Bootstrap tests for spatiotemporal heterogeneity in geographically and temporally weighted regression models with autocorrelated responses

A geographically and temporally weighted regression model with a spatiotemporally autoregressive term in the response variable (termed LARGTWR model) can simultaneously handle spatiotemporal heterogeneity in the regression relationship and spatiotemporal autocorrelation in the response variable. Statistical inference issues related to spatiotemporal heterogeneity in both the regression relationship and the spatiotemporal lag term are crucial for accurately interpreting the spatiotemporal characteristics of the regression relationship and the response variable’s autocorrelation. To this end, we propose two residual-based bootstrap tests using the local linear two-stage least squares (2SLS-LL) estimation method: one targeting spatiotemporal lag term heterogeneity and the other examining regression coefficient non-stationarity. Conducting simulation experiments aims to evaluate the performances of the proposed bootstrap tests. The results demonstrate that the proposed tests have satisfactory power and robustness to the model error distribution. Moreover, a real-life dataset is analyzed to demonstrate the application of the proposed tests.