Multivariate Time Series Forecasting

Multivariate time series forecasting often struggles to capture long-range dependencies due to fixed lookback windows. Retrieval-augmented forecasting addresses this by retrieving historical segments from memory, but existing approaches rely on a channel-agnostic strategy that applies the same references to all variables. This neglects inter-variable heterogeneity, where different channels exhibit distinct periodicities and spectral profiles. We propose CRAFT (Channel-wise retrieval-augmented forecasting), a novel framework that performs retrieval independently for each channel. To ensure efficiency, CRAFT adopts a two-stage pipeline: a sparse relation graph constructed in the time domain prunes irrelevant candidates, and spectral similarity in the frequency domain ranks references, emphasizing dominant periodic components while suppressing noise. Experiments on seven public benchmarks demonstrate that CRAFT outperforms state-of-the-art forecasting baselines, achieving superior accuracy with practical inference efficiency.

Accurate prediction of multivariate time series is essential for emerging network intelligent control, observability, and management functions. Existing statistical-based and shallow machine learning models have shown limited prediction capabilities on multivariate time series. They prioritize improvements in average prediction accuracy, while overlooking heterogeneous dependency structures and performance variability across individual time series. Recent advances in large language models have introduced new directions for multivariate time series forecasting; however, their application in conjunction with explicit structural dependency modeling remains relatively underexplored, especially in networked environments. In this paper, we present a topology-aware learning framework for large-scale network traffic prediction that explicitly models both temporal dynamics and structural dependencies in multivariate network time series. We first investigate a graph attention model designed to capture topology-induced correlations among network traffic time series. We then evaluate a fine-tuned large language model-based representations for improved generalization across heterogeneous traffic patterns. To further address the diversity of cross-correlations in high-dimensional traffic data, we introduce a clustering-based preprocessing stage that groups traffic flows with similar dependency characteristics prior to model training, reducing input complexity and improving learning stability. Experiments on real backbone traffic data show consistent improvements over statistical and recurrent neural network baselines. In addition to average accuracy, we evaluate performance across individual time series and observe reduced variability in prediction quality.

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.

The Nash-Sutcliffe efficiency ($\text{NSE}$) 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 $L_{\text{NS}} = 1 - \text{NSE}$. We prove that $L_{\text{NS}}$ 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 $\text{NSE}$ across multiple series is the sample analog of minimizing the expected $L_{\text{NS}}$. 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 $L_{\text{NS}}$, 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 $\text{NSE}$ than the earlier formulation. Our results establish a decision-theoretic foundation for $\text{NSE}$-based model estimation and forecast evaluation in large datasets, while further clarifying the benefits of global over local machine learning models.

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.

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.

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.

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.

We introduce Temporal Variational Implicit Neural Representations (TV-INRs), a probabilistic framework for modeling irregular multivariate time series that enables efficient and accurate individualized imputation and forecasting. By integrating implicit neural representations with latent variable models, TV-INRs learn distributions over time-continuous generator functions conditioned on signal-specific covariates. Unlike existing INR approaches that require extensive training, fine-tuning or meta-learning, our method achieves accurate individualized predictions through a single forward pass. Our experiments demonstrate that with a single TV-INRs instance, we can accurately solve diverse imputation and forecasting tasks, offering a computationally efficient and scalable solution for real-world applications. TV-INRs performs particularly well in low-data regimes, where on several datasets it achieves substantially lower imputation error, including order-of-magnitude improvements.

Teleoperation systems must be aware of the human's workload during missions to maintain operator performance. Prior work employed wearable physiological sensor response metrics to estimate current human workload; however, these estimates only enable robots to respond to under- or overload conditions reactively. Current human workload prediction approaches are limited to very short prediction horizons and fail to investigate variable lag horizons' impact on those predictions. This manuscript investigates physiological sensor driven human workload prediction focusing on the impact of lag horizons on both univariate and multivariate time series forecasting models, with longer prediction horizons than the workload prediction state-of-the-art (i.e., > 30 seconds using Long Short-Term Memory networks). Models were trained using data from a 64 participant non-sedentary supervisory environment NASA Multi-Attribute Task Battery-II human subjects evaluation. A key finding is that univariate workload predictions required 240 second lag horizons, whereas multivariate workload predictions sufficed with 120 second lag horizons. This finding indicates additional workload components reduce lag horizon requirements, enabling more efficient models with longer prediction horizons.

Conventional forecasting methods are trained end-to-end on unimodal time series, which limits their ability to exploit textual information and undermines their generalization in data-scarce scenarios. Recently, large language models (LLMs) and time series foundation models (TSFMs) have demonstrated powerful capabilities in complex textual reasoning and zero-shot temporal modeling, respectively. Integrating these strengths to construct a multimodal time series foundation model that jointly leverages temporal and textual information for zero-shot future inference has emerged as a promising research direction. However, the scarcity of large-scale, high-quality multimodal datasets remains a fundamental obstacle. To address this challenge, we propose ChronoSteer, a decoupled agentic framework that learns cross-modal alignment from synthetic paired supervision. Specifically, a pretrained LLM first converts textual events into revision instructions that steer the initial unimodal prediction produced by a frozen TSFM. These revision instructions form an intermediate instruction space that bridges the semantic gap between text and time series while fully leveraging pretrained knowledge. Technically, the instructions are discretized into a compact codebook of instruction anchors, effectively mitigating semantic divergence while reducing the cost of dataset construction. Finally, we adopt a two-stage training strategy to recover the fine-grained magnitude information lost during discretization. Furthermore, we release a leakage-controlled multimodal benchmark constructed with temporal separation and textual context available before the prediction window. When paired with an LLM and trained on synthetic cross-modal alignment data, ChronoSteer achieves a 25.8% improvement in zero-shot prediction accuracy over its unimodal backbone, and outperforms prior state-of-the-art unimodal and multimodal ...

Rainfall is an important environmental driver of water-quality variations through processes such as runoff, pollutant transport, dilution, and resuspension. Traditional mechanistic models can explicitly describe these processes but often require substantial process specification and site-specific calibration, limiting their flexibility under changing hydrological conditions. In this work, we explore a data-driven alternative by proposing RaiNet to jointly model multiscale water-quality dynamics and station-specific rainfall effects across relative lags and temporal scales. RaiNet employs LocTrend to capture irregular water-quality dynamics, constructs station-oriented rainfall events from gridded precipitation, and introduces XGateFusion for conditional lag-aware fusion across scales. We further release three real-world multimodal datasets comprising over 150,000 temporally aligned water quality observations and gridded precipitation raster images. Experiments show that RaiNet outperforms general time-series, water quality, diffusion-based, and spatiotemporal models by over 20%, while component-wise analyses confirm the distinct contribution of each module.

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