Abstract: We propose a spatial autoregressive model with generalized disturbances to simultaneously model the spatial effects between the response variables and those between the disturbance terms. By directly modeling the covariance matrix of the disturbance terms as a polynomial function of a row-normalized adjacency matrix with a prespecified upper order that may tend to infinity, our model includes the traditional spatial autoregressive model with moving average disturbances and that with autoregressive disturbances as special cases. We propose a quasi-maximum likelihood estimator (QMLE) for estimating the model, and use an approximate maximum likelihood estimator (AMLE), which is feasible for large-scale networks, to alleviate the computational cost. We establish the asymptotic properties of both estimators (i.e., QMLE and AMLE), without imposing any distribution assumptions. Because the number of matrix predictors diverges, we propose a type of extended Bayesian information criterion method for model selection, and demonstrate its selection consistency. The results of our simulation studies and an analysis of the spatial effects in mutual fund cash inflows demonstrate the usefulness of the proposed model.

Key words and phrases: Approximate maximum likelihood estimator, extended Bayesian information criterion, generalized disturbances, quasi-maximum likelihood estimator, spatial autoregressive model.