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Mixture results for extremal behaviour of strongly dependent nonstationary Gaussian sequences

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Abstract

Let {X n } be a nonstationary Gaussian sequence. In this work we introduce a condition onr ij =Cor(X i ,X j ),i,j≥1 that models a strong dependence struture. We prove that the limit of the point process of exceedances is a Cox process i.c. a point process whose distribution is a mixture of distributions of simple Poisson processes, regulated by a standard normal law. Moreover, we study the joint limit distribution of the maxima and minima, under linear normalization, and we again find a doubly stochastic behaviour.

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Authors and Affiliations

  1. C.E.A., University of Lisbon, Portugal

    M. Graça Temido

  2. Departmento de Matemática, Faculdade de Ciencias e Tecnologia, Universidade de Coimbra, Apartado 3008, 3000, Coimbra, Portugal

    M. Graça Temido

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  1. M. Graça Temido
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Correspondence to M. Graça Temido.

Additional information

This work was partially supported by JNICT/PRAXIS XXI/FEDER

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Graça Temido, M. Mixture results for extremal behaviour of strongly dependent nonstationary Gaussian sequences. Test 9, 439–453 (2000). https://doi.org/10.1007/BF02595744

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  • DOI: https://doi.org/10.1007/BF02595744

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