Semiparametric spatio‐temporal models with unknown and banded autoregressive coefficient matrices

Abstract

We consider a new class of semiparametric spatio‐temporal models with unknown and banded autoregressive coefficient matrices. The setting represents a type of sparse structure in order to include as many panels as possible. We apply the local linear method and least squares method for Yule–Walker equation to estimate trend function and spatio‐temporal autoregressive coefficient matrices respectively. We also balance the over‐determined and under‐determined phenomena in part by adjusting the order of extracting sample information. Both the asymptotic normality and convergence rates of the proposed estimators are established. We demonstrate, using both simulation and case studies, that the proposed estimators are stable among different sample sizes, and more efficient than the traditional method with known spatial weight matrices.