A first‐order, ratio‐based nonparametric separability test for spatiotemporal point processes

Abstract

Testing whether the intensity function of a spatiotemporal point process is separable should be one of the first steps in the analysis of any observed pattern. Under separability, the risk of observing an event at time t is spatially invariant, that is, the ratio between the intensity functions of the spatiotemporal point process and its spatial marginal does not depend on the spatial location of events. Considering this property, this work proposes testing separability through a regression test that checks the dependence of the ratio function on the spatial locations. To implement the test, we introduce a kernel estimator of the log‐ratio function and a cross‐validation bandwidth selector. The simulation studies conducted to analyze the performance of the test point out the need to use a permutation test to calibrate the null distribution. Comparison with nonparametric separability tests currently available reported that the no‐effect test provides a better calibration under the null hypothesis, and it is competitive in power with the current tests under the alternative hypothesis. The performance of the test is also illustrated throughout its application to the analysis of the spatiotemporal patterns of wildfires registered in Galicia (NW Spain) during 2006.