The tail empirical process of regularly varying functions of geometrically ergodic Markov chains

Abstract : We consider a stationary regularly varying time series which can be expressed as a function of a geometrically ergodic Markov chain. We obtain practical conditions for the weak convergence of the tail array sums and feasible estimators of cluster statistics. These conditions include the so-called geometric drift or Foster-Lyapunov condition and can be easily checked for most usual time series models with a Markovian structure. We illustrate these conditions on several models and statistical applications. A counterexample is given to show a different limiting behavior when the geometric drift condition is not fulfilled.
Type de document :
Pré-publication, Document de travail
2018
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https://hal.archives-ouvertes.fr/hal-01228825
Contributeur : Olivier Wintenberger <>
Soumis le : vendredi 21 septembre 2018 - 09:47:24
Dernière modification le : vendredi 4 janvier 2019 - 17:33:38
Document(s) archivé(s) le : samedi 22 décembre 2018 - 13:12:26

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tepmult-final.pdf
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  • HAL Id : hal-01228825, version 2
  • ARXIV : 1511.04903

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Rafał Kulik, Philippe Soulier, Olivier Wintenberger, Rafa Kulik. The tail empirical process of regularly varying functions of geometrically ergodic Markov chains. 2018. 〈hal-01228825v2〉

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