On the extremal behavior of a Pareto process: an alternative for ARMAX modeling

Marta Ferreira

Kybernetika (2012)

  • Volume: 48, Issue: 1, page 31-49
  • ISSN: 0023-5954

Abstract

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In what concerns extreme values modeling, heavy tailed autoregressive processes defined with the minimum or maximum operator have proved to be good alternatives to classical linear ARMA with heavy tailed marginals (Davis and Resnick [8], Ferreira and Canto e Castro [13]). In this paper we present a complete characterization of the tail behavior of the autoregressive Pareto process known as Yeh-Arnold-Robertson Pareto(III) (Yeh et al. [32]). We shall see that it is quite similar to the first order max-autoregressive ARMAX, but has a more robust parameter estimation procedure, being therefore more attractive for modeling purposes. Consistency and asymptotic normality of the presented estimators will also be stated.

How to cite

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Ferreira, Marta. "On the extremal behavior of a Pareto process: an alternative for ARMAX modeling." Kybernetika 48.1 (2012): 31-49. <http://eudml.org/doc/246793>.

@article{Ferreira2012,
abstract = {In what concerns extreme values modeling, heavy tailed autoregressive processes defined with the minimum or maximum operator have proved to be good alternatives to classical linear ARMA with heavy tailed marginals (Davis and Resnick [8], Ferreira and Canto e Castro [13]). In this paper we present a complete characterization of the tail behavior of the autoregressive Pareto process known as Yeh-Arnold-Robertson Pareto(III) (Yeh et al. [32]). We shall see that it is quite similar to the first order max-autoregressive ARMAX, but has a more robust parameter estimation procedure, being therefore more attractive for modeling purposes. Consistency and asymptotic normality of the presented estimators will also be stated.},
author = {Ferreira, Marta},
journal = {Kybernetika},
keywords = {extreme value theory; Markov chains; autoregressive processes; tail dependence; Markov chains; tail dependence; extreme value theory; autoregressive processes},
language = {eng},
number = {1},
pages = {31-49},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On the extremal behavior of a Pareto process: an alternative for ARMAX modeling},
url = {http://eudml.org/doc/246793},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Ferreira, Marta
TI - On the extremal behavior of a Pareto process: an alternative for ARMAX modeling
JO - Kybernetika
PY - 2012
PB - Institute of Information Theory and Automation AS CR
VL - 48
IS - 1
SP - 31
EP - 49
AB - In what concerns extreme values modeling, heavy tailed autoregressive processes defined with the minimum or maximum operator have proved to be good alternatives to classical linear ARMA with heavy tailed marginals (Davis and Resnick [8], Ferreira and Canto e Castro [13]). In this paper we present a complete characterization of the tail behavior of the autoregressive Pareto process known as Yeh-Arnold-Robertson Pareto(III) (Yeh et al. [32]). We shall see that it is quite similar to the first order max-autoregressive ARMAX, but has a more robust parameter estimation procedure, being therefore more attractive for modeling purposes. Consistency and asymptotic normality of the presented estimators will also be stated.
LA - eng
KW - extreme value theory; Markov chains; autoregressive processes; tail dependence; Markov chains; tail dependence; extreme value theory; autoregressive processes
UR - http://eudml.org/doc/246793
ER -

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