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TitleTail and dependence behaviour of levels that persist for a fixed period of time
Author(s)Ferreira, Marta Susana
Castro, Luisa Canto e
KeywordsMax-autoregressive processes
Tail index
Extremal index
Tail dependence index
Tail empirical quantile function
Issue date9-Nov-2007
Citation"Extremes". ISSN 1386-1999. 11:2 (Nov. 2007) 113-133.
Abstract(s)This work emerges from a study of the extremal behavior of a daily maximum sea water levels series, $\{X_i\}$ , presented in Draisma \cite{drai}. In its approach, a new series, $\{Y_i\}$ , is defined, consisting of water levels that persist for a fixed period of time. In this paper, we study the tail behavior of $\{Y_i\}$ , in case $\{X_i\}$ is independent and identically distributed (i.i.d.) and in case $\{X_i\}$ is a max-autoregressive sequence (we will consider two different max-autoregressive processes), whose distribution function is in the Fr\'echet domain of attraction. We also determine Ledford and Tawn tail dependence index (\cite{tawn1}, \cite{tawn2}) and we analyze the asymptotic tail dependence of the random pair $(Y_i,Y_{i+m})$, in all considered cases. According to Drees \cite{drees1}, we obtain the limit behavior of the tail empirical quantile function associated with a random sample $(Y_1,Y_2,...Y_n)$ and hence the asymptotic normality of a class of estimators of the tail index that includes Hill estimator.
ISSN1386-1999 (on line)
1572-915X (print)
AccessRestricted access (UMinho)
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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