On weak convergence of the tail empirical process for copula time series

In the literature of statistics of extremes the conditions used to obtain the results of weak convergence of the tail empirical process for dependent sequences are given. In the model of time series with heavy tails constructed by the transformation of the Gaussian time series with Gaussian description of dependency we can show that the conditions, which are technically difficult to check in practice, could be replaced by easily checked conditions on decreasing of the correlation function of time series.