A test for detecting spatial heteroscedasticity of the geographically weighted regression model based on residual trend analysis

{A residual-based test is proposed to detect spatial heteroscedasticity of the geographically weighted regression model. Simulations are ran to desmonstrate a significant improvement in the performance of the method.} In geographical weighted regression analysis, it is usually assumed that the model error term has spatial homoscedasticity. However, in many practical situations, rarely can we know a priori whether the error term is homoscedastic or not. If the error term is heteroscedastic, an inaccurate coefficient estimate or a misleading inferential result may be obtained when the estimation approaches of the model with homoscedastic errors are used. Therefore, it is necessary to develop a method for detecting spatial heteroscedasticity before the geographically weighted regression model is used. In this paper, a statistic is constructed based on the square root of the absolute value of the residuals obtained by the local linear geographically weighted estimation. A residual-based bootstrap approximation is applied to compute the p value of the test. Also, some simulation comparisons are conducted to assess the performance of the proposed statistic, and the results show that the proposed test method has high accuracy and satisfactory power in detecting spatial heteroscedasticity, especially when the variance function of the error term is spatially complicated. Two real-world data sets are analyzed to demonstrate the application of the proposed test method and the paper is ended with a conclusion.