. Our conference work introduced HAN-T, a hierarchical architecture in which scale-specific Transformer encoders process short, mid, and long-horizon streams and a learned attention fuser weighs their contributions. This article replaces the quadratic attention encoders with selective state space (Mamba) encoders while retaining attention only in the fuser, where the input is a three-token set rather than a long sequence. The resulting hybrid, HAN-Mamba, summarizes each stream through a recurrent state whose input-dependent gating matches two structural properties of volatility: persistent but decaying memory and abrupt regime shifts. On the Optiver Realized Volatility Prediction benchmark under time-aware five-fold cross-validation, HAN-Mamba improves mean RMSPE over HAN-T (0.1942 vs. 0.1965) with 33% fewer parameters. Its linear-time encoders further allow the high-frequency context to be extended from 60 to 240 buckets, reducing error to 0.1927 where the attention variant saturates, and support constant-time streaming updates at inference. Ablations attribute the gains to the encoder swap, confirm that the hierarchical prior transfers across sequence-model families, and show that the permutation-invariant attention fuser remains the correct mechanism for cross-scale integration.

Mihai Bogdan Deaconu, Ioan Daniel Pop

Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, Romania

Time Series Forecasting Financial Time Series Multiscale Time-Series Modeling Finance Selective SSMs

Oct 7, 2026cs.LG

Matching of signal, noise and hardware timescales for filtering and forecasting of correlated noise signals

Physical reservoir computing exploits the nonlinear dynamics of physical systems to process time-dependent data with greater energy efficiency than conventional machine learning approaches. However, physical reservoirs have fixed intrinsic response timescales, whereas real-world signals combine deterministic and stochastic components across multiple timescales. Here we show, using a nanoporous niobium oxide reservoir, synthetic noisy signals and cryptocurrency-price volatility, that the relationship among noise correlation time, reservoir memory and forecast horizon determines whether correlated noise is filtered or predicted. Noise varying faster than the relevant reservoir memory and forecast horizon is averaged by the reservoir, whereas the temporal structure of slower-varying noise is sufficient for algorithmic forecasting. We introduce the reservoir memory horizon and forecasting regime index to distinguish these operating regimes. These contributions demonstrate that timescale matching can guide the encoding of input time series and development of physical reservoir architectures that filter, analyse and predict stochastic signal components across distinct temporal scales.

Joshua Donald, Alex Gabbitas, Arthur G. T. Coveney +2

Department of Physics, Loughborough University, Loughborough, LE11 3TU, United Kingdom

Reservoir Computing Time Series Forecasting Multiscale Time-Series Modeling

Oct 4, 2026cs.LG

LogSig-SSM: Time-Series Modelling with Multi-Scale Log-Signature Compression for State-Space Models

Time-series data are often sampled irregularly at high frequencies and exhibit long-range dependencies, which makes long-horizon modelling difficult. Continuous-time models such as neural controlled differential equations (NCDEs) and neural rough differential equations (NRDEs) can handle irregular sampling, but they scale poorly to long sequences. Selective state-space models (SSMs) such as Mamba scale linearly with sequence length, but they provide limited recurrent mixing across hidden dimensions within a single block. We propose LogSig-SSM (Log-Signature Compression for State-Space Models), which first compresses long multivariate time series into a shorter sequence of tokens using multi-scale windowed log-signatures, and then processes these tokens with a selective SSM backbone. LogSig-SSM is scalable and robust to irregular sampling, combining log-signature tokens that capture higher-order cross-channel interactions with a selective SSM that models long-range dependencies. The model also admits a continuous-time interpretation as an NCDE/NRDE-style system driven by a log-signature-based input, in which selectivity induces an input-dependent rescaling of the latent dynamics. Across four benchmarks, namely long-sequence classification on UEA, high-frequency physiological regression on PPG-DaLiA, multivariate weather forecasting, and irregularly sampled clinical prediction on PhysioNet Sepsis, LogSig-SSM outperforms or matches strong SSM and continuous-time baselines while training up to

30\times

faster and using up to

37\times

less GPU memory than Mamba on the longest sequences.

Felix Oury, Nicolas Calvo Peiro, Reiko J. Tanaka

Department of Computing Imperial College London · Department of Bioengineering Imperial College London

Irregular Time-Series Modeling Multivariate Time Series Forecasting Selective SSMs Time Series Classification Multiscale Time-Series Modeling

Oct 1, 2026cs.LG

Inferring Multi-Timescale Neural Dynamics with Switching Linear Dynamical Systems

Neural activity often exhibits multiple timescales that can vary with behavioral states and task conditions. Identifying these timescales from neural recordings is important for better understanding neural computation and function. However, traditional approaches based on autocorrelation fitting are difficult to scale to high-dimensional population recordings and can become unreliable when neural dynamics change with behavior. State-space models have been a powerful framework for modeling high-dimensional neural population activity through latent dynamical systems, but standard formulations and inference methods do not explicitly account for multiple timescales and therefore do not guarantee accurate recovery of the underlying temporal structure. Motivated by these questions, we introduce the Multi-Timescale Switching Linear Dynamical System (MTS-SLDS), a framework for identifying regime-specific latent timescales from continuous or spiking neural observations. MTS-SLDS combines a multi-lag moment initialization, which captures temporal structure across multiple observation lags, with \textit{regime-conditioned} Laplace-EM inference, which reduces mixing of dynamical statistics across uncertain regimes. Characteristic timescales can then be extracted directly from the eigenvalues of the learned latent transition matrices. In synthetic and neural experiments with Gaussian and Poisson spike observations, MTS-SLDS accurately recovers timescales and switching structure over multiple datasets.

Lulu Gong, Yongxu Zhang, Shreya Saxena

Center for Neurocomputation and Machine Intelligence, Wu Tsai Institute, Department of Biomedical Engineering, Yale University, New Haven, CT 06510, USA

Stochastic Linear Dynamical Systems Latent Dynamics Modeling Regime-Switching Dynamical Systems Multiscale Time-Series Modeling

Sep 29, 2026cs.LG

NeurDuo-EEG: A Long-Sequence EEG Foundation Model with Persistent State and Explicit Memory

Electroencephalography (EEG) is recorded continuously over hours, with relevant dynamics spanning timescales from milliseconds to hours. Most EEG foundation models nevertheless process fixed windows independently, limiting their ability to capture information encoded in long-timescale dynamics. State-space architectures enable persistent recurrent processing, but long-range information remains implicitly compressed in recurrent states. We present NeurDuo-EEG, a causal EEG foundation model with channel-resolved persistent memory. NeurDuo-EEG introduces multi-timescale memory management with learned consolidation and selective retrieval, enabling persistent modelling of continuous EEG with fixed-size state. It is pre-trained on 3,955 hours of EEG from 17 public datasets using multichannel autoregressive prediction of discrete spectral codes. Across three short-window and two long-sequence downstream tasks, NeurDuo-EEG achieves the best performance on four of five benchmarks, including all three short-window tasks and seizure detection, where AUC-PR improves from

0.285

to

0.471

over the strongest non-NeurDuo baseline. NeurDuo-EEG also remains competitive on sleep staging and supports efficient streaming inference, with nearly constant per-chunk latency as the available history grows to one hour. Notably, the Small variant achieves this with only 4.7M backbone parameters. These results demonstrate the value of persistent, multi-timescale modelling for both long-sequence and short-window EEG analysis. Our code is available at https://github.com/YifaNNW/NeurDuo-EEG.

Yifan Wang, Haiping Liu, Yang Cui +13

University of Manchester · ETH Zürich · Shanghai Jiao Tong University +5

Memory-Augmented Neural Networks Electroencephalography EEG Seizure Detection Multiscale Time-Series Modeling EEG Foundation Models

Sep 29, 2026cs.LG

No Scale Left Behind: Multi-Scale Autoencoder with Bi-directional Attention for Time Series Anomaly Detection

Time series anomaly detection (TSAD) plays a crucial role in healthcare, finance, industrial monitoring, and other sectors. Within and between these settings, anomalies span vastly different temporal scales, from sub-second point spikes to multi-hour drift patterns. However, most existing TSAD methods commit to a single temporal granularity, and multi-scale designs either analyze different scales in isolation or are constrained to a predefined coarse-to-fine hierarchy, both failing to sufficiently capture multi-scale interactions. To resolve this limitation, we propose Multi-Scale Autoencoder with Cross-Scale Attention for TSAD (MSCAD), a simple yet powerful semi-supervised TSAD framework founded on parallel autoencoder branches corresponding to different patch sizes. A stack of symmetric bidirectional cross-scale attention blocks enables every pair of scales to exchange information before reconstruction without allowing any single scale to be privileged. On the comprehensive TSB-AD benchmark (40 datasets, 530 series), MSCAD achieves large performance gains against 50 baselines across multiple metrics, with VUS-PR of 0.57(+9.6%) on the univariate split and 0.47(+9.3%) on the multivariate split compared to the state-of-the-art.

Jiaheng Guo, Haochen Zhang, Yu-Chao Huang +3

UNITES Lab, University of North Carolina at Chapel Hill

Reconstruction-Based Anomaly Detection Attention Mechanisms Time-Series Anomaly Detection Multi-Scale Attention Multiscale Time-Series Modeling

Sep 28, 2026cs.LG

Context-dependent time-series prediction via HyperReservoirs

Time series prediction is a common application of reservoir computing. When the training and testing time series data contains multiple dynamical regimes, because an underlying parameter is changing, or the data in fact consists of multiple distinct systems, simple application of the reservoir computing principle produces high prediction errors. Here, we propose a HyperReservoir as an extended model of reservoir computing especially designed for such cases. The HyperReservoir combines a main reservoir with a smaller context reservoir, where the latter modulates the output weights of the former. This structure resembles the hypernetworks from deep neural network literature. However, in contrast, HyperReservoirs retain the simple training via linear regression of standard reservoir computing. We compare the proposed architecture with a conventional ESN, in which context acts at the input, and a full-matrix Conceptor, in which context modulates the reservoir state space. We evaluate all three models on time-series prediction tasks based on Lorenz and Rössler systems, including for varying bifurcation parameters and time sampling scales. We find that the HyperReservoir achieves the lowest mean test error in all three tasks, and particularly outperforms conceptors on data that is sampled from the same attractor but at different time scales.

Kohei Tsuchiyama, Takatomo Mihana, Ryoichi Horisaki +1

Department of Information Physics and Computing, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

Time Series Forecasting Reservoir Computing Multiscale Time-Series Modeling Chaotic Time-Series Prediction

Sep 24, 2026cs.LG

Neuralized Multi-Wavelet Decomposition for Time Series Classification and Forecasting

Time series analysis is fundamental in domains such as finance, healthcare, and meteorology. Real-world time series often exhibit multiscale characteristics shaped by diverse latent factors, resulting in intricate temporal patterns and rich frequency structures. However, existing approaches typically focus on either frequency-domain decomposition or time-domain pattern extraction in isolation, neglecting their joint structure. This decoupled modeling limits representation expressiveness and undermines performance in tasks requiring simultaneous temporal and spectral reasoning. To address this gap, we propose m-WCN, a novel end-to-end deep learning framework that neuralizes multi-wavelet decomposition for joint extraction of temporal patterns and frequency components. By approximating the classical GHM multi-wavelet transform with trainable convolutional operators and enforcing orthogonality constraints, m-WCN produces interpretable multi-resolution representations. Built on this foundation, we introduce two task-specific architectures: TFBC for time series classification, which boosts discriminative features across frequency scales, and FTB for forecasting, which ensembles frequency-aware predictors. Extensive experiments on 64 UCR datasets and seven public forecasting benchmarks demonstrate the effectiveness of our approach. Built on the neuralized m-WCN, our TFBC and FTB outperform various baseline models across diverse datasets, achieving average improvements of 19.97% in classification and 19.92% in forecasting tasks.

Xiaohan Jiang, Jingyuan Wang, Jiahao Ji +3

School of Computer Science and Engineering, Beihang University, Beijing, China · School of Computer Science and Engineering and the School of Economics and Management, Beihang University, Beijing, China · School of Computer Science and Engineering, Beihang University, Beijing, China, and are also with the MOE Engineering Research Center of Advanced Computer Application Technology, Beihang University, China +1

Time Series Classification Frequency-Domain Feature Learning Time Series Forecasting Wavelet Methods Multiscale Time-Series Modeling

Sep 21, 2026cs.LG

Multi-Term Fourier Graph Neural Network with Sample Relationship Learning for Enhanced Remaining Useful Life Prediction

Predicting the remaining useful life (RUL) is essential for effective predictive maintenance. Spatio-Temporal Graph Neural Networks (ST-GNNs), which can model both temporal and spatial relationships by representing time series data as a sequence of graphs, have shown exceptional performance in RUL prediction. However, current ST-GNNs face several drawbacks. First, they require domain expertise or significant computational power to establish graph structures prior to deploying GNNs. Second, the models are restricted to capture temporal dependencies within a predefined fixed-size lookback window. This restriction ignores the common issue of varying time series lengths, leading the prediction model to miss short-term or long-term dependencies. Finally, conventional models often fail to capture the inherent relationships between samples generated from adjacent time windows, which are crucial for improving both the accuracy and robustness of predictions. To address the aforementioned issues, we introduce a novel framework called Multi-Term Fourier Graph Neural Network with Sample Relationship Learning (MTFGN-SRL). Rather than treating the sample as a sequence of graphs, we consider it as a single complete graph and utilize a Fourier Graph Neural Network (FGN) to capture the spatio-temporal information in the frequency domain. We propose a multi-term learning module that utilizes multiple lookback windows to generate samples with varying terms, which are then fed into the FGN to enhance the extraction of useful information from the data. Finally, we develop a sample relationship learning module by training a heterogeneous GNN to identify inter-sample relationships, resulting in enhanced accuracy and robustness in predictions. Evaluations on the CMAPSS dataset demonstrate MTFGN-SRL's superior performance over state-of-the-art methods in RUL prediction.

Ya Song, Laurens Bliek, Yaoxin Wu +1

Information Systems, Department of Industrial Engineering & Innovation Sciences, Eindhoven University of Technology, Eindhoven, The Netherlands

Graph Neural Networks RUL Estimation Multiscale Time-Series Modeling Spatiotemporal GNNs

Sep 8, 2026cs.LG

HypLTSF: A Hyperbolic Geometric View of Multi-Scale Hierarchies for Long-Term Time Series Forecasting

Multi-scale modeling has become an effective approach for long-term time series forecasting, capturing temporal patterns that range from fine-grained local dynamics to coarse global trends. Representations across these temporal scales are inherently hierarchical, with coarser scales abstracting and aggregating information from finer ones. While existing approaches readily exchange information across these scales, the hierarchy itself is typically left as an emergent byproduct of such interactions rather than captured as a geometric structure in its own right. In this paper, we introduce HypLTSF, a framework that endows the multi-scale hierarchy with a concrete geometric form by embedding scale-wise representations into the Poincaré ball, whose exponentially expanding volume naturally accommodates hierarchical structures. To align this geometry with the temporal hierarchy, HypLTSF imposes two constraints: (1) a radial constraint that orders embeddings by their level of abstraction, and (2) an angular constraint that groups fine-scale patterns sharing a common coarser-scale ancestor. Extensive experiments on long-term time series forecasting benchmarks show that HypLTSF achieves state-of-the-art performance, suggesting that explicitly modeling the multi-scale hierarchy as a geometric structure is effective for forecasting.

Namwoo Kim, Hyungryul Baik, Yoonjin Yoon

Urban AI Institute, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea · Department of Mathematical Science, KAIST, Daejeon, Republic of Korea · Department of Civil and Environmental Engineering, KAIST, Daejeon, Republic of Korea

Long-Term Time Series Forecasting Hierarchical Representation Learning Multiscale Time-Series Modeling Hyperbolic Representation Learning

Aug 26, 2026cs.LG

Frequency-aware forecasting for short-term typhoon gust prediction

Accurate gust forecasting under typhoon conditions remains challenging due to the highly non-stationary and multi-scale characteristics of extreme wind fluctuations. Existing deep learning models often struggle to simultaneously capture long-term trends and rapid local variations, resulting in degraded performance during extreme events. We propose WDANet, a frequency-aware forecasting framework that integrates stationary wavelet decomposition, a Feature-wise Linear Modulation (FiLM) strategy, and a dual-branch encoder-decoder architecture, enabling separate modeling of trend and fluctuation components. Taking the offshore regions of the Western Pacific in China as an example, we conduct fine-grid wind gust prediction research. The results demonstrate that WDANet shows advantages for short lead times under the experimental setting across a 24-h forecasting horizon and achieves higher prediction accuracy than ECMWF-HRES within the first 6 h. During extreme wind events, WDANet more accurately captures gust peaks and attains the best RMSE and MAE performance. These results highlight its potential for offshore wind power operation, disaster warning, and risk mitigation.

Xuefei Wang, Tingyi Liu, Heng Zhang +2

School of Artificial Intelligence, Hubei University, Wuhan, China. · School of Economics and Management, Wuhan University, Wuhan, China. · School of Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China. +1

Frequency-Domain Feature Learning Multiscale Time-Series Modeling Weather Forecasting

Aug 20, 2026cs.LG

Systematic Evaluation of TabPFN-TS and Chronos-2 for Zero-Shot Heat Load Forecasting in District Heating Networks

District heating energy hubs require reliable heat load forecasts for efficient operational scheduling. Forecasting models trained on historical data may require retraining as networks evolve. Zero-shot time-series foundation models and in-context forecasting therefore offer a promising alternative: they can adapt at inference time from recent observations rather than by repeated retraining. This study systematically evaluates TabPFN-TS and Chronos-2 for probabilistic heat load forecasting in two German district heating networks and compares them with trained baselines. We assess whether TabPFN-TS, whose underlying model is pretrained entirely on synthetic tabular rather than time-series data, can capture complex district heating dynamics. We analyze covariate choice, context length, temporal resolution, and forecast horizon on selected operating weeks, evaluate the selected configuration over the full year, and assess cross-network transfer. The principal benchmark assumes perfect weather forecasts; a separate sensitivity analysis uses retrospective weather predictions. Hourly 24-hour forecasting with a 12-week rolling context and ambient temperature provides a parsimonious configuration; longer context windows do not improve accuracy. Both TSFMs outperform all trained baselines in deterministic accuracy in the full-year benchmarks. Chronos-2 achieves the best deterministic scores, with TabPFN-TS remaining close: their CVRMSE values on the main data set are 12.48% and 13.07%, respectively. Chronos-2 also achieves lower continuous ranked probability scores in both networks, with TabPFN-TS remaining close. a TSFM-based Multi-Resolution Residual-Correction Forecaster combines an hourly base forecast with short-term high-resolution corrections. Relative to direct high-resolution forecasting, it generally reduces errors in total heat demand over 12-hour periods and recorded prediction times.

Ben Spoek, Karim K. Ben Hicham, Kai Derzsi +3

Chair of Energy Efficient Buildings and Indoor Climate, RWTH Aachen University, Mathieustr. 10, 52074 Aachen, Germany · Process Systems Engineering, RWTH Aachen University, Forckenbeckstr. 51, 52074 Aachen, Germany

Zero-Shot Time Series Forecasting Time Series Forecasting Building Energy Management Time-Series Foundation Models Multiscale Time-Series Modeling Probabilistic Time Series Forecasting

Aug 10, 2026cs.AI

AirFlow: Context Preserving and Multi-Rate State Modeling for Air Quality Forecasting

Accurate air quality forecasting is essential for public health and urban environmental management, but remains challenging because pollutant channels differ in periodicity and distribution drift, while their concentration trajectories contain both multi-scale dependencies and rapid changes. Recent methods have improved spatial dependency learning and meteorological covariate modeling. However, pollutant channels are still passed through the same normalization rule and temporal backbone, using a shared latent representation for channel-specific distributions and changes at different rates. To address this limitation, we propose AirFlow, a pollutant-aware dual-stream framework that operates on station multivariate observations without additional graph propagation or predefined signal decomposition. Specifically, AirFlow designs two novel blocks: (1) a statistic-guided normalization routing mechanism that selects a normalization path for each pollutant according to its 24-hour autocorrelation and distribution drift; and (2) a hierarchical dual-stream state model that combines multi-scale state space propagation with learnable response coefficients, where gated bidirectional cross-attention exchanges information and adaptively fuses the resulting representations. Experiments on real-world data from multiple cities show that AirFlow achieves the best performance in 34 of 36 metrics comparisons, with reductions of up to 11.11% root mean square error over the state-of-the-art baseline. AirFlow also requires only 0.0483M parameters and 0.0215G FLOPs, achieving high forecasting accuracy with low computational overhead.

Fan Yang, Nan Chen, Yijie Dong +2

School of Software Technology, Zhejiang University Hangzhou, Zhejiang 310000, China

Multivariate Time Series Forecasting Air Quality Prediction Non-Stationary Time Series Forecasting Multiscale Time-Series Modeling State Space Models

Aug 8, 2026cs.LG

FreSH: Frequency-Segmented Hierarchical Multi-Expert Framework for Multivariate Time Series Classification

Multivariate Time Series Classification (MTSC) demands models that can effectively capture complex temporal patterns across multiple scales while remaining computationally efficient. However, existing approaches generally struggle to reconcile fine-grained representation learning, especially under class imbalance and real-world constraints. In this paper, we present FreSH, a Frequency-Segmented Hierarchical Multi-Expert Framework designed to address these challenges. FreSH introduces a new perspective for MTSC by enabling adaptive, multi-scale analysis of temporal signals, allowing different aspects of the data to be modeled in a complementary and coordinated manner. By combining localized specialization with holistic context modeling, FreSH achieves strong representational capacity without incurring excessive computational overhead. An adaptive fusion strategy further enhances flexibility, enabling the model to dynamically emphasize the most informative components of the input. In addition, we incorporate a more robust optimization objective that improves learning stability across varying sample difficulties and class distributions. Extensive evaluations on 30 UEA benchmark datasets and real-world vibration data demonstrate that FreSH consistently outperforms state-of-the-art methods in classification accuracy, while substantially reducing model size and efficiency.

Pingping Liu, Muyao Wang, Zijian Zhang +5

1Jilin University · 2Hong Kong Polytechnic University · 3Pengcheng Laboratory +1

Multivariate Time Series Classification Time Series Classification Mixture of Experts Frequency-Domain Feature Learning Hierarchical Representation Learning Multiscale Time-Series Modeling

Aug 4, 2026cs.LG

CAMP: A Cycle-Aware Multi-Scale Patch Mixer for Time Series Forecasting

Real-world time series are often governed by recurring patterns, but their dominant periods may vary across datasets, forecasting settings, and individual input windows. Existing cycle-aware forecasters commonly rely on a single period selected at the dataset level, which can be restrictive when periodic behavior changes over time or when multiple cycles coexist. Moreover, patch-based models typically process all patch positions uni- formly, although patches farther from the forecast boundary may require broader contextual refinement, while recent patches contain information that should be preserved more directly. Af- ter cyclic behavior is removed, the remaining dynamics may also span multiple temporal resolutions and cannot be adequately de- scribed at a single scale. We introduce CAMP, a Cycle-Aware Multi-Scale Patch Mixer designed to address these challenges. The Adaptive Cycle Learning module identifies dominant fre- quencies separately for each input window and generates both historical and future cyclic components without requiring a pre- defined cycle length. The Horizon-Guided Patch Mixer intro- duces position-dependent refinement, allowing earlier patches to incorporate broader temporal context while preserving infor- mation close to the forecast boundary. CAMP further models the de-cycled residual through temporally aligned multi-resolution representations, enabling complementary dynamics at different scales to be captured within one forecasting framework. Across seven long-term forecasting benchmarks, CAMP achieves the best average MSE on six datasets and the best or tied-best MAE on six. It also obtains the highest MSE win count across sixteen settings on four PEMS traffic benchmarks.

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

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

Long-Term Time Series Forecasting Time Series Forecasting Multiscale Time-Series Modeling

Jul 28, 2026cs.AI

A Cost-Effective Multimodal LLM Reasoning Framework for Question Answering over Irregular Clinical Time Series

Question answering (QA) over irregular clinical time series (ICTS) plays a pivotal role in a wide range of healthcare applications. Although recent multimodal time-series large language models (LLMs) have shown considerable promise in general-purpose time-series QA, they remain poorly equipped to model the sparsity, asynchrony, and irregular sampling patterns of clinical observations. To fill this gap, we propose ClinPRISM, a cost-effective multimodal LLM reasoning framework for question answering over ICTS data. First, we devise an irregularity-aware multi-scale encoder to capture sparse clinical evidence at diverse temporal scales. Then, we propose a temporal evidence distiller to integrate representations across these scales and compress them into a small number of LLM-compatible tokens. Moreover, we introduce a progressive alignment strategy that sequentially aligns the irregular trajectories with the LLM's textual embedding space. To facilitate training, we construct 30,000 clinical time series paired with multi-scale descriptions, together with 41,000 instruction-tuning instances spanning 11 tasks. Using a 4-billion-parameter LLM backbone, ClinPRISM achieves state-of-the-art performance on the held-out evaluation benchmark while using only 16 time-series tokens and achieving an average inference latency of 0.15 seconds per question.

Frank Nie, Ethan B Liu, Yuan Zhu +2

Shandong University China · University of Auckland New Zealand

Irregular Time-Series Modeling Efficient Multimodal Inference Time Series QA Multimodal Large Language Models Multiscale Time-Series Modeling

Jul 25, 2026stat.ML

Adaptive Multi-Scale Forecasting and Gate-Localized Conformal Prediction for Multivariate Nonstationary Time Series

We propose ABF-T-GLCP, a model-agnostic framework for forecasting and uncertainty quantification in nonstationary multivariate time series. The central idea is to learn an adaptive predictive state representation for point forecasting and reuse it for conformal calibration. The forecasting module combines horizon-specific temporal experts through a learned gate and refines predictions using sparse predictive transfer across related series. The uncertainty module, Gate-Localized Conformal Prediction (GLCP), uses the learned gate state, together with temporal recency, to select locally relevant calibration residuals, thereby coupling uncertainty calibration to the predictive regimes used by the forecasting model. This shared representation allows point forecasts and prediction intervals to adapt consistently under evolving temporal dynamics while retaining the model-agnostic nature of conformal prediction and yielding approximate local coverage under mild stability conditions. Experiments on a large-scale high-frequency commodity forecasting benchmark show consistent gains in point forecasting accuracy and substantially narrower prediction intervals with empirical coverage close to the nominal level. Additional results indicate that the framework extends beyond the motivating financial application.

Ziling Ma, Junshu Jiang, Ángel López-Oriona +2

Statistics Department, Computer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia · NeuroAI Laboratory, Computer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia

Multivariate Time Series Forecasting Conformal Prediction Non-Stationary Time Series Forecasting Adaptive Conformal Inference Multiscale Time-Series Modeling

Jul 23, 2026cs.AI

MSBraM: A Multi-scale Self-supervised Brain Foundation Model for Hierarchical EEG Dynamics Learning

Self-supervised foundation models have recently shown strong potential for electroencephalogram (EEG)-based analysis. However, existing approaches struggle to capture the inherently multi-scale temporal structure of EEG signals, where local neural patterns and long-range dependencies jointly encode task-relevant information. This limitation hampers cross-scale representation learning and generalization across diverse downstream tasks. To address this challenge, we propose MSBraM, a Multi-Scale self-supervised Brain foundation Model designed to learn hierarchical EEG representations. MSBraM follows a two-stage pretraining framework. First, a multi-scale neural tokenizer discretizes raw EEG signals into semantic codes at different temporal resolutions via vector-quantized reconstruction. Second, the model is pretrained to predict masked codes using a curriculum multi-scale masking strategy, progressively integrating fine-grained local patterns with global temporal context. We pretrain MSBraM on over 2,400 hours of EEG data and evaluate it across 10 downstream tasks on 12 public datasets. Extensive experiments show that MSBraM achieves superior performance on other state-of-the-art pretrained models, demonstrating strong generalization and transferability. These results indicate that explicitly modeling multi-scale temporal dynamics is critical for effective EEG foundation models.

Tao Zhou, Jing Han, Lingyu Shu +1

Hunan University Changsha, China

Electroencephalography Self-Supervised Pre-Training Hierarchical Representation Learning Multiscale Time-Series Modeling EEG Foundation Models

Jul 22, 2026stat.ML

SPECTRA: State-Space Exogenous Context and Temporal-Frequency Resolution Architecture for Probabilistic Energy Forecasting

Modern power systems increasingly require probabilistic forecasts amid interacting uncertainties from renewable intermittency, flexible demand, market volatility, and weather-dependent generation. However, existing methods often treat multi-scale decomposition, exogenous-variable alignment, and probabilistic output as separate steps, obscuring how predictable structures and uncertainty-bearing fluctuations jointly shape the forecast distribution. This paper proposes a state-space exogenous-context and temporal-frequency resolution architecture for general probabilistic energy forecasting. Its central premise is that trend-periodic components primarily determine the baseline trajectory, whereas high-frequency residuals and external perturbations govern the spread and asymmetry of forecast uncertainty. Accordingly, the architecture adaptively separates deterministic and residual streams, aligns exogenous context with both, refines the deterministic backbone through multi-resolution spectral-temporal state-space modeling, and estimates ordered quantile boundaries from their complementary representations. Experiments on load, price, solar, and wind forecasting achieve the best continuous ranked probability score in 14 of 18 settings, reducing average CRPS by 5.74% and upper-tail quantile risk by 7.27% over the strongest baselines. These results support deterministic-stochastic separation as an effective design principle for general probabilistic energy forecasting.

Hang Ye, Xinyan Jiang, Yuedong Shi +5

Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai 201210, China · University of Chinese Academy of Sciences, Beijing 101408, China · School of Physical Science and Technology, Shanghaitech University, Shanghai 201210, China +2

Probabilistic Forecasting Electricity Load Forecasting Multiscale Time-Series Modeling Probabilistic Time Series Forecasting State Space Models Power Systems

Jul 20, 2026cs.LG

Lightweight Wrappers for Adapting Time Series Foundation Models to Regional Drought Forecasting

Large \emph{Time Series Foundation Models} (TSFMs) demonstrate strong zero-shot forecasting capabilities across diverse domains. However, their application to regional climate forecasting faces practical challenges: model weights are often proprietary, local training records are limited, and computational budgets are constrained, making traditional fine-tuning approaches infeasible. To address these constraints, we introduce a lightweight, black-box adaptation framework (requiring no access to backbone parameters and no backbone fine-tuning) that enhances frozen TSFMs at inference time through two plug-and-play wrappers: \textbf{SMR\textsuperscript{2}} (Stationarity aware multi-resolution Residual), which decomposes the input into multi-resolution temporal views, learns stride specific residual corrections that capture regional dynamics, then adaptively ensembles them into a single forecast, and \textbf{MBB} (Moving Block Bootstrap), which preserves temporal dependencies through block resampling and ensembles over temporally coherent residual perturbations to stabilize the point forecast. Both wrappers instantiate the same bagging style principle: they build diverse views of the input or its residuals, forecast each with the same frozen backbone, and aggregate, so all adaptation comes from inference time ensembling rather than any weight update. Evaluated on one month ahead Standardized Precipitation Evapotranspiration Index (SPEI) prediction across multiple sites in South Australia, our framework consistently improves forecasting performance across several backbone models, demonstrating up to 26% mean squared error (MSE) reduction over the corresponding frozen backbone while enabling practical deployment in resource constrained regional forecasting systems.

Wentao Gao, Jiuyong Li, Lin Liu +4

Adelaide University · Adelaide, Australia · CSIRO Technology +1

Test-Time Adaptation Time Series Forecasting Time-Series Foundation Models Multiscale Time-Series Modeling

Jul 20, 2026cs.LG

Residual-Guided Multi-Resolution Refinement of Foundation Models: A Case Study in Drought Forecasting

Regional climate prediction presents unique challenges for time series foundation models, which typically process temporal patterns through single-pass inference. Expert climatologists, in contrast, employ multi-scale temporal analysis and iterative refinement based on systematic error diagnosis. We present RGMR (Residual-Guided Multi-Resolution Refinement), an inference-time framework that adapts pre-trained foundation models to perform structured coarse-to-fine refinement for climate forecasting without updating backbone parameters. Applied to drought forecasting using the Standardized Precipitation Evapotranspiration Index (SPEI), RGMR is architecture-agnostic across the three TSFM backbones evaluated per site (TimesFM, TimeGPT, TabPFN) and consistently lowers test-set MSE on three South Australian sites and three additional regions outside South Australia. Applied to TimesFM, the wrapper reduces one-month-ahead SPEI MSE by up to 18.9% across the three South Australian sites (mean reduction

\approx

18.7%). Overall, RGMR provides a practical route for deploying frozen TSFMs in regional climate forecasting workflows.

Wentao Gao, Jiuyong Li, Lin Liu +4

Adelaide University, Adelaide, SA, Australia · CSIRO Technology, Canberra, Australia · CSIRO Environment, Canberra, Australia

Time Series Forecasting Climate Modeling Time-Series Foundation Models Multiscale Time-Series Modeling

Jul 18, 2026cs.LG

HyBDM: Multi-Scale Hybrid Experts for Time Series Forecasting with Bidirectional Dependency Modeling

Time series forecasting (TSF) is vital to many applications, yet existing models often struggle to capture the heterogeneous long-range global patterns and short-range local variations in multivariate time series. While some approaches partially model these dependencies, they often do not jointly exploit temporal and feature-wise information. To address this challenge, we propose HyBDM, a multi-scale hybrid model that decomposes temporal dynamics into global patterns and local variations, which are modeled by two specialized experts. The Global Patterns Expert employs an enhanced BiConv-Mamba module that integrates bidirectional convolutions, an M-SSM layer, a forgetting mechanism, and a GDD-MLP module for cross-channel modeling. The Local Variations Expert uses a Local Window Transformer (LWT) to perform efficient locality-aware attention with reduced computational complexity. In addition, a Multi-Scale Patcher and a Long-Short Router enable multi-resolution representations and adaptive fusion of the two experts. Experiments on six benchmark datasets show that HyBDM outperforms state-of-the-art methods in both forecasting accuracy and computational efficiency, demonstrating its effectiveness in bridging global-local dependencies for multivariate TSF.

Wenqiang Ma, Chen Cheng, Xue Cheng +1

Soul of Harlequin Lab

Multivariate Time Series Forecasting Multi-Scale Feature Fusion Mixture-of-Experts Models Time Series Transformers Multiscale Time-Series Modeling

Jul 14, 2026cs.LG

Lightweight Multi-Scale Anomaly Detection for Resource-Constrained Edge Devices

Time-series anomaly detection is increasingly important in IoT systems, sensor networks, and edge monitoring applications, where models must operate under strict constraints on memory, latency, and power consumption. While recent deep-learning approaches have improved detection accuracy, many remain computationally expensive and often fail to capture subtle anomalies due to limited multi-scale sensitivity. Autoencoders are widely used for anomaly detection because they reconstruct normal patterns well, leading to elevated reconstruction errors for anomalous inputs. Their simplicity and efficiency also make them suitable lightweight backbones for handling multi-scale inputs. To address these challenges, we propose a Lightweight MultiScale AutoEncoder (LMSAE) network for univariate time-series anomaly detection, designed to be compact and computationally efficient. LMSAE leverages the Discrete Wavelet Transform (DWT) to extract multi-scale features and employs a multi-scale loss function to improve sensitivity to subtle or hidden anomalies. Experiments on benchmark datasets demonstrate competitive or superior detection performance despite using significantly fewer parameters and a model size of less than 500 KB. LMSAE also achieves low-latency, low-power inference on the NVIDIA Jetson Nano, with 9x reduction in inference latency and 2x reduction in power consumption, making it ideal for edge deployment.

Raheen Junaid Wani, Smruti R. Sarangi

School of Information Technology Indian Institute of Technology, Delhi New Delhi, India 110016 · Department of Computer Science Indian Institute of Technology, Delhi New Delhi, India 110016

Autoencoders Edge Inference Reconstruction-Based Anomaly Detection Time-Series Anomaly Detection Multiscale Time-Series Modeling

Jul 12, 2026cs.LG

Multi-Scale Convolution with Optimal Transport Attention Effect on Multivariate Time Series

The analysis of Multivariate Time Series (MTS) plays an important role in a lot of real-world practical applications, but it still remains some challenging problem about capturing multi-granularity structural patterns and suppressing noise appropriately. Multi-Scale Convolution with Optimal Transport Attention (MSC-OT) is proposed in this paper. MSC-OT is a useful architecture to optimize the attention mechanism. It combines multi-scale convolution with Sinkhorn optimal transport method based on inverted embedding. The inverted embedding approach embeds each variable as a token and allows the model to capture cross-variate relationships better. MSC-OT consists of two part: (1) Multi-Scale Convolution Enhancement, that applies multi-scale convolutions to attention score matrices based on inverted embedding, capturing local structural patterns in the variate-interaction space induced by compressed temporal representations; (2) Sinkhorn Optimal Transport Regularization, that formulates attention computation as an optimal transport problem and employs iterative matrix scaling to ensure balanced information flow across variates. Adaptive Fusion Strategy utilizes softmax-normalized learnable weights to dynamically combine base attention, convolution-enhanced, and OT-regularized scores. Experiments on widely-used datasets, including ETT, Electricity, Traffic, Solar-Energy, and Exchange-Rate, show that MSC-OT achieves well performance in both short-term and long-term forecasting tasks. Ablation experiments further validate the effectiveness of each proposed component and their synergistic contributions to improving prediction accuracy for multivariate time series forecasting.

HaoChong Fu, Jian Xu

Institute of Collaborative Innovation · University of Macau · Macau, China +2

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

Jul 9, 2026cs.LG

RhyMix: A Lightweight Adaptive Multi-Rhythm Network for Long-Term Time Series Forecasting

Real-world time series exhibit complex dynamics characterized by multiple simultaneous temporal patterns: short-term fluctuations, periodic seasonal cycles, long-term trends, and irregular abrupt changes. However, many existing forecasting architectures rely on single-path temporal modeling--transformers capture long-range dependencies but smooth local variations, convolutions capture local patterns but have limited receptive fields, and linear models are efficient but cannot capture nonlinear dynamics. To address this, we introduce RhyMix (RHYthm MIXture), a hybrid neural architecture designed around a parallel dual-path modeling paradigm with adaptive gating mechanisms. RhyMix integrates two complementary encoding branches: (i) a Cyclic Path that incorporates explicit seasonal inductive bias through learnable cyclic embeddings, capturing predictable rhythmic patterns; and (ii) a lightweight Multi-Scale Temporal Convolutional Network with Channel Attention Path that employs multi-scale depthwise dilated convolutions to capture temporal dependencies across different receptive fields. A key innovation is the use of adaptive gating at multiple levels: a path gate dynamically combines four specialized forecasting heads (Direct, Trend-Seasonal Decomposition, Local Convolution, and Periodic Fusion) per sample and channel, while a hybrid gate adaptively balances the Cyclic and MSTCN-CA Paths based on input characteristics. This design ensures the model adapts to specific temporal patterns while maintaining linear complexity in sequence length, channels, and prediction horizon. Across extensive benchmarks on 12 real-world datasets for long-term forecasting, RhyMix achieves state-of-the-art performance on 10 of 12 datasets. The model remains lightweight (~40K params) with linear complexity and low-latency inference (<5ms),suitable for resource-constrained edge devices and real-time deployment.

Sumit Satishrao Shevtekar, Chandresh Kumar Maurya

Long-Term Time Series Forecasting Time Series Forecasting Temporal Convolutional Networks Multiscale Time-Series Modeling

Jul 2, 2026cs.LG

Zeus: Towards Tuning-Free Foundation Model for Time Series Analysis

We present Zeus, a unified tuning-free Time Series Foundation Model (TSFM) that delivers superior performance across diverse analysis tasks without any task-specific fine-tuning. Unlike prior studies that primarily focus on zero-shot forecasting but require task-specific tuning for other tasks, Zeus bridges this gap by addressing two fundamental challenges in multi-task generalization. First, to reconcile point-level granularity with long-sequence scalability, Zeus incorporates a multi-scale Transformer featuring point-wise tokenization and a U-shaped hierarchy, effectively balancing fine-grained fidelity with computational efficiency. Second, to accommodate varying inductive biases across different tasks, Zeus introduces Multi-Objective Temporal Masking (MOTM), a unified strategy that supports heterogeneous tasks (e.g., extrapolation, interpolation, and global abstraction) within a single framework. Extensive experiments across five representative tasks demonstrate that Zeus consistently achieves competitive results in tuning-free settings, underscoring its potential as a general-purpose TSFM.

Yisong Fu, Zezhi Shao, Chengqing Yu +4

State Key Laboratory of AI Safety, Institute of Computing Technology, Chinese Academy of Sciences · University of Chinese Academy of Sciences · Xiamen Institute of Data Intelligence

Zero-Shot Time Series Forecasting Multi-Task Learning Sequence Modeling Time-Series Foundation Models Multiscale Time-Series Modeling

Jun 26, 2026cs.LG

TA-SparseMG: Trend-Aware Sparse Forecasting via Multi-Scale Gating for Long-Term Time Series

Long-term time series forecasting finds extensive applications in domains such as power demand, traffic flow, meteorological observation, and renewable energy dispatch. Forecasting dynamically varying long-term time series poses inherent challenges, including statistical nonstationarity, local high-frequency disturbances, and coupled cross-period dependencies, which make it difficult for lightweight models to balance parameter efficiency and forecasting performance. To address this issue, this study presents TA-SparseMG, a lightweight cross-period forecasting model built on SparseTSF's sparse cross-period modeling framework. It incorporates three key modules: a trend-aware reversible instance normalization module, a scale-adaptive gated denoising module, and a multiscale gated-attention MLP forecasting module. The trend-aware normalization module captures input-window statistics and calibrates forecast-window distributions, effectively mitigating distribution shift. The scale-adaptive gated denoising module performs feature smoothing and residual suppression before period rearrangement, thereby reducing interference from high-frequency perturbations. The multiscale gated attention prediction module strengthens the prediction head's adaptive representational capacity via conditional gating and feature modulation. Extensive experiments across multiple LTSF benchmarks demonstrate that the proposed TA-SparseMG consistently achieves superior, stable performance. Ablation studies confirm that each module independently improves distribution adaptation, input robustness, and cross-period feature mapping capability.

Wenchao Liu, Hongbing Wang, Youji Zhu +2

School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China. · School of Big Data and Computer Science, Guizhou Normal University, Guiyang 550025, China.

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

Jun 25, 2026cs.CL

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

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

Defu Cao, Zijie Lei, Muyan Weng +2

University of Southern California · Meta · Google DeepMind

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

Jun 23, 2026cs.LG

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

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

Cheng He, Zhenyu Guan, Xijie Liang +6

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

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

Jun 18, 2026cs.LG

PaAno+: Multiscale Encoding and Cross-Variable Attention for Time Series Anomaly Detection

Time-series anomaly detection has significant practical value for industrial and medical monitoring, as well as other critical domains. Current Transformer- and large-model-based detection approaches incur excessive computational overhead, while existing lightweight alternatives are constrained by insufficient feature extraction and inadequate modeling of dependencies across multivariate variables. To mitigate the above drawbacks, this study develops a lightweight, efficient anomaly detection model, dubbed PaAno, within the patch-oriented representation learning paradigm. In the encoder module, a multiscale feature-extraction backbone is constructed using convolutional kernels with differentiated receptive fields to capture hierarchical temporal characteristics; subsequent cross-scale adaptive attention aggregation, combined with residual connection optimization, further stabilizes feature representation learning. A cross-variable fusion attention module is embedded to explicitly characterize inter-variable correlations, empowering the model to identify anomalous patterns amid intricate operational conditions. Moreover, a novel pretext task based on temporal patch-window sorting is customized to uncover intrinsic structural properties of time series, and triplet loss is leveraged to optimize the patch embedding space for enhanced feature discrimination. Extensive experiments on the TSB-AD benchmark demonstrate that the proposed PaAno achieves state-of-the-art detection accuracy on both univariate and multivariate tasks, yielding significant performance gains across evaluation metrics, including VUS-PR, relative to the original PaAno. Leveraging a compact network design, the presented model achieves favorable computational efficiency, enabling deployment on resource-limited terminals for real-time anomaly inference.

Youji Zhu, Hongbing Wang, Wenchao Liu +2

School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China. · School of Big Data and Computer Science, Guizhou Normal University, Guiyang 550025, China.

Self-Supervised Time Series Representation Learning Time-Series Anomaly Detection Multiscale Time-Series Modeling