We consider a new class of spatio-temporal models with sparse autoregressive coefficient matrices and exogenous variable. To estimate the model, we first profile the exogenous variable out of the response. This leads to a profiled model structure. Next, to overcome endogeneity issue, we propose a class of generalized methods of moment (GMM) estimators to estimate the autoregressive coefficient matrices. A novel bagging-based estimator is further developed to conquer the over-determined issue which also occurs in Chang et al. (2015) and Dou et al. (2016). An adaptive forward–backward greedy algorithm is proposed to learn the sparse structure of the autoregressive coefficient matrices. A new BIC-type selection criteria is further developed to conduct variable selection for GMM estimators. Asymptotic properties are further studied. The proposed methodology is illustrated with extensive simulation studies. A social network dataset is analyzed for illustration purpose.

我们考虑了一类新的具有稀疏自回归系数矩阵和外生变量的时空模型。为了估计模型，我们首先从响应中分析外生变量。这导致了一个剖析模型结构。接下来，为了克服内生性问题，我们提出了一类广义矩估计方法 (GMM) 来估计自回归系数矩阵。进一步开发了一种新颖的基于套袋的估计器，以克服 Chang 等人也出现的过度确定问题。(2015) 和 Dou 等人。(2016)。提出了一种自适应前向-后向贪婪算法来学习自回归系数矩阵的稀疏结构。进一步开发了一种新的 BIC 型选择准则，以对 GMM 估计量进行变量选择。进一步研究了渐近特性。所提出的方法通过广泛的模拟研究进行了说明。出于说明目的，分析了社交网络数据集。