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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.
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https://hal.archives-ouvertes.fr/hal-01228825
Contributor : Olivier Wintenberger <>
Submitted on : Friday, September 21, 2018 - 9:47:24 AM
Last modification on : Friday, April 10, 2020 - 5:13:32 PM
Document(s) archivé(s) le : Saturday, December 22, 2018 - 1:12:26 PM

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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. Stochastic Processes and their Applications, Elsevier, 2019, 129 (11), pp.4209-4238. ⟨hal-01228825v2⟩

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