On the multivariate upcrossings index

Clara Viseu; Luísa Pereira; Ana Paula Martins; Helena Ferreira

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arXiv · 1006.1596

On the multivariate upcrossings index

Clara Viseu·Luísa Pereira·Ana Paula Martins·Helena Ferreira

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Abstract

The notion of multivariate upcrossings index of a stationary sequence ${\bf{X}}=\{(X_{n,1},\ldots,X_{n,d})\}_{n\geq 1}$ is introduced and its main properties are derived, namely the relations with the multivariate extremal index and the clustering of upcrossings. Under asymptotic independence conditions on the marginal sequences of ${\bf{X}}$ the multivariate upcrossings index is obtained from the marginal upcrossings indices. For a class of stationary multidimensional sequences assumed to satisfy a mild oscillation restriction, the multivariate upcrossings index is computed from the joint distribution of a finite number of variables. The upcrossings index is calculated for two examples of bivariate sequences.

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Clara Viseu, Luísa Pereira, Ana Paula Martins, Helena Ferreira. 2010-06-08. On the multivariate upcrossings index. https://arxiv.org/abs/1006.1596

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