Multivariate Time Series Forecasting

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Overview

The field predicts several changing quantities together, such as electricity demand across regions, weather at multiple stations, or patients’ vital signs, where one variable may provide clues about another. Common approaches include linear and MLP models, recurrent networks, Transformers and state-space models, as well as graph, frequency-based, and decomposition methods; newer work also explores probabilistic generation, foundation models, and irregularly sampled data. Models are commonly compared on benchmarks such as ETT, Electricity, Traffic, Weather, and GIFT-Eval, with growing attention to long horizons, uncertainty, and transfer across datasets. A central tension is that cross-variable links and extra context can improve forecasts when informative, but noisy, shifting, or irrelevant relationships can hurt accuracy, so robustness and efficiency matter alongside average error.

Latest papers

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307 papers52 papers in the last four weeks, up 58% on the four weeks before. 0.3% of all new papers.

Mar 9, 2026

GCGNet: Graph-Consistent Generative Network for Time Series Forecasting with Exogenous Variables

Exogenous variables offer valuable supplementary information for predicting future endogenous variables. Forecasting with exogenous variables needs to consider both past-to-future dependencies (i.e., temporal correlations) and the influence of exogenous variables on endogenous variables (i.e., channel correlations). This is pivotal when future exogenous variables are available, because they may directly affect the future endogenous variables. Many methods have been proposed for time series forecasting with exogenous variables, focusing on modeling temporal and channel correlations. However, most of them use a two-step strategy, modeling temporal and channel correlations separately, which limits their ability to capture joint correlations across time and channels. Furthermore, in real-world scenarios, time series are frequently affected by various forms of noises, underscoring the critical importance of robustness in such correlations modeling. To address these limitations, we propose GCGNet, a Graph-Consistent Generative Network for time series forecasting with exogenous variables. Specifically, GCGNet first employs a Variational Generator to produce coarse predictions. A Graph Structure Aligner then further guides it by evaluating the consistency between the generated and true correlations, where the correlations are represented as graphs, and are robust to noises. Finally, a Graph Refiner is proposed to refine the predictions to prevent degeneration and improve accuracy. Extensive experiments on 12 real-world datasets demonstrate that GCGNet outperforms state-of-the-art baselines.

Zhengyu Li, Xiangfei Qiu, Yuhan Zhu +4

East China Normal University

Exogenous Time Series ForecastingRobust Time Series ForecastingTime Series ForecastingMultivariate Time Series Forecasting
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Mar 9, 2026

Joint Return and Risk Modeling with Deep Neural Networks for Portfolio Construction

Portfolio construction traditionally relies on separately estimating expected returns and covariance matrices using historical statistics, often leading to suboptimal allocation under time-varying market conditions. This paper proposes a joint return and risk modeling framework based on deep neural networks that enables end-to-end learning of dynamic expected returns and risk structures from sequential financial data. Using daily data from ten large-cap US equities spanning 2010 to 2024, the proposed model is evaluated across return prediction, risk estimation, and portfolio-level performance. Out-of-sample results during 2020 to 2024 show that the deep forecasting model achieves competitive predictive accuracy (RMSE = 0.0264) with economically meaningful directional accuracy (51.9%). More importantly, the learned representation effectively captures volatility clustering and regime shifts. When integrated into portfolio optimization, the proposed Neural Portfolio strategy achieves an annual return of 36.4% and a Sharpe ratio of 0.91, outperforming equal weight and historical mean-variance benchmarks in terms of risk-adjusted performance. These findings demonstrate that jointly modeling return and covariance dynamics can provide consistent improvements over traditional allocation approaches. The framework offers a scalable and practical alternative for data-driven portfolio construction under nonstationary market conditions.

Keonvin Park

Interdisciplinary Program in Artificial Intelligence, Seoul National University, Seoul, 08829, South Korea

Quantitative FinancePortfolio OptimizationCovariance EstimationMultivariate Time Series Forecasting
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Mar 8, 2026

Enhanced Random Subspace Local Projections for High-Dimensional Time Series Analysis

High-dimensional time series forecasting suffers from severe overfitting when the number of predictors exceeds available observations, making standard local projection methods unstable and unreliable. We propose an enhanced Random Subspace Local Projection (RSLP) framework designed to deliver robust impulse response estimation in the presence of hundreds of correlated predictors. The method introduces weighted subspace aggregation, category-aware subspace sampling, adaptive subspace size selection, and a bootstrap inference procedure tailored to dependent data. These enhancements substantially improve estimator stability at longer forecast horizons while providing more reliable finite-sample inference. Experiments on synthetic data, macroeconomic indicators, and the FRED-MD dataset demonstrate a 33 percent reduction in estimator variability at horizons h >= 3 through adaptive subspace size selection. The bootstrap inference procedure produces conservative confidence intervals that are 14 percent narrower at policy-relevant horizons in very high-dimensional settings (FRED-MD with 126 predictors) while maintaining proper coverage. The framework provides practitioners with a principled approach for incorporating rich information sets into impulse response analysis without the instability of traditional high-dimensional methods.

Eman Khalid, Moimma Ali Khan, Zarmeena Ali +3

Department of Computer Science, National University of Computer and Emerging Sciences, Islamabad, Pakistan

Multivariate Time Series Forecasting
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Mar 7, 2026

Permutation-Equivariant 2D State Space Models: Theory and Canonical Architecture for Multivariate Time Series

Multivariate time series (MTS) modeling often implicitly imposes an artificial ordering over variables, violating the inherent exchangeability found in many real-world systems where no canonical variable axis exists. We formalize this limitation as a violation of the permutation symmetry principle and require state-space dynamics to be permutation-equivariant along the variable axis. In this work, we theoretically characterize the complete canonical form of linear variable coupling under this symmetry constraint. We prove that any permutation-equivariant linear 2D state-space system naturally decomposes into local self-dynamics and a global pooled interaction, rendering ordered recurrence not only unnecessary but structurally suboptimal. Motivated by this theoretical foundation, we introduce the Variable-Invariant Two-Dimensional State Space Model (VI 2D SSM), which realizes the canonical equivariant form via permutation-invariant aggregation. This formulation eliminates sequential dependency chains along the variable axis, reducing the dependency depth from O(C)\mathcal{O}(C) to O(1)\mathcal{O}(1) and simplifying stability analysis to two scalar modes. Furthermore, we propose VI 2D Mamba, a unified architecture integrating multi-scale temporal dynamics and spectral representations. Extensive experiments on forecasting, classification, and anomaly detection benchmarks demonstrate that our model achieves state-of-the-art performance with superior structural scalability, validating the theoretical necessity of symmetry-preserving 2D modeling.

Seungwoo Jeong, Heung-Il Suk

Department of Artificial Intelligence, Korea University, Seoul 02841, Republic of Korea

State Space ModelsMultivariate Time Series ForecastingMultivariate Time Series Classification
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Mar 6, 2026

MM-ISTS: Cooperating Irregularly Sampled Time Series Forecasting with Multimodal Vision-Text LLMs

Irregularly sampled time series (ISTS) are widespread in real-world scenarios, exhibiting asynchronous observations on uneven time intervals across diverse variables. Existing ISTS forecasting methods often solely utilize historical observations to predict future ones while falling short in learning contextual semantics and fine-grained temporal patterns. To address these problems, we propose MM-ISTS, a multimodal ISTS forecasting framework augmented by vision-text large language models, which bridges temporal, visual, and textual modalities. MM-ISTS encompasses a two-stage encoding mechanism. In particular, a Cross-Modal Vision-Text Encoding module is proposed to automatically generate informative visual images and textual data, enabling the capture of intricate temporal patterns and comprehensive contextual understanding, in collaboration with multimodal LLMs (MLLMs). In parallel, ISTS encoding extracts complementary yet enriched temporal features from historical ISTS observations, including multi-view embedding fusion and a Temporal-Variable Encoder. Further, we propose an Adaptive Query-Based Feature Extractor to compress MLLM token embeddings while preserving useful knowledge, which in turn reduces computational costs. In addition, a Multimodal Alignment module with Modality-Aware Gating is designed to alleviate the modality gaps. Extensive experiments on real data offer insight into the effectiveness of the proposed solutions.

Zhi Lei, Chenxi Liu, Hao Miao +3

East China Normal University, Shanghai, China · Centre for Artificial Intelligence and Robotics, Hong Kong Institute of Science & Innovation, Chinese Academy of Sciences, Hong Kong, China · Department of Computing, The Hong Kong Polytechnic University, Hong Kong, China

Irregular Time-Series ModelingMultivariate Time Series ForecastingLLM-Based Time Series ForecastingMultimodal Learning
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Mar 6, 2026

UniMamba: A Unified Spatial-Temporal Modeling Framework with State-Space and Attention Integration

Multivariate time series forecasting is fundamental to numerous domains such as energy, finance, and environmental monitoring, where complex temporal dependencies and cross-variable interactions pose enduring challenges. Existing Transformer-based methods capture temporal correlations through attention mechanisms but suffer from quadratic computational cost, while state-space models like Mamba achieve efficient long-context modeling yet lack explicit temporal pattern recognition. Therefore we introduce UniMamba, a unified spatial-temporal forecasting framework that integrates efficient state-space dynamics with attention-based dependency learning. UniMamba employs a Mamba Variate-Channel Encoding Layer enhanced with FFT-Laplace Transform and TCN to capture global temporal dependencies, and a Spatial Temporal Attention Layer to jointly model inter-variate correlations and temporal evolution. A Feedforward Temporal Dynamics Layer further fuses continuous and discrete contexts for accurate forecasting. Comprehensive experiments on eight public benchmark datasets demonstrate that UniMamba consistently outperforms state-of-the-art forecasting models in both forecasting accuracy and computational efficiency, establishing a scalable and robust solution for long-sequence multivariate time-series prediction.

Xingsheng Chen, Xianpei Mu, Deyu Yi +6

School of Computing and Data Science, The University of Hong Kong, Hong Kong, China · School of Information Engineering, Beijing Institute of Graphic Communication, Beijing, China · Innovation Engineering College, Macau University of Science and Technology, Macau, China +1

Multivariate Time Series ForecastingLong-Term Time Series ForecastingSelective SSMsSpatiotemporal Forecasting
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Mar 6, 2026

Bi Directional Feedback Fusion for Activity Aware Forecasting of Indoor CO2 and PM2.5

Indoor air quality (IAQ) forecasting plays a critical role in safeguarding occupant health, ensuring thermal comfort, and supporting intelligent building control. However, predicting future concentrations of key pollutants such as carbon dioxide (CO2) and fine particulate matter (PM2.5) remains challenging due to the complex interplay between environmental factors and highly dynamic occupant behaviours. Traditional data driven models primarily rely on historical sensor trajectories and often fail to anticipate behaviour induced emission spikes or rapid concentration shifts. To address these limitations, we present a dual stream bi directional feedback fusion framework that jointly models indoor environmental evolution and action derived embeddings representing human activities. The proposed architecture integrates a context aware modulation mechanism that adaptively scales and shifts each stream based on a shared, evolving fusion state, enabling the model to selectively emphasise behavioural cues or long term environmental trends. Furthermore, we introduce dual timescale temporal modules that independently capture gradual CO2 accumulation patterns and short term PM2.5 fluctuations. A composite loss function combining weighted mean squared error, spike aware penalties, and uncertainty regularisation facilitates robust learning under volatile indoor conditions. Extensive validation on real-world IAQ datasets demonstrates that our approach significantly outperforms state of the art forecasting baselines while providing interpretable uncertainty estimates essential for practical deployment in smart buildings and health-aware monitoring systems.

Harshala Gammulle, Lidia Morawska, Sridha Sridharan +1

Signal Processing, Artificial Intelligence and Vision Technologies (SAIVT) Lab, Queensland University of Technology, Brisbane, Australia. · International Laboratory for Air Quality and Health (ILAQH), Queensland University of Technology, Brisbane, Australia.

Air Quality PredictionMultivariate Time Series ForecastingMultimodal Sensor Fusion
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Mar 1, 2026

A Deep Learning Framework for Heat Demand Forecasting using Time-Frequency Representations of Decomposed Features

District Heating Systems are essential infrastructure for delivering heat to consumers across a geographic region sustainably, yet efficient management relies on optimizing diverse energy sources, such as wood, gas, electricity, and solar, in response to fluctuating demand. Aligning supply with demand is critical not only for ensuring reliable heat distribution but also for minimizing carbon emissions and extending infrastructure lifespan through lower operating temperatures. However, accurate multi-step forecasting to support these goals remains challenging due to complex, non-linear usage patterns and external dependencies. In this work, we propose a novel deep learning framework for day-ahead heat demand prediction that leverages time-frequency representations of historical data. By applying Continuous Wavelet Transform to decomposed demand and external meteorological factors, our approach enables Convolutional Neural Networks to learn hierarchical temporal features that are often inaccessible to standard time domain models. We systematically evaluate this method against statistical baselines, state-of-the-art Transformers, and emerging foundation models using multi-year data from three distinct Danish districts, a Danish city, and a German city. The results show a significant advancement, reducing the Mean Absolute Error by 36% to 43% compared to the strongest baselines, achieving forecasting accuracy of up to 95% across annual test datasets. Qualitative and statistical analyses further confirm the accuracy and robustness by reliably tracking volatile demand peaks where others fail. This work contributes both a high-performance forecasting architecture and critical insights into optimal feature composition, offering a validated solution for modern energy applications.

Adithya Ramachandran, Satyaki Chatterjee, Thorkil Flensmark B. Neergaard +3

Time Series ForecastingMultivariate Time Series ForecastingFrequency-Domain Feature Learning
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Mar 1, 2026

Learning with the Nash-Sutcliffe loss

The Nash-Sutcliffe efficiency (NSE\text{NSE}) is a widely used, positively oriented relative measure for evaluating forecasts across multiple time series. However, it lacks a decision-theoretic foundation for this purpose. To address this, we examine its negatively oriented counterpart, which we refer to as Nash-Sutcliffe loss, defined as LNS=1−NSEL_{\text{NS}} = 1 - \text{NSE}. We prove that LNSL_{\text{NS}} is strictly consistent for an elicitable and identifiable multi-dimensional functional, which we name the Nash-Sutcliffe functional. This functional is a data-weighted component-wise mean. The common practice of maximizing the average NSE\text{NSE} across multiple series is the sample analog of minimizing the expected LNSL_{\text{NS}}. Consequently, this operation implicitly assumes that all series originate from a single non-stationary, stochastic process. We introduce Nash-Sutcliffe linear regression, a multi-dimensional model estimated by minimizing the average LNSL_{\text{NS}}, which reduces to a data-weighted least squares formulation. By reorienting the sample average loss function, we extend the previously proposed evaluation and estimation framework to forecasting multiple stationary dependent time series with differing stochastic properties. This constitutes a more natural empirical implementation of the NSE\text{NSE} than the earlier formulation. Our results establish a decision-theoretic foundation for NSE\text{NSE}-based model estimation and forecast evaluation in large datasets, while further clarifying the benefits of global over local machine learning models.

Hristos Tyralis, Georgia Papacharalampous

1Support Command, Hellenic Air Force, Elefsina Air Base, 19 200, Elefsina, Greece · Department of Land, Environment, Agriculture and Forestry, University of Padova, Viale dell'Università 16, 35020, Legnaro, Italy

Multivariate Time Series ForecastingTime Series ForecastingLinear Regression
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Mar 1, 2026

Navigating Time's Possibilities: Plausible Counterfactual Explanations for Multivariate Time-Series Forecast through Genetic Algorithms

Counterfactual learning has become promising for understanding and modeling causality in complex and dynamic systems. This paper presents a novel method for counterfactual learning in the context of multivariate time series analysis and forecast. The primary objective is to uncover hidden causal relationships and identify potential interventions to achieve desired outcomes. The proposed methodology integrates genetic algorithms and rigorous causality tests to infer and validate counterfactual dependencies within temporal sequences. More specifically, we employ Granger causality to enhance the reliability of identified causal relationships, rigorously assessing their statistical significance. Then, genetic algorithms, in conjunction with quantile regression, are used to exploit these intricate causal relationships to project future scenarios. The synergy between genetic algorithms and causality tests ensures a thorough exploration of the temporal dynamics present in the data, revealing hidden dependencies and enabling the projection of outcomes under hypothetical interventions. We evaluate the performance of our algorithm on real-world data, showcasing its ability to handle complex causal relationships, revealing meaningful counterfactual insights, and allowing for the prediction of outcomes under hypothetical interventions.

Gianlucca Zuin, Adriano Veloso

Universidade Federal de Minas Gerais, C.S. Dept. Belo Horizonte, Brazil. · Kunumi. Belo Horizonte, Brazil.

Counterfactual PredictionCounterfactual ExplanationsMultivariate Time Series ForecastingTime-Series Causal Discovery
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Feb 28, 2026

Phys-Diff: A Physics-Inspired Latent Diffusion Model for Tropical Cyclone Forecasting

Tropical cyclone (TC) forecasting is critical for disaster warning and emergency response. Deep learning methods address computational challenges but often neglect physical relationships between TC attributes, resulting in predictions lacking physical consistency. To address this, we propose Phys-Diff, a physics-inspired latent diffusion model that disentangles latent features into task-specific components (trajectory, pressure, wind speed) and employs cross-task attention to introduce prior physics-inspired inductive biases, thereby embedding physically consistent dependencies among TC attributes. Phys-Diff integrates multimodal data including historical cyclone attributes, ERA5 reanalysis data, and FengWu forecast fields via a Transformer encoder-decoder architecture, further enhancing forecasting performance. Experiments demonstrate state-of-the-art performance on global and regional datasets.

Lei Liu, Xiaoning Yu, Kang Chen +4

University of Science and Technology of China, Hefei, China · Hefei University of Technology, Hefei, China

Tropical Cyclone Intensity ForecastingWeather ForecastingPhysics-Informed Diffusion ModelsLatent Diffusion ModelsSpatiotemporal ForecastingMultivariate Time Series Forecasting
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Feb 27, 2026

Disentangled Mode-Specific Representations for Tensor Time Series via Contrastive Learning

Multi-mode tensor time series (TTS) can be found in many domains, such as search engines and environmental monitoring systems. Learning representations of a TTS benefits various applications, but it is also challenging since the complexities inherent in the tensor hinder the realization of rich representations. In this paper, we propose a novel representation learning method designed specifically for TTS, namely MoST. Specifically, MoST uses a tensor slicing approach to reduce the complexity of the TTS structure and learns representations that can be disentangled into individual non-temporal modes. Each representation captures mode-specific features, which are the relationship between variables within the same mode, and mode-invariant features, which are in common in representations of different modes. We employ a contrastive learning framework to learn parameters; the loss function comprises two parts intended to learn representation in a mode-specific way and mode-invariant way, effectively exploiting disentangled representations as augmentations. Extensive experiments on real-world datasets show that MoST consistently outperforms the state-of-the-art methods in terms of classification and forecasting accuracy. Code is available at https://github.com/KoheiObata/MoST.

Kohei Obata, Taichi Murayama, Zheng Chen +2

SANKEN, Osaka University, Osaka, Japan · Yokohama National University, Kanagawa, Japan

Time Series Representation LearningDisentangled Representation LearningMultivariate Time Series ClassificationMultivariate Time Series Forecasting
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Feb 27, 2026

SDMixer: Sparse Dual-Mixer for Time Series Forecasting

Multivariate time series forecasting is widely applied in fields such as transportation, energy, and finance. However, the data commonly suffers from issues of multi-scale characteristics, weak correlations, and noise interference, which limit the predictive performance of existing models. This paper proposes a dual-stream sparse Mixer prediction framework that extracts global trends and local dynamic features from sequences in both the frequency and time domains, respectively. It employs a sparsity mechanism to filter out invalid information, thereby enhancing the accuracy of cross-variable dependency modeling. Experimental results demonstrate that this method achieves leading performance on multiple real-world scenario datasets, validating its effectiveness and generality. The code is available at https://github.com/SDMixer/SDMixer

Xiang Ao

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

Multivariate Time Series ForecastingTime Series ForecastingMultiscale Time-Series Modeling
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Feb 25, 2026

DualWeaver: Synergistic Feature Weaving Surrogates for Multivariate Forecasting with Univariate Time Series Foundation Models

Time-series foundation models (TSFMs) have achieved strong univariate forecasting through large-scale pre-training, yet effectively extending this success to multivariate forecasting remains challenging. To address this, we propose DualWeaver, a novel framework that adapts univariate TSFMs (Uni-TSFMs) for multivariate forecasting by using a pair of learnable, structurally symmetric surrogate series. Generated by a shared auxiliary feature-fusion module that captures cross-variable dependencies, these surrogates are mapped to TSFM-compatible series via the forecasting objective. The symmetric structure enables parameter-free reconstruction of final predictions directly from the surrogates, without additional parametric decoding. A theoretically grounded regularization term is further introduced to enhance robustness against adaptation collapse. Extensive experiments on diverse real-world datasets show that DualWeaver outperforms state-of-the-art multivariate forecasters in both accuracy and stability. We release the code at https://github.com/li-jinpeng/DualWeaver.

Jinpeng Li, Zhongyi Pei, Huaze Xue +3

School of Software, BNRist, Tsinghua University · Tencent

Multivariate Time Series ForecastingTime Series ForecastingTime-Series Foundation ModelsSurrogate Modeling
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Feb 25, 2026

Learning global river system hydrodynamics with a topology-informed foundation model

Accurate river prediction is essential for water, food, and energy security, yet extending it reliably from sparse in-situ gauges to the full river network remains an open challenge. Although machine learning has transformed Earth-system modelling, the same sparse and uneven observations have largely confined its advances for rivers to discrete basins rather than connected river systems. Here we introduce GraphRiverCast (GRC), a topology-informed river foundation model for reach-level prediction across the global river network. Exploiting the connectivity and energetics of rivers, it is trained on sparse gauges and predicts daily multivariate hydrodynamics with no prior river conditions. GRC outperforms strong physics-based and machine-learning models. Attribution experiments show that, compared with standard autoregressive models that rely more on temporal recurrence, GRC reconstructs river states from topology and forcing, learning the dynamics themselves and inheriting the self-correcting character of river systems. Its skill therefore barely decays with lead time, even far beyond its training horizon. It also generalises to ungauged reaches and finer-resolution networks, bringing reliable hydrodynamic prediction to poorly monitored regions. More broadly, harnessing the structure and energetics of a system offers a strategy for machine learning in other observation-limited Earth systems.

Hancheng Ren, Gang Zhao, Shuo Wang +12

College of Water Sciences, Beijing Normal University, Beijing, China. · School of Geography and the Environment, University of Oxford, Oxford, UK. · Department of Transdisciplinary Science and Engineering, Institute of Science Tokyo, Tokyo, Japan. +6

HydrologyStreamflow ForecastingSpatiotemporal ForecastingSpatiotemporal GNNsMultivariate Time Series Forecasting
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Feb 25, 2026

TiMi: Empower Time Series Transformers with Multimodal Mixture of Experts

Multimodal time series forecasting has garnered significant attention for its potential to provide more accurate predictions than traditional single-modality models by leveraging rich information inherent in other modalities. However, due to fundamental challenges in modality alignment, existing methods often struggle to effectively incorporate multimodal data into predictions, particularly textual information that has a causal influence on time series fluctuations, such as emergency reports and policy announcements. In this paper, we reflect on the role of textual information in numerical forecasting and propose Time series transformers with Multimodal Mixture-of-Experts, TiMi, to unleash the causal reasoning capabilities of LLMs. Concretely, TiMi utilizes LLMs to generate inferences on future developments, which serve as guidance for time series forecasting. To seamlessly integrate both exogenous factors and time series into predictions, we introduce a Multimodal Mixture-of-Experts (MMoE) module as a lightweight plug-in to empower Transformer-based time series models for multimodal forecasting, eliminating the need for explicit representation-level alignment. Experimentally, our proposed TiMi demonstrates consistent state-of-the-art performance on sixteen real-world multimodal forecasting benchmarks, outperforming advanced baselines while offering both strong adaptability and interpretability.

Jiafeng Lin, Yuxuan Wang, Huakun Luo +2

School of Software, BNRist, Tsinghua University.

Time Series TransformersLLM-Based Time Series ForecastingMultimodal FusionMultivariate Time Series ForecastingMixture of Experts
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Feb 25, 2026

Learning Recursive Multi-Scale Representations for Irregular Multivariate Time Series Forecasting

Irregular Multivariate Time Series (IMTS) are characterized by uneven intervals between consecutive timestamps, which carry sampling pattern information valuable and informative for learning temporal and variable dependencies. In addition, IMTS often exhibit diverse dependencies across multiple time scales. However, many existing multi-scale IMTS methods use resampling to obtain the coarse series, which can alter the original timestamps and disrupt the sampling pattern information. To address the challenge, we propose ReIMTS, a Recursive multi-scale modeling approach for Irregular Multivariate Time Series forecasting. Instead of resampling, ReIMTS keeps timestamps unchanged and recursively splits each sample into subsamples with progressively shorter time periods. Based on the original sampling timestamps in these long-to-short subsamples, an irregularity-aware representation fusion mechanism is proposed to capture global-to-local dependencies for accurate forecasting. Extensive experiments demonstrate an average performance improvement of 27.1% in the forecasting task across different models and real-world datasets. Our code is available at https://github.com/Ladbaby/PyOmniTS.

Boyuan Li, Zhen Liu, Yicheng Luo +1

School of Computer Science and Engineering, South China University of Technology

Irregular Time-Series ModelingMultivariate Time Series ForecastingMultiscale Time-Series ModelingMulti-Scale Feature Fusion
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Feb 24, 2026

Benchmarking State Space Models, Transformers, and Recurrent Networks for US Grid Forecasting

Selecting the right deep learning model for power grid forecasting is challenging, as performance heavily depends on the data available to the operator. This paper presents a comprehensive benchmark of five modern neural architectures: two state space models (PowerMamba, S-Mamba), two Transformers (iTransformer, PatchTST), and a traditional LSTM. We evaluate these models on hourly electricity demand across six diverse US power grids for forecast windows between 24 and 168 hours. To ensure a fair comparison, we adapt each model with specialized temporal processing and a modular layer that cleanly integrates weather covariates. Our results reveal that there is no single best model for all situations. When forecasting using only historical load, PatchTST and the state space models provide the highest accuracy. However, when explicit weather data is added to the inputs, the rankings reverse: iTransformer improves its accuracy three times more efficiently than PatchTST. By controlling for model size, we confirm that this advantage stems from the architecture's inherent ability to mix information across different variables. Extending our evaluation to solar generation, wind power, and wholesale prices further demonstrates that model rankings depend on the forecast task: PatchTST excels on highly rhythmic signals like solar, while state space models are better suited for the chaotic fluctuations of wind and price. Ultimately, this benchmark provides grid operators with actionable guidelines for selecting the optimal forecasting architecture based on their specific data environments.

Sunki Hong, Jisoo Lee

Gramm AI

Forecasting BenchmarksElectricity Load ForecastingMultivariate Time Series ForecastingState Space ModelsTime Series TransformersRecurrent Neural Networks
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Feb 23, 2026

Multivariate time-series forecasting of ASTRI-Horn monitoring data: A Normal Behavior Model

This study presents a Normal Behavior Model (NBM) developed to forecast monitoring time-series data from the ASTRI-Horn Cherenkov telescope under normal operating conditions. The analysis focused on 15 physical variables acquired by the Telescope Control Unit between September 2022 and July 2024, representing sensor measurements from the Azimuth and Elevation motors. After data cleaning, resampling, feature selection, and correlation analysis, the dataset was segmented into fixed-length intervals, in which the first I samples represented the input sequence provided to the model, while the forecast length, T, indicated the number of future time steps to be predicted. A sliding-window technique was then applied to increase the number of intervals. A Multi-Layer Perceptron (MLP) was trained to perform multivariate forecasting across all features simultaneously. Model performance was evaluated using the Mean Squared Error (MSE) and the Normalized Median Absolute Deviation (NMAD), and it was also benchmarked against a Long Short-Term Memory (LSTM) network. The MLP model demonstrated consistent results across different features and I-T configurations, and matched the performance of the LSTM while converging faster. It achieved an MSE of 0.019+/-0.003 and an NMAD of 0.032+/-0.009 on the test set under its best configuration (4 hidden layers, 720 units per layer, and I-T lengths of 300 samples each, corresponding to 5 hours at 1-minute resolution). Extending the forecast horizon up to 6.5 hours-the maximum allowed by this configuration-did not degrade performance, confirming the model's effectiveness in providing reliable hour-scale predictions. The proposed NBM provides a powerful tool for enabling early anomaly detection in online ASTRI-Horn monitoring time series, offering a basis for the future development of a prognostics and health management system that supports predictive maintenance.

Federico Incardona, Alessandro Costa, Farida Farsian +8

INAF, Osservatorio Astrofisico di Catania, Catania, I-95123, Italy · INAF, Osservatorio Astronomico di Brera, Merate, I-23807, Italy · INAF, Istituto di Astrofisica Spaziale e Fisica Cosmica, Milano, I-20133, Italy +1

Multivariate Time Series Forecasting
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Feb 23, 2026

NEXUS: A compact neural architecture for high-resolution spatiotemporal air quality forecasting in Delhi National Capital Region

Urban air pollution in megacities poses critical public health challenges, particularly in Delhi National Capital Region (NCR) where severe degradation affects millions. We present NEXUS (Neural Extraction and Unified Spatiotemporal) architecture for forecasting carbon monoxide, nitrogen oxide, and sulfur dioxide. Working with four years (2018--2021) of atmospheric data across sixteen spatial grids, NEXUS achieves R2^2 exceeding 0.94 for CO, 0.91 for NO, and 0.95 for SO2_2 using merely 18,748 parameters -- substantially fewer than SCINet (35,552), Autoformer (68,704), and FEDformer (298,080). The architecture integrates patch embedding, low-rank projections, and adaptive fusion mechanisms to decode complex atmospheric chemistry patterns. Our investigation uncovers distinct diurnal rhythms and pronounced seasonal variations, with winter months experiencing severe pollution episodes driven by temperature inversions and agricultural biomass burning. Analysis identifies critical meteorological thresholds, quantifies wind field impacts on pollutant dispersion, and maps spatial heterogeneity across the region. Extensive ablation experiments demonstrate each architectural component's role. NEXUS delivers superior predictive performance with remarkable computational efficiency, enabling real-time deployment for air quality monitoring systems.

Rampunit Kumar, Aditya Maheshwari

Lightweight Neural NetworksAir Quality PredictionSpatiotemporal ForecastingMultivariate Time Series Forecasting
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Feb 20, 2026

Sub-City Real Estate Price Index Forecasting at Weekly Horizons Using Satellite Radar and News Sentiment

Reliable real estate price indicators are typically published at city level and low frequency, limiting their use for neighborhood-scale monitoring and long-horizon planning. We study whether sub-city price indices can be forecasted at weekly frequency by combining physical development signals from satellite radar with market narratives from news text. Using over 350,000 transactions from Dubai Land Department (2015-2025), we construct weekly price indices for 19 sub-city regions and evaluate forecasts from 2 to 34 weeks ahead. Our framework fuses regional transaction history with Sentinel-1 SAR backscatter, news sentiment combining lexical tone and semantic embeddings, and macroeconomic context. Results are strongly horizon dependent: at horizons up to 10 weeks, price history alone matches multimodal configurations, but beyond 14 weeks sentiment and SAR become critical. At long horizons (26-34 weeks), the full multimodal model reduces mean absolute error from 4.48 to 2.93 (35% reduction), with gains statistically significant across regions. Nonparametric learners consistently outperform deep architectures in this data regime. These findings establish benchmarks for weekly sub-city index forecasting and demonstrate that remote sensing and news sentiment materially improve predictability at strategically relevant horizons.

Baris Arat, Hasan Fehmi Ates, Emre Sefer

Ozyegin University, Istanbul, Turkey

Time Series ForecastingLong-Term Time Series ForecastingMultivariate Time Series Forecasting
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Feb 19, 2026

AdaptStress: Online Adaptive Learning for Interpretable and Personalized Stress Prediction Using Multivariate and Sparse Physiological Signals

Continuous stress forecasting could potentially contribute to lifestyle interventions. This paper presents a novel, explainable, and individualized approach for stress prediction using physiological data from consumer-grade smartwatches. We develop a time series forecasting model that leverages multivariate features, including heart rate variability, activity patterns, and sleep metrics, to predict stress levels across 16 temporal horizons (History window: 3, 5, 7, 9 days; forecasting window: 1, 3, 5, 7 days). Our evaluation involves 16 participants monitored for 10-15 weeks. We evaluate our approach across 16 participants, comparing against state-of-the-art time series models (Informer, TimesNet, PatchTST) and traditional baselines (CNN, LSTM, CNN-LSTM) across multiple temporal horizons. Our model achieved performance with an MSE of 0.053, MAE of 0.190, and RMSE of 0.226 in optimal settings (5-day input, 1-day prediction). A comparison with the baseline models shows that our model outperforms TimesNet, PatchTST, CNN-LSTM, LSTM, and CNN under all conditions, representing improvements of 36.9%, 25.5%, and 21.5% over the best baseline. According to the explanability analysis, sleep metrics are the most dominant and consistent stress predictors (importance: 1.1, consistency: 0.9-1.0), while activity features exhibit high inter-participant variability (0.1-0.2). Most notably, the model captures individual-specific patterns where identical features can have opposing effects across users, validating its personalization capabilities. These findings establish that consumer wearables, combined with adaptive and interpretable deep learning, can deliver relevant stress assessment adapted to individual physiological responses, providing a foundation for scalable, continuous, explainable mental health monitoring in real-world settings.

Xueyi Wang, Claudine J. C. Lamoth, Elisabeth Wilhelm

Engineering and Technology institute Groningen (ENTEG), University of Groningen, Groningen, 9742AG, the Netherlands · Department of Human Movement Sciences, University Medical Center Groningen, Groningen, Netherlands

Wearable Health MonitoringExplainable Time Series ForecastingTime Series ForecastingOnline LearningMultivariate Time Series Forecasting
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Feb 18, 2026

HPMixer: Hierarchical Patching for Multivariate Time Series Forecasting

In long-term multivariate time series forecasting, effectively capturing both periodic patterns and residual dynamics is essential. To address this within standard deep learning benchmark settings, we propose the Hierarchical Patching Mixer (HPMixer), which models periodicity and residuals in a decoupled yet complementary manner. The periodic component utilizes a learnable cycle module [7] enhanced with a nonlinear channel-wise MLP for greater expressiveness. The residual component is processed through a Learnable Stationary Wavelet Transform (LSWT) to extract stable, shift-invariant frequency-domain representations. Subsequently, a channel-mixing encoder models explicit inter-channel dependencies, while a two-level non-overlapping hierarchical patching mechanism captures coarse- and fine-scale residual variations. By integrating decoupled periodicity modeling with structured, multi-scale residual learning, HPMixer provides an effective framework. Extensive experiments on standard multivariate benchmarks demonstrate that HPMixer achieves competitive or state-of-the-art performance compared to recent baselines.

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

ISMLL, University of Hildesheim

Multivariate Time Series ForecastingLong-Term Time Series ForecastingMultiscale Time-Series ModelingResidual Learning
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Feb 17, 2026

Meteorological data and Sky Images meets Neural Models for Photovoltaic Power Forecasting

Due to the rise in the use of renewable energies as an alternative to traditional ones, and especially solar energy, there is increasing interest in studying how to address photovoltaic forecasting in the face of the challenge of variability in photovoltaic energy production, using different methodologies. This work develops a hybrid approach for short and long-term forecasting based on two studies with the same purpose. A multimodal approach that combines images of the sky and photovoltaic energy history with meteorological data is proposed. The main goal is to improve the accuracy of ramp event prediction, increase the robustness of forecasts in cloudy conditions, and extend capabilities beyond nowcasting, to support more efficient operation of the power grid and better management of solar variability. Deep neural models are used for both nowcasting and forecasting solutions, incorporating individual and multiple meteorological variables, as well as an analytical solar position. The results demonstrate that the inclusion of meteorological data, particularly the surface long-wave, radiation downwards, and the combination of wind and solar position, significantly improves current predictions in both nowcasting and forecasting tasks, especially on cloudy days. This study highlights the importance of integrating diverse data sources to improve the reliability and interpretability of solar energy prediction models.

Ines Montoya-Espinagosa, Antonio Agudo

Universitat Pompeu Fabra, Barcelona, Spain. · Institut de Robòtica i Informàtica Industrial, CSIC-UPC, Barcelona, Spain.

Solar Power ForecastingMultivariate Time Series Forecasting
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Feb 4, 2026

Probabilistic NDVI Forecasting from Sparse Satellite Time Series and Weather Covariates

Short-term forecasting of vegetation dynamics is a key enabler for data-driven decision support in precision agriculture. Normalized Difference Vegetation Index (NDVI) forecasting from satellite observations, however, remains challenging due to sparse and irregular sampling caused by cloud masking, as well as the heterogeneous climatic conditions under which crops evolve. In this work, we propose a probabilistic forecasting framework for field-level NDVI prediction under sparse, irregular clear-sky acquisitions. The architecture separates the encoding of historical NDVI and meteorological observations from future exogenous covariates, fusing both representations for multi-step quantile prediction. To address irregular revisit patterns and horizon-dependent uncertainty, we introduce a temporal-distance weighted quantile loss that aligns the training objective with the effective forecasting horizon. In addition, we incorporate cumulative and extreme-weather feature engineering to capture delayed meteorological effects relevant to vegetation response. Experiments on European satellite data show that the proposed approach outperforms statistical, deep learning, and time-series baselines on both pointwise and probabilistic evaluation metrics. Ablation studies confirm that target history is the primary driver of performance, with meteorological covariates providing additional gains in the full multimodal setting. The code is available at https://github.com/arco-group/ndvi-forecasting.

Irene Iele, Giulia Romoli, Daniele Molino +4

Unit of Artificial Intelligence and Computer Systems, Universit`a Campus Bio-Medico di Roma, Italy · Department of Diagnostics and Intervention, Biomedical Engineering and Radiation Physics, Ume˚a University, Sweden · Department of Naval, Electrical, Electronics and Telecommunications Engineering, University of Genoa, Italy

Irregular Time-Series ModelingMultivariate Time Series ForecastingAgricultural Remote SensingSpatiotemporal ForecastingProbabilistic Time Series Forecasting
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Feb 2, 2026

Spectral Text Fusion: A Frequency-Aware Approach to Multimodal Time-Series Forecasting

Multimodal time series forecasting is crucial in real-world applications, where decisions depend on both numerical data and contextual signals. The core challenge is to effectively combine temporal numerical patterns with the context embedded in other modalities, such as text. While most existing methods align textual features with time-series patterns one step at a time, they neglect the multiscale temporal influences of contextual information such as time-series cycles and dynamic shifts. This mismatch between local alignment and global textual context can be addressed by spectral decomposition, which separates time series into frequency components capturing both short-term changes and long-term trends. In this paper, we propose SpecTF, a simple yet effective framework that integrates the effect of textual data on time series in the frequency domain. Our method extracts textual embeddings, projects them into the frequency domain, and fuses them with the time series' spectral components using a lightweight cross-attention mechanism. This adaptively reweights frequency bands based on textual relevance before mapping the results back to the temporal domain for predictions. Experimental results demonstrate that SpecTF significantly outperforms state-of-the-art models across diverse multi-modal time series datasets while utilizing considerably fewer parameters. Code is available at https://github.com/hiepnh137/SpecTF.

Huu Hiep Nguyen, Minh Hoang Nguyen, Dung Nguyen +1

Applied Artificial Intelligence Initiative Deakin University Geelong, Australia

Multivariate Time Series ForecastingFrequency-Domain Time Series ModelingTime Series ForecastingMultimodal FusionMultiscale Time-Series Modeling
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Jan 29, 2026

Multi-Modal Time Series Prediction via Mixture of Modulated Experts

Real-world time series exhibit complex and evolving dynamics, making accurate forecasting extremely challenging. Recent multi-modal forecasting methods leverage textual information such as news reports to improve prediction, but most rely on token-level fusion that mixes temporal patches with language tokens in a shared embedding space. However, such fusion can be ill-suited when high-quality time-text pairs are scarce and when time series exhibit substantial variation in characteristics, thus complicating cross-modal alignment. In parallel, mixture-of-experts (MoE) architectures have proven effective for both time series modeling and multi-modal learning, yet many existing MoE-based modality integration methods still depend on token-level fusion. To address this, we propose Expert Modulation, a new mechanism for multi-modal time series prediction that conditions both routing and expert computation on textual signals, enabling direct and efficient cross-modal control over expert behavior. Through theoretical analysis and experiments, our proposed method demonstrates strong improvements in multi-modal time series prediction. The current code implementation is available at https://github.com/BruceZhangReve/MoME

Lige Zhang, Ali Maatouk, Jialin Chen +3

Emory University · Yale University · Amazon

Multivariate Time Series ForecastingTime Series ForecastingMixture-of-Experts ModelsMultimodal Fusion
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Jan 18, 2026

Patch-Level Tokenization with CNN Encoders and Attention for Improved Transformer Time-Series Forecasting

Transformer-based models have shown strong performance in time-series forecasting by leveraging self-attention to model long-range temporal dependencies. However, their effectiveness depends critically on the quality and structure of input representations derived from raw multivariate time-series data, particularly as sequence length and data scale increase. This paper proposes a two-stage forecasting framework that explicitly separates local temporal representation learning from global dependency modelling. In the proposed approach, a convolutional neural network operates on fixed-length temporal patches to extract short-range temporal dynamics and non-linear feature interactions, producing compact patch-level token embeddings. Token-level self-attention is applied during representation learning to refine these embeddings, after which a Transformer encoder models inter-patch temporal dependencies to generate forecasts. The method is evaluated on a synthetic multivariate time-series dataset with controlled static and dynamic factors, using an extended sequence length and a larger number of samples. Experimental results demonstrate that the proposed framework consistently outperforms a convolutional baseline under increased temporal context and remains competitive with a strong patch-based Transformer model. These findings indicate that structured patch-level tokenization provides a scalable and effective representation for multivariate time-series forecasting, particularly when longer input sequences are considered.

Saurish Nagrath, Saroj Kumar Panigrahy, Soubhagya Sankar Barpanda

School of Computer Science and Engineering, VIT-AP University, Amaravati, Andhra Pradesh, 522241, India

Multivariate Time Series ForecastingTime Series TransformersTime Series TokenizationTime Series Representation Learning
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Dec 17, 2025

EMFusion: Uncertainty-Aware Conditional Diffusion Model for Multivariate Narrow-band Exposure Forecasting

The rapid growth in wireless infrastructure has increased the need to accurately estimate and forecast electromagnetic field (EMF) levels to ensure ongoing compliance, assess potential health impacts, and support efficient network planning. While existing studies rely on univariate forecasting of wideband aggregate EMF data, multivariate narrow-band EMF forecasting is needed to capture the inter-operator and inter-frequency variations essential for proactive network planning. To this end, this paper introduces EMFusion, a conditional diffusion-based EMF forecasting framework that integrates diverse contextual factors, such as time of day, season, and holidays, while providing uncertainty-aware probabilistic forecasts. The proposed architecture features a residual U-Net backbone enhanced by a cross-attention mechanism that dynamically integrates external conditions to guide the generation process. Furthermore, EMFusion integrates an imputation-based sampling strategy that treats forecasting as a structural inpainting task, ensuring temporal coherence even with irregular measurements. Unlike standard point forecasters, EMFusion generates empirical probabilistic prediction intervals from the learned conditional distribution, providing uncertainty-aware probabilistic forecasting rather than simple point estimation. Numerical experiments conducted on the multivariate narrow-band EMF datasets demonstrate that EMFusion with the contextual information of working hours outperforms the baseline models with or without conditions. The proposed EMFusion outperforms the best baseline by 23.85% in continuous ranked probability score (CRPS) and 13.93% in normalized root mean square error.

Zijiang Yan, Yixiang Huang, Jianhua Pei +2

department of Electrical Engineering and Computer Science, York University, Toronto, Canada · School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China · China Southern Grid Electric Power Dispatch Control Center, Guangzhou, China +3

Multivariate Time Series ForecastingConditional Diffusion ModelsProbabilistic Time Series Forecasting
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Dec 8, 2025

Weighted Contrastive Learning for Anomaly-Aware Time-Series Forecasting

Reliable forecasting of multivariate time series under anomalous conditions is crucial in applications such as ATM cash logistics, where sudden demand shifts can disrupt operations. Modern deep forecasters achieve high accuracy on normal data but often fail when distribution shifts occur. We propose Weighted Contrastive Adaptation (WECA), a Weighted contrastive objective that aligns normal and anomaly-augmented representations, preserving anomaly-relevant information while maintaining consistency under benign variations. Evaluations on a nationwide ATM transaction dataset with domain-informed anomaly injection show that WECA improves SMAPE on anomaly-affected data by 6.1 percentage points compared to a normally trained baseline, with negligible degradation on normal data. These results demonstrate that WECA enhances forecasting reliability under anomalies without sacrificing performance during regular operations.

Joel Ekstrand, Tor Mattsson, Zahra Taghiyarrenani +3

Center for Applied Intelligent Systems Research, Halmstad University, Halmstad, Sweden · Mikael Linden Consulting AB, Stockholm, Sweden

Multivariate Time Series ForecastingContrastive LearningTime Series Forecasting
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