A model for space-time threshold exceedances with an application to extreme rainfall

In extreme value studies models for observations exceeding a fixed high threshold have the advantage of exploiting the available extremal information, while avoiding bias from low values. In the context of space-time data, the challenge is to develop models for threshold exceedances that account for both spatial and temporal dependence. We address this issue through a modelling approach that embeds spatial dependence within a time series formulation. The model allows for different forms of limiting dependence in the spatial and temporal domains as the threshold level increases. In particular, temporal asymptotic independence is assumed, as this is often supported by empirical evidence, especially in environmental applications, while both asymptotic dependence and asymptotic independence are considered for the spatial domain. Inference from the observed exceedances is carried out through a combination of pairwise likelihood and a censoring mechanism. For those model specifications for which direct maximization of the censored pairwise likelihood is unfeasible, we propose an indirect inference procedure which leads to satisfactory results in a simulation study. The approach is applied to a dataset of rainfall amounts recorded over a set of weather stations in the North Brabant province of the Netherlands. The application shows that the range of extremal patterns that the model can cover is wide and that it has a competitive performance with respect to an alternative existing model for space-time threshold exceedances.