Please use this identifier to cite or link to this item: http://hdl.handle.net/1822/11078

 Title: Asymptotic and pre-asymptotic tail behavior of a power max-autoregressive model Author(s): Ferreira, Marta SusanaCastro, Luisa Canto e Keywords: Markov ChainsExtreme value theoryDependence conditionsAuto-asymptotic-tail-dependence functionTail indexExtremal index Issue date: 2010 Publisher: Probstat Forum Journal: Probstat Forum Citation: FERREIRA, Marta; CASTRO, Luisa Canto e - Asymptotic and pre-asymptotic tail behavior of a power max-autoregressive model. "ProbStat Forum" [Em linha]. 3:08 (2010) 91-107. [Consult. 17 Nov. 2010]. Disponível em : http://probstat.org.in/PSF-0610.pdf. ISSN 0974-3235. Abstract(s): Max-autoregressive models for time series data are useful when we want to make inference about rare events, mainly in areas like hydrology, geophysics and finance. Here we present a power max-autoregressive ($p$ARMAX) process, $\{X_i\}$, defined in such a way that the asymptotic tail dependence coefficient of Ledford and Tawn, computed for observations lag $m$ apart ($\eta_m$), exhibits a power decay with $m$ for larger values of $c$, the main parameter of the process, namely, $\eta_m=c^m$, $c\in(1/2,1)$. We also look at the threshold-dependent form of the extremal index, which is an important functional when extending discussions of extreme values from independent and identically distributed (i.i.d.) sequences to stationary ones. We state an approach for this functional as well as its connection with the coefficient $\eta$ for the $p$ARMAX process. Type: Article URI: http://hdl.handle.net/1822/11078 ISSN: 0974-3235 Publisher version: http://probstat.org.in/ Peer-Reviewed: yes Access: Restricted access (UMinho) Appears in Collections: CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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