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

@article{Kulik2019TheTE,
  title={The tail empirical process of regularly varying functions of geometrically ergodic Markov chains},
  author={Rafal Kulik and Philippe Soulier and Olivier Wintenberger and Rafal Kulik},
  journal={Stochastic Processes and their Applications},
  year={2019}
}
We consider a stationary regularly varying time series which can be expressedas a function of a geometrically ergodic Markov chain. We obtain practical conditionsfor the weak convergence of the tail array sums and feasible estimators ofcluster statistics. These conditions include the so-called geometric drift or Foster-Lyapunovcondition and can be easily checked for most usual time series models witha Markovian structure. We illustrate these conditions on several models and… Expand
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