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

publication date

  • July 2014

start page

  • 1221

end page

  • 1233

issue

  • 5

volume

  • 28

international standard serial number (ISSN)

  • 1436-3240

electronic international standard serial number (EISSN)

  • 1436-3259

abstract

  • 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.

keywords

  • extreme value theory; generalized pareto distribution; peaks over threshold; subsampling; stationarity and non-stationary time series; time-series; exceedances; thresholds; statistics; order