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

Autor:	Kulik, Rafal, Soulier, Philippe, Wintenberger, Olivier, Kulik, Rafa
Rok vydání:	2015
Předmět:	Mathematics - Statistics Theory
Druh dokumentu:	Working Paper
Popis:	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 statisticalapplications. A counterexample is given to show a different limiting behaviorwhen the geometric drift condition is not fulfilled.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1511.04903 Zobrazit plný text záznamu View this record from Arxiv