The Annals of Statistics

Heavy tail modeling and teletraffic data: special invited paper

Sidney I. Resnick

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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 Feigin and Resnick as well 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.

Article information

Ann. Statist., Volume 25, Number 5 (1997), 1805-1869.

First available in Project Euclid: 20 November 2003

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62M09: Non-Markovian processes: estimation

Heavy tails regular variation Hill estimator Poisson processes linear programming autoregressive processes parameter estimation weak convergence consistency time series analysis estimation independence


Resnick, Sidney I. Heavy tail modeling and teletraffic data: special invited paper. Ann. Statist. 25 (1997), no. 5, 1805--1869. doi:10.1214/aos/1069362376.

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