Kybernetika 48 no. 1, 31-49, 2012

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

Marta Ferreira

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.

Keywords:

Markov chains, tail dependence, extreme value theory, autoregressive processes

Classification:

60G70, 60J20

paper.pdf

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