Joint extremal behavior of hidden and observable time series with applications to GARCH processes

Research output: Journal contributionsJournal articlesResearchpeer-review

Standard

Joint extremal behavior of hidden and observable time series with applications to GARCH processes. / Ehlert, Andree; Fiebig, Ulf Rainer; Janßen, Anja et al.
In: Extremes, Vol. 18, No. 1, 03.2015, p. 109-140.

Research output: Journal contributionsJournal articlesResearchpeer-review

Harvard

APA

Vancouver

Ehlert A, Fiebig UR, Janßen A, Schlather M. Joint extremal behavior of hidden and observable time series with applications to GARCH processes. Extremes. 2015 Mar;18(1):109-140. doi: 10.1007/s10687-014-0206-9

Bibtex

@article{316bf737260143bc8076d8ff4ee5f242,
title = "Joint extremal behavior of hidden and observable time series with applications to GARCH processes",
abstract = "For a class of generalized hidden Markov models (Xt,Yt)t∈ℤ we analyze the limiting behavior of the (suitably scaled) unobservable part (Yt)t∈ℤ under an observable extreme event |X0|>x, as x→∞. 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 X0. 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).",
keywords = "(asymmetric) GARCH processes, ARCH processes, Extremal index, Joint extremal behavior, Multivariate regular variation, Tail chain, Time series, Economics",
author = "Andree Ehlert and Fiebig, {Ulf Rainer} and Anja Jan{\ss}en and Martin Schlather",
year = "2015",
month = mar,
doi = "10.1007/s10687-014-0206-9",
language = "English",
volume = "18",
pages = "109--140",
journal = "Extremes",
issn = "1386-1999",
publisher = "Springer US",
number = "1",

}

RIS

TY - JOUR

T1 - Joint extremal behavior of hidden and observable time series with applications to GARCH processes

AU - Ehlert, Andree

AU - Fiebig, Ulf Rainer

AU - Janßen, Anja

AU - Schlather, Martin

PY - 2015/3

Y1 - 2015/3

N2 - For a class of generalized hidden Markov models (Xt,Yt)t∈ℤ we analyze the limiting behavior of the (suitably scaled) unobservable part (Yt)t∈ℤ under an observable extreme event |X0|>x, as x→∞. 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 X0. 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).

AB - For a class of generalized hidden Markov models (Xt,Yt)t∈ℤ we analyze the limiting behavior of the (suitably scaled) unobservable part (Yt)t∈ℤ under an observable extreme event |X0|>x, as x→∞. 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 X0. 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).

KW - (asymmetric) GARCH processes

KW - ARCH processes

KW - Extremal index

KW - Joint extremal behavior

KW - Multivariate regular variation

KW - Tail chain

KW - Time series

KW - Economics

UR - http://www.scopus.com/inward/record.url?scp=84925485593&partnerID=8YFLogxK

U2 - 10.1007/s10687-014-0206-9

DO - 10.1007/s10687-014-0206-9

M3 - Journal articles

AN - SCOPUS:84925485593

VL - 18

SP - 109

EP - 140

JO - Extremes

JF - Extremes

SN - 1386-1999

IS - 1

ER -