Asymptotics for statistical functionals of long-memory sequences

We present two general results that can be used to obtain asymptotic properties for statistical functionals based on linear long-memory sequences. As examples for the first one we consider l- and v-statistics, in particular tail-dependent l-statistics as well as v-statistics with unbounded kernels. As an example for the second result we consider degenerate v-statistics. To prove these results we also establish a weak convergence result for empirical processes of linear long-memory sequences, which improves earlier ones.