High-dimensional panels of time series often arise in finance and macroeconomics, where co-movements within groups of panel components occur. Extracting these groupings from the data provides a coarse-grained description of the complex system in question and can inform subsequent prediction tasks. We develop a novel methodology to model such a panel as a restricted vector autoregressive process, where the coefficient matrix is the weighted adjacency matrix of a stochastic block model. This network time series model, which we call the Network Informed Restricted Vector Autoregression (NIRVAR) model, yields a coefficient matrix that has a sparse block-diagonal structure. We propose an estimation procedure that embeds each panel component in a low-dimensional latent space and clusters the embedded points to recover the blocks of the coefficient matrix. Crucially, the method allows for network-based time series modelling when the underlying network is unobserved. We derive the bias, consistency and asymptotic normality of the NIRVAR estimator. Simulation studies suggest that the NIRVAR estimated embedded points are Gaussian distributed around the ground truth latent positions. On three applications to finance, macroeconomics, and transportation systems, NIRVAR outperforms competing models in terms of prediction and provides interpretable results regarding group recovery.

翻译：高维时间序列面板在金融学和宏观经济学中频繁出现，其中面板各组分间常存在群组内的协同变动。从数据中提取这些群组结构，可为相关复杂系统提供粗粒度描述，并有助于后续预测任务。本文提出一种新颖方法，将此类面板建模为约束向量自回归过程，其系数矩阵为随机块模型的加权邻接矩阵。该网络时间序列模型（我们称之为网络信息约束向量自回归模型，简称NIRVAR模型）生成的系数矩阵具有稀疏块对角结构。我们提出一种估计流程：将每个面板组分嵌入低维潜空间，并对嵌入点进行聚类以恢复系数矩阵的块结构。该方法的关键优势在于，即使底层网络未被观测，仍可实现基于网络的时间序列建模。我们推导了NIRVAR估计量的偏差、相合性及渐近正态性。模拟研究表明，NIRVAR估计的嵌入点围绕真实潜位置呈高斯分布。在金融、宏观经济和交通系统的三个应用案例中，NIRVAR在预测性能上优于竞争模型，并在群组恢复方面提供了可解释的结果。