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：我们提出FNETS方法，用于对呈现强序列相关性和截面相关性的高维时间序列进行网络估计与预测。该方法基于因子调整向量自回归（VAR）模型，该模型首先通过**共同**因子解释变量的广泛协同运动，随后将变量间剩余的**异质**动态依赖关系建模为稀疏VAR过程。FNETS的网络估计包含三步：（i）通过动态主成分分析进行因子调整，（ii）通过$\ell_1$正则化Yule-Walker估计量估计潜在VAR过程，以及（iii）估计偏相关矩阵和长期偏相关矩阵。在此过程中，我们学习了构成VAR过程基础的三个网络：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，以及同时汇总超前-滞后和同期关系的无向网络。此外，FNETS提供了一套针对因子驱动过程和异质VAR过程的预测方法。在允许尾部比高斯分布更厚的一般条件下，我们推导出网络估计与预测中估计量的统一相合速率，该速率在面板维度和样本量发散时成立。仿真研究与实际数据应用验证了FNETS的良好性能。