Copulas for heavy tailed time series with strong time dependencies

Gaussian copula time series with heavy tails and strong time dependency are considered. Copula time series is a series where copula function is applied to each variable in the series. Copula function is nonlinear function that takes Gaussian variables to variables from maximum domain of attraction Frechet. The first part of the dissertation is devoted to the description of the functions from this class. The limit theorem for maximums of copula time series is proven. In the second part of the dissertation the reverse problem is considered. Namely, the problem of statistical analysis for time series potentially having heavy tails with the use of technique for asymptotic analysis of Gaussian sequences. The estimator of copula function is developed, its consistency and asymptotic normality are proven.