发表机构
School of Electrical and Electronic Engineering, Nanyang Technological University（南洋理工大学电气与电子工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对非平稳多元图信号预测，提出角色特定预测几何，区分长期均衡与短期瞬态关系，实验验证其有效性并优于G-VARMA基线。
AI 中文摘要
当节点级轨迹非平稳但节点间及特征间存在稳定关系时，多元图信号预测具有挑战性。在误差修正表示中，长期均衡恢复与短期瞬态传播代表不同的预测角色，且无需共享共同的跨特征几何结构。我们引入角色特定预测几何，其中有向长期关系作用于估计的均衡坐标，而有向短期关系作用于滞后差分。矩阵值长期响应在图传播前混合均衡坐标，而短期响应使用图滤波的瞬态设计；直接多步估计器耦合相邻预测时域的预测修正。时间交叉拟合与Frisch-Waugh-Lovell部分化处理赋予所选边相对于图-时间主干的条件预测解释。长期算子通过均衡子空间保持右因子化，因此消除源共同趋势方向。受控实验恢复了所有植入的长期关系（20/20）、所有植入的短期关系（20/20），以及每个双重实现中的两个角色族（10/10）。在四个真实世界基准中，所提出的预测器在三个数据集上优于G-VARMA主干，且在五折金融基准上所有25个折-时域比较均有利。
英文摘要
Forecasting multivariate graph signals is challenging when node-level trajectories are nonstationary but stable relations persist across nodes and features. In an error-correction representation, long-run equilibrium restoration and short-run transient propagation represent different predictive roles and need not share a common cross-feature geometry. We introduce role-specific predictive geometries in which directed Long relations act on estimated equilibrium coordinates, whereas directed Short relations act on lagged differences. Matrix-valued Long responses mix equilibrium coordinates before graph propagation, while Short responses use graph-filtered transient designs; a direct multi-horizon estimator couples forecast corrections across adjacent horizons. Temporal cross-fitting and Frisch-Waugh-Lovell partialling-out give selected edges a conditional predictive interpretation relative to a graph-temporal backbone. The Long operator remains right-factorized through the equilibrium subspace and therefore annihilates source common-trend directions. Controlled experiments recover all planted Long relations (20/20), all planted Short relations (20/20), and both role families in every Dual realization (10/10). Across four real-world benchmarks, the proposed predictor improves on the G-VARMA backbone in three datasets, with all 25 fold-horizon comparisons favorable on the five-fold financial benchmark.
