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Heavy tail modeling and teletraffic data. (With discussions and rejoinder). (English) Zbl 0942.62097
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 qq-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.
MSC:
62M09Non-Markovian processes: estimation
94A99Communication and information
90B99Operations research and management science
62M10Time series, auto-correlation, regression, etc. (statistics)