The Annals of Statistics

Heavy tail modeling and teletraffic data: special invited paper

Sidney I. Resnick

Full-text: Open access

Abstract

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

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

Dates
First available: 20 November 2003

Permanent link to this document
http://projecteuclid.org/euclid.aos/1069362376

Mathematical Reviews number (MathSciNet)
MR1474072

Digital Object Identifier
doi:10.1214/aos/1069362376

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

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

Citation

Resnick, Sidney I. Heavy tail modeling and teletraffic data: special invited paper. The Annals of Statistics 25 (1997), no. 5, 1805--1869. doi:10.1214/aos/1069362376. http://projecteuclid.org/euclid.aos/1069362376.


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