  In an earlier paper Rakonczai et al. (2014), we have emphasized the effective
sample size for 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 generalisation of
the block bootstrap methodology, 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 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 to the used test statistic. The
critical values can be computed by the proposed new block bootstrap simulation,
where the block sizes are determined e.g. by fitting a VAR model to the
observations. The results are illustrated for models of the used temperature
data.
