caa a22 4500 605463816 CHVBK 20210128100255.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s10687-015-0217-1 doi (NATIONALLICENCE)springer-10.1007/s10687-015-0217-1 Statistics for tail processes of Markov chains [Elektronische Daten] [Holger Drees, Johan Segers, Michał Warchoł] At high levels, the asymptotic distribution of a stationary, regularly varying Markov chain is conveniently given by its tail process. The latter takes the form of a geometric random walk, the increment distribution depending on the sign of the process at the current state and on the flow of time, either forward or backward. Estimation of the tail process provides a nonparametric approach to analyze extreme values. A duality between the distributions of the forward and backward increments provides additional information that can be exploited in the construction of more efficient estimators. The large-sample distribution of such estimators is derived via empirical process theory for cluster functionals. Their finite-sample performance is evaluated via Monte Carlo simulations involving copula-based Markov models and solutions to stochastic recurrence equations. The estimators are applied to stock price data to study the absence or presence of symmetries in the succession of large gains and losses. Springer Science+Business Media New York, 2015 Heavy-tailed Markov chains nationallicence Regular variation nationallicence Stationary time series nationallicence Tail process nationallicence Time reversibility nationallicence Drees Holger Department of Mathematics, University of Hamburg, Bundesstraße 55, 20146, Hamburg, Germany aut Segers Johan Institut de Statistique, Biostatistique et Sciences Actuarielles, Université Catholique de Louvain, Voie du Roman Pays 20, B-1348, Louvain-la-Neuve, Belgium aut Warchoł Michał Institut de Statistique, Biostatistique et Sciences Actuarielles, Université Catholique de Louvain, Voie du Roman Pays 20, B-1348, Louvain-la-Neuve, Belgium aut Extremes Springer US; http://www.springer-ny.com 18/3(2015-09-01), 369-402 1386-1999 18:3<369 2015 18 10687 https://doi.org/10.1007/s10687-015-0217-1 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10687-015-0217-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Drees Holger Department of Mathematics, University of Hamburg, Bundesstraße 55, 20146, Hamburg, Germany aut NATIONALLICENCE 700 1- Segers Johan Institut de Statistique, Biostatistique et Sciences Actuarielles, Université Catholique de Louvain, Voie du Roman Pays 20, B-1348, Louvain-la-Neuve, Belgium aut NATIONALLICENCE 700 1- Warchoł Michał Institut de Statistique, Biostatistique et Sciences Actuarielles, Université Catholique de Louvain, Voie du Roman Pays 20, B-1348, Louvain-la-Neuve, Belgium aut NATIONALLICENCE 773 0- Extremes Springer US; http://www.springer-ny.com 18/3(2015-09-01), 369-402 1386-1999 18:3<369 2015 18 10687