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October 1997 Heavy tail modeling and teletraffic data: special invited paper
Sidney I. Resnick
Ann. Statist. 25(5): 1805-1869 (October 1997). DOI: 10.1214/aos/1069362376


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.


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Sidney I. Resnick. "Heavy tail modeling and teletraffic data: special invited paper." Ann. Statist. 25 (5) 1805 - 1869, October 1997.


Published: October 1997
First available in Project Euclid: 20 November 2003

zbMATH: 0942.62097
MathSciNet: MR1474072
Digital Object Identifier: 10.1214/aos/1069362376

Primary: 62M09 , 62M10

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

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 5 • October 1997
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