Sparse spatio-temporal autoregressions by profiling and bagging

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.