Extremes of Integer-Valued Moving Average Models with Regularly Varying Tails

In this paper we study the limiting distribution of the maximum term of non-negative integer-valued moving average sequences of the form X _n = _{i = – i} Z _{n – i} where { Z _n} is an iid sequence of non-negative integer-valued random variables with regularly varying tails, _iZ _n–i denotes binomial thinning. Several models are considered allowing different dependence structures on the thinning operations. For these models we manage to establish results which are similar to the ones obtained for the classic linear moving average: { X _n} > has an extremal index = \max_i{ _i } / ( _i ), where is the index of regular variation, irrespectively of the dependence structure considered. The paper is concluded with a simulation study to illustrate the results.