Gaussian copula time series with heavy tails and strong time dependence

A class of functions $f$ is described for which the random variable $X=f(\xi)$, where $\xi$ is a standard normal random variable, belongs to Fréchet maximum domain of attraction. For any $f$ from this class, a limit theorem for the maximum of the sequence $X(k)=f(\xi_{k})$, $k=1,2,\dots$, is proved, where $\xi_{k}$ is a Gaussian stationary sequence with a slowly decreasing correlation.