A semiparametric dynamic higher-order spatial autoregressive model.

Conventional higher-order spatial autoregressive models assume that all regression coefficients are constant, which ignores dynamic feature that may exist in spatial data. In this paper, we introduce a semiparametric dynamic higher-order spatial autoregressive model by allowing regression coefficients in classical higher-order spatial autoregressive models to smoothly vary with a continuous explanatory variable, which enables us to explore dynamic feature in spatial data. We develop a sieve two-stage least squares method for the proposed model and derive asymptotic properties of resulting estimators. Furthermore, we develop two testing methods to check appropriateness of certain linear constraint condition on the spatial lag parameters and stationarity of the regression relationship, respectively. Simulation studies show that the proposed estimation and testing methods perform quite well in finite samples. The Boston house price data are finally analyzed to demonstrate the proposed model and its estimation and testing methods. [ABSTRACT FROM AUTHOR]