A second-order test to detect spatio-temporal anisotropic effects in point patterns

Abstract

Second-order spatio-temporal orientation methods provide a natural tool for the analysis of anisotropic spatio-temporal point process data. In this paper, we generalize a method based on the spatial point pair orientation distribution function to test for evidence of spatio-temporal anisotropy, by exploring the fact that the space–time orientation function is the distribution function of a uniform random variable on [0,π) for any second-order intensity reweighted stationary and isotropic spatio-temporal point process. We present a numerical procedure based on this result to test for anisotropic effects, illustrated through a simulation study considering several space–time structures including Poisson and cluster configurations. The resulting testing procedure is applied to analyse the spatio-temporal distribution of earthquakes in Southern California for the period 1984–2004. Our results confirm that our approach is able to detect directional components at distinct spatio-temporal scales.