Reduced-Rank Autoregressive Model for High-Dimensional Multivariate Network Time Series

Abstract: 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.