Extreme Value Theory for GARCH Processes

Richard A. Davis () and Thomas Mikosch ()
Additional contact information
Richard A. Davis: Columbia University, Department of Statistics
Thomas Mikosch: University of Copenhagen, Laboratory of Actuarial Mathematics

Chapter 8 in Handbook of Financial Time Series, 2009, pp 187-200 from Springer

Abstract: Abstract We consider the extreme value theory for a stationary GARCH process with iid innovations. One of the basic ingredients of this theory is the fact that, under general conditions, GARCH processes have power law marginal tails and, more generally, regularly varying finite-dimensional distributions. Distributions with power law tails combined with weak dependence conditions imply that the scaled maxima of a GARCH process converge in distribution to a Fréchet distribution. The dependence structure of a GARCH process is responsible for the clustering of exceedances of a GARCH process above high and low level exceedances. The size of these clusters can be described by the extremal index. We also consider the convergence of the point processes of exceedances of a GARCH process toward a point process whose Laplace functional can be expressed explicitly in terms of the intensity measure of a Poisson process and a cluster distribution.

Keywords: Point Process; Limit Theory; Stochastic Volatility Model; Extremal Index; Tail Index (search for similar items in EconPapers)
Date: 2009
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-71297-8_8

Ordering information: This item can be ordered from
http://www.springer.com/9783540712978

DOI: 10.1007/978-3-540-71297-8_8

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().