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

Rafał Kulik, Philippe Soulier and Olivier Wintenberger

Stochastic Processes and their Applications, 2019, vol. 129, issue 11, 4209-4238

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.

Date: 2019
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DOI: 10.1016/j.spa.2018.11.014

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