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

Rafał Kulik (1) , Philippe Soulier (2) , Olivier Wintenberger (3, 4)

1 Department of Mathematics and Statistics [Ottawa]
2 MODAL'X - Modélisation aléatoire de Paris X
3 UCPH - University of Copenhagen = Københavns Universitet
4 LSTA - Laboratoire de Statistique Théorique et Appliquée

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 weighted versions of the multivariate tail empirical process. 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.

Domaines: Statistiques [math.ST]

Rafał Kulik, Philippe Soulier, Olivier Wintenberger. The tail empirical process of regularly varying functions of geometrically ergodic Markov chains. 2015. ⟨hal-01228825v1⟩