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Article Dans Une Revue Stochastic Processes and their Applications Année : 2019

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

Résumé

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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Dates et versions

hal-01228825 , version 1 (16-11-2015)
hal-01228825 , version 2 (21-09-2018)

Identifiants

Citer

Rafał Kulik, Philippe Soulier, Olivier Wintenberger. The tail empirical process of regularly varying functions of geometrically ergodic Markov chains. Stochastic Processes and their Applications, 2019, 129 (11), pp.4209-4238. ⟨10.1016/j.spa.2018.11.014⟩. ⟨hal-01228825v2⟩
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