## The extremal index of a higher-order stationary Markov chain.(English)Zbl 0942.60038

The author presents a method of computing the so-called extremal index [see 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.

### MSC:

 60G70 Extreme value theory; extremal stochastic processes 60J05 Discrete-time Markov processes on general state spaces 60G10 Stationary stochastic processes 60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)

Zbl 0178.53201
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### References:

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