We propose FNETS, a methodology for network estimation and forecasting of high-dimensional time series exhibiting strong serial- and cross-sectional correlations. We operate under a factor-adjusted vector autoregressive (VAR) model which, after accounting for pervasive co-movements of the variables by {\it common} factors, models the remaining {\it idiosyncratic} dynamic dependence between the variables as a sparse VAR process. Network estimation of FNETS consists of three steps: (i) factor-adjustment via dynamic principal component analysis, (ii) estimation of the latent VAR process via $\ell_1$-regularised Yule-Walker estimator, and (iii) estimation of partial correlation and long-run partial correlation matrices. In doing so, we learn three networks underpinning the VAR process, namely a directed network representing the Granger causal linkages between the variables, an undirected one embedding their contemporaneous relationships and finally, an undirected network that summarises both lead-lag and contemporaneous linkages. In addition, FNETS provides a suite of methods for forecasting the factor-driven and the idiosyncratic VAR processes. Under general conditions permitting tails heavier than the Gaussian one, we derive uniform consistency rates for the estimators in both network estimation and forecasting, which hold as the dimension of the panel and the sample size diverge. Simulation studies and real data application confirm the good performance of FNETS.

翻译：本文提出FNETS方法，用于估计和预测具有强序列相关性和横截面相关性的高维时间序列网络。我们在因子调整向量自回归（VAR）模型框架下开展工作：首先通过公共因子捕捉变量的普遍协同运动，然后将变量间剩余的个性化动态依赖关系建模为稀疏VAR过程。FNETS的网络估计包含三个步骤：（i）基于动态主成分分析的因子调整；（ii）通过ℓ₁正则化Yule-Walker估计量估计潜在VAR过程；（iii）估计偏相关矩阵和长程偏相关矩阵。据此，我们揭示了支撑VAR过程的三个网络：表示变量间Granger因果关系的定向网络、嵌入同期关系的无向网络，以及同时概括超前滞后与同期关联的无向网络。此外，FNETS提供了一整套用于预测因子驱动过程和个性化VAR过程的方法。在允许尾部重于高斯分布的通用条件下，我们推导了网络估计与预测中估计量的一致收敛速率，该结论适用于面板维度与样本量同步发散的情形。仿真研究与实际数据应用验证了FNETS的优异性能。