The extremal index of a higher-order stationary Markov chain
The author presents a method of computing the so-called extremal index [see \textit{R. M. Loynes}, Ann. Math. Stat. 36, 993-999 (1965; Zbl 0178.53201)] of a real-valued \(k\)th order, \(k\geq 1\), stationary Markov chain. The method is based on the assumption that the joint distribution of \(k+1\) consecutive variables is in the domain of attraction of some multivariate extreme value distribution. Four examples illustrate how the method works.
scientific article; zbMATH DE number 1319922
scientific article