Abstract: The varying coefficient spatial autoregressive model is a generalisation of a varying coefficient model in spatial data analysis. It has been widely valued and studied because of its many application backgrounds. To apply the models, the first problem is to confirm whether the coefficients in the model change with respect to a variable. Based on the Bootstrap test, the identification of constant-coefficient terms in the varying coefficient spatial autoregressive models is studied, which provides a basis for the confirmation of a semi-varying coefficient spatial autoregressive model. Furthermore, some simulation experiments are conducted to evaluate the validity of the Bootstrap approximation in the case of a finite sample size. Meanwhile, when the error term distribution is different. The value of the spatial autoregressive parameter changes, and the collinearity among the explanatory variables varies, the accuracy of the bootstrap approximation to their null distributions and the power of the test are investigated. The simulation results demonstrate that the proposed Bootstrap method can accurately approximate the zero distribution of test statistics, and the test has a good effect.

Key words: varying coefficient spatial autoregressive models, Bootstrap test, constant coefficients, spatial dependence