On the tail index estimation of an autoregressive Pareto process

Marta Ferreira

Discussiones Mathematicae Probability and Statistics (2013)

  • Volume: 33, Issue: 1-2, page 65-77
  • ISSN: 1509-9423

Abstract

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In this paper we consider an autoregressive Pareto process which can be used as an alternative to heavy tailed MARMA. We focus on the tail behavior and prove that the tail empirical quantile function can be approximated by a Gaussian process. This result allows to derive a class of consistent and asymptotically normal estimators for the shape parameter. We will see through simulation that the usual estimation procedure based on an i.i.d. setting may fall short of the desired precision.

How to cite

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Marta Ferreira. "On the tail index estimation of an autoregressive Pareto process." Discussiones Mathematicae Probability and Statistics 33.1-2 (2013): 65-77. <http://eudml.org/doc/270855>.

@article{MartaFerreira2013,
abstract = {In this paper we consider an autoregressive Pareto process which can be used as an alternative to heavy tailed MARMA. We focus on the tail behavior and prove that the tail empirical quantile function can be approximated by a Gaussian process. This result allows to derive a class of consistent and asymptotically normal estimators for the shape parameter. We will see through simulation that the usual estimation procedure based on an i.i.d. setting may fall short of the desired precision.},
author = {Marta Ferreira},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {extreme value theory; autoregressive processes; tail index estimation; autoregressive Pareto process; Gaussian process},
language = {eng},
number = {1-2},
pages = {65-77},
title = {On the tail index estimation of an autoregressive Pareto process},
url = {http://eudml.org/doc/270855},
volume = {33},
year = {2013},
}

TY - JOUR
AU - Marta Ferreira
TI - On the tail index estimation of an autoregressive Pareto process
JO - Discussiones Mathematicae Probability and Statistics
PY - 2013
VL - 33
IS - 1-2
SP - 65
EP - 77
AB - In this paper we consider an autoregressive Pareto process which can be used as an alternative to heavy tailed MARMA. We focus on the tail behavior and prove that the tail empirical quantile function can be approximated by a Gaussian process. This result allows to derive a class of consistent and asymptotically normal estimators for the shape parameter. We will see through simulation that the usual estimation procedure based on an i.i.d. setting may fall short of the desired precision.
LA - eng
KW - extreme value theory; autoregressive processes; tail index estimation; autoregressive Pareto process; Gaussian process
UR - http://eudml.org/doc/270855
ER -

References

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