Comparing generalized Pareto models fitted to extreme observations: an application to the largest temperatures in Spain

In this paper, a subsampling-based testing procedure for the comparison of the exceedance distributions of stationary time series is introduced. The proposed testing procedure has a number of advantages including the fact that the assumption of stationary can be relaxed for some specific forms of non-stationary and also that the two time series are not required to be independently-generated. For this purpose, a test based on the Kolmogorov–Smirnov and the L ₁-Wasserstein distances between generalized Pareto distributions is introduced and studied in some detail. The performance of the testing procedure is illustrated through a simulation study and with an empirical application to a set of data concerning daily maximum temperature in the 17 autonomous communities of Spain for the period 1990–2004. The autonomous communities were clustered according to the similarities of the fitted generalized Pareto models and then mapped. The cluster analysis reveals a clear distinction between the four northeast communities on the shores of the Bay of Biscay (which are the regions exhibiting milder temperatures) and the remaining regions. A second cluster corresponds to the southern Mediterranean area and the central region which corresponds to the communities with highest temperatures.