Rare events, temporal dependence, and the extremal index

Segers, Johan
(2006) Journal of Applied Probability — Vol. 43, n° 2, p. 463-485 (2006)

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Abstract
Classical extreme value theory for stationary sequences of random variables can to a large extent be paraphrased as the study of exceedances over a high threshold. A special role within the description of the temporal dependence between such exceedances is played by the extremal index. Parts of this theory can be generalized not only to random variables on an arbitrary state space hitting certain failure sets, but even to a triangular array of rare events on an abstract probability space. In the case of M4 (maxima of multivariate moving maxima) processes, the arguments take a simple and direct form.

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Segers, J. (2006). Rare events, temporal dependence, and the extremal index. Journal of Applied Probability, 43(2), 463-485. https://doi.org/10.1239/jap/1152413735 (Original work published 2006)