Second‐order analysis of anisotropic spatiotemporal point process data

Abstract

Second‐order orientation methods provide a natural tool for the analysis of spatial point process data. In this paper, we extend to the spatiotemporal setting the spatial point pair orientation distribution function. The new space–time orientation distribution function is used to detect space–time anisotropic configurations. An edge‐corrected estimator is defined and illustrated through a simulation study. We apply the resulting estimator to data on the spatiotemporal distribution of fire ignition events caused by humans in a square area of 30 × 30 km2 for 4 years. Our results confirm that our approach is able to detect directional components at distinct spatiotemporal scales. © 2014 The Authors. Statistica Neerlandica © 2014 VVS.