The goal of this paper is two-fold: (1) We review classical and recent measures of serial extremal dependence in a strictly stationary time series as well as their estimation. (2) We discuss recent concepts of heavy-tailed time series, including regular variation and max-stable processes.

In the early 1990s, Avram and Taqqu showed that regularly varying moving average processes with all coefficients nonnegative and the tail index α strictly between 0 and 2 satisfy the functional limit theorem. They also conjectured that an equivalent statement holds under a certain less...