Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1147515 | Journal of Statistical Planning and Inference | 2012 | 13 Pages |
Abstract
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), mâN, 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Andreia Hall, Maria da Graça Temido,