The behavior of multivariate maxima of moving maxima processes

Zhengjun Zhang, Richard L. Smith
2004
In the characterization of multivariate extreme indices of multivariate stationary processes, multivariate maxima of moving maxima processes, or M4 processes for short, have been introduced by Smith and Weissman. Central to the introduction of M4 processes is that the extreme observations of multivariate stationary processes may be characterized in terms of a limiting max-stable process under quite general conditions and a max-stable process can be arbitrarily closely approximated by a M4
more » ... s. In this paper, we derive some additional basic probabilistic properties for a finite class of M4 processes of which each contains finite range clustered moving patterns, called signature patterns, when extreme events occur. We use these properties to construct statistical estimation schemes for model parameters.
doi:10.17615/e33m-gp07 fatcat:dozfnbsw2fdyllqketqwqrkvti