Testing the weak stationarity of a spatio-temporal point process

A common assumption in analyzing spatial and spatio-temporal point processes is stationarity, while in many real applications because of the environmental effects the stationarity condition is not often met. We propose two types of test statistics to test stationarity for spatio-temporal point processes, by adapting, Palahi, Pukkala & Mateu (2009) and by considering the square difference between observed and expected (under stationarity) intensities. We study the efficiency of the new statistics by simulated data, and we apply them to test the stationarity of real data.