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Zbl 0942.62097
Resnick, Sidney I.
Heavy tail modeling and teletraffic data. (With discussions and rejoinder). (English)
[J] Ann. Stat. 25, No.5, 1805-1869 (1997). ISSN 0090-5364; ISSN 2168-8966/e

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 {\it P.D. Feigin} and {\it 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 2000:: *62M09 Non-Markovian processes: estimation
94A99 Communication and information
90B99 Operations research and management science
62M10 Time series, etc. (statistics)

Keywords: regular variation; Poisson processes; autoregressive processes; weak convergence; consistency; time series analysis; independence; heavy tails; linear programming; Hill estimator

Citations: Zbl 0819.62070; Zbl 0884.62094

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