Testing for local structure in spatiotemporal point pattern data

The detection of clustering structure in a point pattern is one of the main focuses of attention in spatiotemporal data mining. Indeed, statistical tools for clustering detection and identification of individual events belonging to clusters are welcome in epidemiology and seismology. Local second-order characteristics provide information on how an event relates to nearby events. In this work, we extend local indicators of spatial association (known as LISA functions) to the spatiotemporal context (which will be then called LISTA functions). These functions are then used to build local tests of clustering to analyse differences in local spatiotemporal structures. We present a simulation study to assess the performance of the testing procedure, and we apply this methodology to earthquake data.