This paper considers statistical inference of time-varying network vector autoregression models for large-scale time series. A latent group structure is imposed on the heterogeneous and node-specific time-varying momentum and network spillover effects so that the number of unknown time-varying coefficients to be estimated can be reduced considerably. A classic agglomerative clustering algorithm with normalized distance matrix estimates is combined with a generalized information criterion to consistently estimate the latent group number and membership. A post-grouping local linear smoothing method is proposed to estimate the group-specific time-varying momentum and network effects, substantially improving the convergence rates of the preliminary estimates which ignore the latent structure. In addition, a post-grouping specification test is conducted to verify the validity of the parametric model assumption for group-specific time-varying coefficient functions, and the asymptotic theory is derived for the test statistic constructed via a kernel weighted quadratic form under the null and alternative hypotheses. Numerical studies including Monte-Carlo simulation and an empirical application to the global trade flow data are presented to examine the finite-sample performance of the developed model and methodology.

翻译：本文研究大规模时间序列的时变网络向量自回归模型的统计推断。针对异质性且节点特定的时变动量效应与网络溢出效应，施加潜在分组结构以大幅减少待估未知时变系数的数量。结合标准化距离矩阵估计的经典凝聚聚类算法与广义信息准则，一致估计潜在分组数及成员归属。提出分组后局部线性平滑方法估计组特异性时变动量与网络效应，显著提升忽略潜在结构的初步估计的收敛速率。此外，通过分组后设定检验验证组特异性时变系数函数参数模型假设的有效性，并推导基于核加权二次型构造的检验统计量在原假设与备择假设下的渐近理论。通过蒙特卡洛模拟及全球贸易流动数据的实证应用，检验所发展模型与方法的有限样本性能。