On the maximum of periodic integer-valued sequences with exponential type tails...

• Author(s): Hall, A. ; Temido, M. G.
• Date: 2007
• Persistent ID: http://hdl.handle.net/10316/11287
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Integer-valued periodic sequences; Max-semistable laws; Binomial thinning
• Document Type: Preprint
• Language: English

Description

In this work we study the limiting distribution of the maximum term of periodic integer-valued sequences with marginal distribution belonging to a particular class where the tail decays exponentially. This class does not belong to the domain of attraction of any max-stable distribution. Nevertheless, we prove that the limiting distribution is max-semistable when we consider the maximum of the first kn observations, for a suitable sequence kn increasing to infinity. We obtain an expression for calculating the extremal index of sequences satisfying certain local conditions similar to conditions D(m)(un), m ∈ N, defined by Chernick et al. (1991). We apply the results to a class of max-autoregressive sequences and a class of moving average models. The results generalize the ones obtained for the stationary case. FCT; Unidade de Investigação Matemática e Aplicações of University of Aveiro; Center for Mathematics of University of Coimbra