Modeling short‐ranged dependence in block extrema with application to polar temperature data

Abstract

AbstractThe block maxima approach is an important method in univariate extreme value analysis. While assuming that block maxima are independent results in straightforward analysis, the resulting inferences maybe invalid when a series of block maxima exhibits dependence. We propose a model, based on a first‐order Markov assumption, that incorporates dependence between successive block maxima through the use of a bivariate logistic dependence structure while maintaining generalized extreme value (GEV) marginal distributions. Modeling dependence in this manner allows us to better estimate extreme quantiles when block maxima exhibit short‐ranged dependence. We demonstrate via a simulation study that our first‐order Markov GEV model performs well when successive block maxima are dependent, while still being reasonably robust when maxima are independent. We apply our method to two polar annual minimum air temperature data sets that exhibit short‐ranged dependence structures, and find that the proposed model yields modified estimates of high quantiles.