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

2015/11/16 by Kulik, Rafal, Soulier, Philippe, Wintenberger, Olivier +1
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1511.04903

Abstract

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.

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