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

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.

Automated summary

A new class of semiparametric spatio-temporal models is proposed for estimating unknown and banded autoregressive coefficient matrices. The study demonstrates the stability and efficiency of the proposed estimators among different sample sizes by using the local linear method and least squares method for Yule-Walker equation. The balance between over-determined and under-determined phenomena is achieved by adjusting the order of extracting sample information.