Abstract
A two-step Lagrange Multiplier test strategy has recently been suggested as a device to reveal spatial nonstationarity and spurious spatial regression. The present paper generalises this procedure by incorporating control for unobserved heteroscedasticity. Using Monte Carlo simulation, the behaviour of several relevant tests for nonstationarity and/or heteroscedasticity is investigated. The two-step Lagrange Multiplier test for spatial nonstationarity turns out to be robust towards heteroscedasticity. While several tests for heteroscedasticity prove inconclusive under certain circumstances, it is shown that a Lagrange Multiplier test for heteroscedasticity based on spatially differenced variables serves well as an indication of heteroscedasticity irrespective of stationarity status.