FNETS：高维时间序列的因子调整网络估计与预测
FNETS: Factor-adjusted network estimation and forecasting for high-dimensional time series
AI总结：
提出FNETS方法，通过因子调整的VAR模型估计高维时间序列的Granger因果、同期及混合网络，并提供预测，在重尾条件下证明了估计的一致性。
摘要：
我们提出了FNETS，这是一种用于具有强序列和截面相关性的高维时间序列的网络估计与预测方法。我们在因子调整的向量自回归（VAR）模型下进行操作，该模型在通过公共因子考虑变量的普遍共同运动后，将变量之间剩余的特质动态依赖性建模为稀疏VAR过程。FNETS的网络估计包括三个步骤：(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估计器估计潜在VAR过程，以及(iii) 估计偏相关和长期偏相关矩阵。在此过程中，我们学习了支撑VAR过程的三个网络，即表示变量之间Granger因果联系的有向网络，嵌入其同期关系的无向网络，以及最后总结超前-滞后和同期联系的无向网络。此外，FNETS提供了一套用于预测因子驱动和特质VAR过程的方法。在允许尾部比Gaussian分布更重的一般条件下，我们推导了网络估计和预测中估计器的均匀一致性速率，这些速率在面板维度和样本量发散时成立。模拟研究和实际数据应用证实了FNETS的良好性能。
英文摘要：
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.
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