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

Publikation: Beiträge in ZeitschriftenZeitschriftenaufsätzeForschungbegutachtet

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, Jahrgang 18, Nr. 1, 03.2015, S. 109-140.

Publikation: Beiträge in ZeitschriftenZeitschriftenaufsätzeForschungbegutachtet

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 Mär;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 Netherlands",
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 -

DOI

Zuletzt angesehen

Publikationen

  1. Effects of grade retention on achievement and self-concept in science and mathematics
  2. Occurrence and Air-sea exchange of phthalates in the Arctic
  3. Engaging creatively with tension in collaborative research
  4. Performance Saga: Interview 08
  5. Mechanisms of short-term soil carbon storage in experimental grasslands
  6. Performance-Determining Variables of a Simulated Skimo Sprint Competition in Elite Junior Skimo Athletes
  7. Studies on the myth's function in Holderlin's 'Feiertagshymne'
  8. Motivation und Verhalten
  9. Positive Adolescent Career Development
  10. National ecosystem restoration pledges are mismatched with social-ecological enabling conditions
  11. Geheime Verwandtschaften
  12. Photodegradation of the UV filter ethylhexyl methoxycinnamate under ultraviolet light
  13. Die Operationalisierung von objektiver und subjektiver Statusinkonsistenz.
  14. Special issue on Responsible Management Learning:
  15. Think globally, learn locally!
  16. Can learning to move foster sustainable development? A systematic literature review examining the potential of sport and physical activity in the context of environmental and sustainability education
  17. Eine Gesellschaft des Interviews / A Society of the Interview
  18. Modulating immune responses and inflammation
  19. Sozialberichterstattung
  20. Against abstraction: Zoe Leonard's "Analogue"
  21. Participation for effective environmental governance? Evidence from Water Framework Directive implementation in Germany, Spain and the United Kingdom
  22. Cybernetics
  23. Mentoring in schulischen Praxisphasen
  24. The contribution of material circularity to sustainability—Recycling and reuse of textiles
  25. Structural forces driving global integration
  26. Effectiveness of an Internet-Based Self-Help Intervention versus Public Mental Health Advice to Reduce Worry during the COVID-19 Pandemic
  27. Anaerobic Inhibition and Biodegradation of Antibiotics in ISO Test Schemes
  28. Predicting satisfaction with democracy in Germany using local economic conditions, social capital, and individual characteristics
  29. The New Media
  30. Didactics of Mathematics in Higher Education as a Scientific Discipline - Conference Proceedings
  31. To Own or to Use
  32. Reflecting on the Roles and Skill Sets of Designers and Design Researchers
  33. Walter Benjamin. Der Autor als Produzent
  34. Touching Things