Summary: Huge data sets from the teletraffic industry exhibit many nonstandard characteristics such as heavy tails and long range dependence. Various estimation methods for heavy tailed time series with positive innovations are reviewed. These include parameter estimation and model identification methods for autoregressions and moving averages. Parameter estimation methods include those of Yule-Walker and the linear programming estimators of P.D. Feigin
and S.I. Resnick
[Stochastic Processes Appl. 51, No. 1, 135-165 (1994; Zbl 0819.62070
); Adv. Appl. Probab. 29, No. 3, 759-805 (1997; Zbl 0884.62094
)] as well as estimators for tail heaviness such as the Hill estimator and the
-estimator. Examples are given using call holding data and interarrivals between packet transmissions on a computer network. The limit theory makes heavy use of point process techniques and random set theory.