caa a22 4500 605463743 CHVBK 20210128100254.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s10687-014-0206-9 doi (NATIONALLICENCE)springer-10.1007/s10687-014-0206-9 Joint extremal behavior of hidden and observable time series with applications to GARCH processes [Elektronische Daten] [Andree Ehlert, Ulf-Rainer Fiebig, Anja Janßen, Martin Schlather] For a class of generalized hidden Markov models ( X t , Y t ) t ∈ ℤ $(X_{t},Y_{t})_{t \in \mathbb {Z}}$ we analyze the limiting behavior of the (suitably scaled) unobservable part ( Y t ) t ∈ ℤ $(Y_{t})_{t\in \mathbb Z}$ under an observable extreme event |X 0|>x, as x → ∞ $x \to \infty $ . We discuss sufficient conditions for the existence of this limit and characterize its special structure. Our approach gives rise to an efficient and flexible algorithm for the Monte Carlo evaluation of extremal characteristics (such as the extremal index) of the observable process. Further, our setup allows to evaluate extremal measures which depend on the extremal behavior of X −1,X −2, , i.e. before X 0. An application to financial asset returns is given by the asymmetric GARCH(1,1) model whose extremal behavior has not been considered before. Our results complement the findings of Segers on the tail chains of single time series (Segers 2007). Springer Science+Business Media New York, 2014 ARCH processes nationallicence (asymmetric) GARCH processes nationallicence Extremal index nationallicence Joint extremal behavior nationallicence Multivariate regular variation nationallicence Tail chain nationallicence Time series nationallicence Ehlert Andree Institute of Economics, Leuphana University of Lüneburg, Scharnhorststr. 1, 21335, Lüneburg, Germany aut Fiebig Ulf-Rainer Institute for Mathematical Stochastics, Georg-August-University Göttingen, Goldschmidtstr. 7, 37077, Göttingen, Germany aut Janßen Anja Department of Mathematics, SPST, University of Hamburg, Bundesstr. 55, 20146, Hamburg, Germany aut Schlather Martin School of Business Informatics and Mathematics, University of Mannheim, 68131, Mannheim, Germany aut Extremes Springer US; http://www.springer-ny.com 18/1(2015-03-01), 109-140 1386-1999 18:1<109 2015 18 10687 https://doi.org/10.1007/s10687-014-0206-9 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/s10687-014-0206-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ehlert Andree Institute of Economics, Leuphana University of Lüneburg, Scharnhorststr. 1, 21335, Lüneburg, Germany aut NATIONALLICENCE 700 1- Fiebig Ulf-Rainer Institute for Mathematical Stochastics, Georg-August-University Göttingen, Goldschmidtstr. 7, 37077, Göttingen, Germany aut NATIONALLICENCE 700 1- Janßen Anja Department of Mathematics, SPST, University of Hamburg, Bundesstr. 55, 20146, Hamburg, Germany aut NATIONALLICENCE 700 1- Schlather Martin School of Business Informatics and Mathematics, University of Mannheim, 68131, Mannheim, Germany aut NATIONALLICENCE 773 0- Extremes Springer US; http://www.springer-ny.com 18/1(2015-03-01), 109-140 1386-1999 18:1<109 2015 18 10687