Generalised block bootstrap and its use in meteorology

Abstract

Abstract.In an earlier paper, Rakonczai et al. (2014) emphasised the importance of investigating the effective sample size in case of autocorrelated data. The simulations were based on the block bootstrap methodology. However, the discreteness of the usual block size did not allow for exact calculations. In this paper we propose a new generalisation of the block bootstrap methodology, which allows for any positive real number as expected block size. We relate it to the existing optimisation procedures and apply it to a temperature data set. Our other focus is on statistical tests, where quite often the actual sample size plays an important role, even in the case of relatively large samples. This is especially the case for copulas. These are used for investigating the dependencies among data sets. As in quite a few real applications the time dependence cannot be neglected, we investigated the effect of this phenomenon on the used test statistic. The critical value can be computed by the proposed new block bootstrap simulation, where the block size is determined by fitting a VAR model to the observations. The results are illustrated for models of the used temperature data.

Bootstrap Methods and Their Applications

“…This chapter contains three applications, based on the following papers of László Varga: Rakonczai et al [67], Varga et al [81] and Varga and Zempléni [80].…”

“…This section is based on article Varga and Zempléni [80]. We use the results of Section 2.2 about VAR processes, Sections 2.4.1 and 2.4.3 about copulas, Section 3.3 about generalised block boot-strap, furthermore Sections 3.5.1 and 3.5.3 about block size determination and copula homogeneity testing.…”

“…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.…”

Mathematical modelling European temperature data: spatial differences in global warming

“…However, especially in the African and Near-Eastern region there are missing periods of various length, which have to be taken into account. The same temperature data set was used in [Varga and Zempléni (2017)], where the changes in the bivariate dependence structure were analysed.…”