Consistent Specification Testing Under Spatial Dependence

Abstract

We propose a series-based nonparametric specification test for a regression function when data are spatially dependent, the “space” being of a general economic or social nature. Dependence can be parametric, parametric with increasing dimension, semiparametric or any combination thereof, thus covering a vast variety of settings. These include spatial error models of varying types and levels of complexity. Under a new smooth spatial dependence condition, our test statistic is asymptotically standard normal. To prove the latter property, we establish a central limit theorem for quadratic forms in linear processes in an increasing dimension setting. Finite sample performance is investigated in a simulation study, with a bootstrap method also justified and illustrated. Empirical examples illustrate the test with real-world data.

Heteroskedasticity Robust Specification Testing in Spatial Autoregression

“…Also, Delgado and Robinson (2015) offer a testing procedure to discriminate non-nested models for covariance structures that can accommodate spatial, spatiotemporal, or panel data structures. More recently, Gupta and Qu (2021) derive a test of correct specification of the regression functional form while allowing for cross-sectional correlation in the error term by means of series estimation of a nonparametric regression function. The Gupta and Qu (2021) approach includes the work of Su and Qu (2017) on regression specification testing as a special case.…”

“…More recently, Gupta and Qu (2021) derive a test of correct specification of the regression functional form while allowing for cross-sectional correlation in the error term by means of series estimation of a nonparametric regression function. The Gupta and Qu (2021) approach includes the work of Su and Qu (2017) on regression specification testing as a special case.…”