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.
Highlights
In the last decades the bootstrap methodology has become more and more widespread in different areas of statistical applications
Our results underline that the block size determination is definitely not yet a completely solved question in spite of the available asymptotic results, as for finite samples and different statistical inference or testing problems the results might be substantially different
We proposed a simple generalisation of the block bootstrap methodology, which fits naturally to the existing algorithms, and which helps to overcome the problem of discreteness in the usual block size
Summary
In the last decades the bootstrap methodology has become more and more widespread in different areas of statistical applications. The bootstrap samples must match the dependence within the data, so the block bootstrap is the suggested method for bootstrapping time series. Schölzel and Friederichs (2008) provided an overview of the possible applications of copula models in meteorology, in joint analysis of temperature and precipitation data. Most of these works use different parametric copula models, but we are more interested in testing for possible changes in the dependency structure, so we introduce the most recent approaches in testing homogeneity of such models, which are based on the empirical copula process. For further details about time series analysis, see, for example, Brockwell and Davis (2013) or Shumway and Stoffer (2011)
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