Sparse spatio-temporal autoregressions by profiling and bagging

We consider a new class of spatio-temporal models with sparse autoregressive coef-ficient 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 coeffi-cient 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.(c) 2021 Elsevier B.V. All rights reserved.