Applications of threshold models and the weighted bootstrap for Hungarian precipitation data

Abstract

This paper presents applications of the peaks-over threshold methodology for both the univariate and the recently introduced bivariate case, combined with a novel bootstrap approach. We compare the proposed bootstrap methods to the more traditional profile likelihood.We have investigated 63 years of the European Climate Assessment daily precipitation data for five Hungarian grid points, first separately for the summer and winter months, then aiming at the detection of possible changes by investigating 20 years moving windows. We show that significant changes can be observed both in the univariate and the bivariate cases, the most recent period being the most dangerous, as the return levels here are the highest. We illustrate these effects by bivariate coverage regions.Keywords daily precipitation data · moving window · profile likelihood · return level · univariate and bivariate generalized Pareto distribution · weighted bootstrap 1 IntroductionDetection of signs for climate changes are in the focus of recent climatology. There is an abundance of publications in the area of temperature changes. Precipitation is equally important, if we consider its economic effect -here the extremes play an especially important role, since these are in

Frequency analyses of extreme precipitation events in Western Black Sea Basin (Turkey) based on climate change projections

“…According to Coles (2001) and Sugahara et al (2009), these types of values can be approximately fitted to a generalized Pareto distribution (GPD) FIGURE 4 Bubble maps related to the maximum daily rainfall intensity during the reference period based on the observed data by the annual maxima (AM) and peaks over threshold (POT) methods [Colour figure can be viewed at wileyonlinelibrary.com] which was introduced by Balkema and de Haan (1974) and Pickands (1975). The GPD has been widely used by researchers in different disciplines such as finance (Gilli and Këllezi, 2006), earthquake analyses (Pisarenko and Sornette, 2003) and climatology-hydrological research (Smith, 1989;Holmes and Moriarty, 1999;Acero et al, 2011;Jahanbaksh Asl et al, 2013;Li et al, 2014;Paxian et al, 2014;Yilmaz et al, 2014;Varga et al, 2016). In the GPD theorem, the CDF, with location parameter (threshold) u, scale parameter σ and shape parameter γ, can be expressed as:…”

“…According to Coles () and Sugahara et al (), these types of values can be approximately fitted to a generalized Pareto distribution (GPD) which was introduced by Balkema and de Haan () and Pickands (). The GPD has been widely used by researchers in different disciplines such as finance (Gilli and Këllezi, ), earthquake analyses (Pisarenko and Sornette, ) and climatology‐hydrological research (Smith, ; Holmes and Moriarty, ; Acero et al , ; Jahanbaksh Asl et al , ; Li et al , ; Paxian et al , ; Yilmaz et al , ; Varga et al , ). In the GPD theorem, the CDF, with location parameter (threshold) u , scale parameter σ and shape parameter γ , can be expressed as: …”

Bootstrap Methods and Their Applications

“…Chapter 4 contains the practical applications of our generalised block bootstrap and weighted likelihood bootstrap, based on the following papers with my co-authors András Zempléni and Pál Rakonczai: Rakonczai et al [67], Varga et al [81] and Varga and Zempléni [80]. Section 4.1 describes the modelling of daily wind speed maxima at two North-German sites, where we used parametric and block bootstrap, too.…”

A Method for Determining the Mass Composition of Ultra-High Energy Cosmic Rays by Predicting the Depth of First Interaction of Individual Extensive Air Showers

“…The bootstrap is a method, developed over two centuries ago, to determine the statistical confidence intervals of data sets [87]. Another use of the bootstrap is for calculating (random) uncertainties of a value for given dataset [88,89]. Being a very simplistic computer-based statistical method, it provides insight about the intrinsic variations [87].…”

“…Being a very simplistic computer-based statistical method, it provides insight about the intrinsic variations [87]. Method relies on producing new samples from a given sample set by re-sampling with replacement [89].…”