Fitting time series with heavy tails and strong time dependence

Earlier, a model of a time series with heavy tails constructed from a Gaussian time series was developed. In the present paper, the reverse problem is considered: an estimator of the copula function is built; the copula function is a nonlinear function that maps Gaussian variables to the variables from Fréchet maximum domain of attraction. The statistical properties of this estimator are considered for a stationary time series with a low rate of covariance decay.