Multivariate network time series are ubiquitous in modern systems, yet existing network autoregressive models typically treat nodes as scalar processes, ignoring cross-variable spillovers. To capture these complex interactions without the curse of dimensionality, we propose the Reduced-Rank Network Autoregressive (RRNAR) model. Our framework introduces a separable bilinear transition structure that couples the known network topology with a learnable low-rank variable subspace. We estimate the model using a novel Scaled Gradient Descent (ScaledGD) algorithm, explicitly designed to bridge the gap between rigid network scalars and flexible factor components. Theoretically, we establish non-asymptotic error bounds under a novel distance metric. A key finding is a network-induced blessing of dimensionality: for sparse networks, the estimation accuracy for network parameters improves as the network size grows. Applications to traffic and server monitoring networks demonstrate that RRNAR significantly outperforms univariate and unstructured benchmarks by identifying latent cross-channel propagation mechanisms.

翻译：多元网络时间序列在现代系统中无处不在，然而现有的网络自回归模型通常将节点视为标量过程，忽略了跨变量的溢出效应。为了在避免维度灾难的同时捕捉这些复杂的相互作用，我们提出了降秩网络自回归模型。该框架引入了一种可分离的双线性转移结构，将已知的网络拓扑与可学习的低秩变量子空间相耦合。我们采用一种新颖的缩放梯度下降算法来估计模型参数，该算法专门设计用于弥合刚性网络标量与灵活因子成分之间的差距。在理论上，我们在一种新的距离度量下建立了非渐近误差界。一个关键发现是网络诱导的维度祝福现象：对于稀疏网络，网络参数的估计精度会随着网络规模的增大而提高。在交通和服务器监控网络中的应用表明，通过识别潜在的跨通道传播机制，降秩网络自回归模型显著优于单变量和非结构化基准模型。