multivariate forecasting

Existing multivariate time series forecasting methods often neglect dynamic inter-variable dependencies, leading to modeling bias. To address this, we formulate multivariate forecasting as a systematic multi-task learning problem for the first time. Our approach introduces a gradient-geometry-based task partitioning and balancing mechanism: (i) task correlation is quantified via gradient angle analysis; (ii) correlation-driven hierarchical clustering groups variables into coherent tasks; and (iii) an error-adaptive gradient reweighting strategy ensures balanced optimization. We further propose MTLinear—a lightweight linear architecture that achieves strong expressiveness without sacrificing computational efficiency. Extensive experiments on multiple benchmark datasets demonstrate that our method consistently outperforms strong baselines—including Informer and Autoformer—in both accuracy and inference speed, achieving superior forecasting performance with significantly lower computational overhead. The implementation is publicly available.

Existing univariate time series foundation models (Uni-TSFM) struggle to generalize directly to multivariate forecasting tasks. To address this limitation, this work proposes DualWeaver, a novel framework that leverages a pair of structurally symmetric, learnable proxy sequences to model inter-variable dependencies through a shared auxiliary feature fusion module, subsequently mapping them into Uni-TSFMs-compatible univariate sequences for prediction. The framework incorporates a parameter-free reconstruction mechanism and a theoretically grounded regularization term to effectively prevent adapter collapse and ensure stable training dynamics. Extensive experiments on multiple real-world datasets demonstrate that DualWeaver significantly outperforms current state-of-the-art methods, achieving leading performance in both forecasting accuracy and stability.

To address the challenges of global temporal modeling and cross-variable dependency capture in multivariate long-horizon time series forecasting under few-shot settings, this paper proposes a novel deep learning framework. Methodologically, it abandons conventional fixed-pattern assumptions and instead designs learnable, diverse pattern functions to adaptively discover subsequence-level temporal patterns; it further introduces a dynamic multivariate correlation matrix to model time-varying inter-variable dependencies. The core contribution lies in the first unified formulation of pattern discovery and dependency modeling as a learnable, diverse, and dynamically coupled mechanism—enabling subsequence-level global relational modeling. Extensive experiments on multiple benchmark datasets demonstrate that the proposed method significantly improves prediction accuracy for long horizons (e.g., 96–192 steps) and high-dimensional multivariate series, achieving state-of-the-art performance.

This paper addresses the challenge of modeling nonlinear and asymmetric dynamic relationships among macroeconomic and financial variables. We propose the first scenario-analysis-oriented, dynamic nonparametric multivariate Bayesian machine learning framework. Methodologically, we adapt classical econometric tools—including conditional forecasting and generalized impulse response analysis—to high-dimensional Bayesian nonparametric models, integrating dynamic factor extensions and Monte Carlo simulation to enable asymmetric shock response estimation and conditional scenario inference. Our key contribution is the first systematic integration of traditional scenario-analysis tools with nonlinear Bayesian machine learning, explicitly capturing structural asymmetry. The framework is validated across three empirical domains: financial stress testing, macroeconomic risk assessment, and cross-border spillover analysis. Results demonstrate substantial improvements in risk measurement accuracy and cross-jurisdictional early-warning capability, offering a novel paradigm for prudential regulation and policy evaluation.

This paper addresses the limited predictive accuracy of multi-model ensembling in complex seasonal time series forecasting. We propose a meta-learning-based dynamic weighted ensemble framework. Methodologically, we systematically compare five meta-learners—linear regression, k-nearest neighbors (KNN), multilayer perceptron (MLP), random forest, and LSTM—under both global and local paradigms, leveraging temporally informed feature engineering to construct meta-features. Our key contribution is the first systematic empirical evaluation of meta-learning-based ensemble strategies specifically for complex seasonal forecasting scenarios. Experimental results across multiple benchmark datasets demonstrate that all proposed meta-learning ensembles significantly outperform simple averaging, achieving average MAE reductions of 12.7%–23.4%. These gains confirm the framework’s superior adaptability to multi-scale, non-stationary seasonal patterns and its strong generalization capability.

This work addresses the challenge of prediction heterogeneity in high-dimensional multivariate time series forecasting, where global models often underperform and naive specialization risks negative transfer. The authors formulate adaptive pooling as a statistical decision problem and propose a validation-driven clustering framework that dynamically determines when and how to specialize sequences based on out-of-sample predictive performance rather than representational similarity. Clusters are iteratively refined using validation errors derived from Huber and pinball losses, while a leakage-free fallback strategy and a rigorous train-validation-test protocol ensure robustness. Evaluated on large-scale traffic datasets, the method significantly outperforms strong baselines and maintains stable performance even under weak heterogeneity.

Existing research on multivariate time series forecasting primarily focuses on holistic model design, often lacking a systematic understanding of the roles played by individual internal components. This work proposes TSCOMP, a benchmark that decomposes deep forecasting methods into fine-grained components—including preprocessing, encoding strategies, network architectures, and optimization techniques—and constructs a large-scale component-level performance corpus comprising over 20,000 evaluations through constrained orthogonal experimental design and multi-view analysis across both mainstream and large-scale model architectures. A zero-shot automated component selection method derived from this corpus consistently outperforms state-of-the-art models across multiple datasets, demonstrating that systematic component composition surpasses manually designed monolithic architectures and highlighting the efficacy and superiority of component-level evaluation.

This study addresses the susceptibility of traditional multivariate GARCH models to model misspecification and noisy covariance proxies, which often leads to biased portfolio risk estimates. It proposes a novel approach that, for the first time, integrates forecast reconciliation techniques into portfolio variance forecasting. By combining predictions from univariate and multivariate GARCH models under known asset weights, the method delivers more robust portfolio risk estimates without requiring an accurately specified covariance structure. Consequently, it maintains superior forecasting accuracy even when the underlying model is misspecified or the covariance proxy is contaminated by noise. Extensive simulations and empirical analyses demonstrate that the proposed approach consistently outperforms standard multivariate GARCH models across various noise and misspecification scenarios, with particularly pronounced advantages in high-dimensional or high-noise settings.

This study addresses the lack of a unified formulation for scalar, multivariate, and functional regression models, which obscures their intrinsic connections. By leveraging an integral operator defined with respect to general measures, the authors propose a unified framework that subsumes all three regression types as special cases of the same operator under different input and output measures. This framework reveals classical regression forms as measure-dependent manifestations of a single operator, clarifies discretized modeling as operator estimation under specific measures, and explains the efficacy of vectorized multivariate regression in linear settings. Theoretically, the authors prove that discrete representations correspond exactly to operator evaluations under discrete measures and converge to the continuous case as the discretization grid refines; moreover, this estimator is equivalent to standard multivariate regression and inherits its classical statistical properties.

This work addresses a critical yet overlooked issue in multivariate time series modeling: existing direct prediction methods often ignore the co-evolutionary dynamics and lagged dependencies among variables, leading to a mismatch between the learning objective and the true underlying temporal structure. To resolve this objective misalignment, the paper introduces CvLoss, a plug-and-play cross-variable loss regularizer that enforces consistency between synchronous and asynchronous variable interactions through constraints on the residual graph of predictions. By integrating graph-structured residual regularization, cross-variable interaction modeling, and a multi-step direct forecasting framework, CvLoss consistently enhances the performance of diverse state-of-the-art models. Extensive experiments across multiple benchmark datasets demonstrate its generality and effectiveness.