Bootstrap LM tests for higher-order spatial effects in spatial linear regression models

This paper first extends the methodology of Yang (J Econom 185:33–59, 2015) to allow for non-normality and/or unknown heteroskedasticity in obtaining asymptotically refined critical values for the LM-type tests through bootstrap. Bootstrap refinements in critical values require the LM test statistics to be asymptotically pivotal under the null hypothesis, and for this we provide a set of general methods for constructing LM and robust LM tests. We then give detailed treatments for two general higher-order spatial linear regression models: namely the \(\mathtt{SARAR}(p,q)\) model and the \(\mathtt{MESS}(p,q)\) model, by providing a complete set of non-normality robust LM and bootstrap LM tests for higher-order spatial effects, and a complete set of LM and bootstrap LM tests robust against both unknown heteroskedasticity and non-normality. Monte Carlo experiments are run, and results show an excellent performance of the bootstrap LM-type tests.