The extremal index for GARCH(1,1) processes

Laurini, Fabrizio and Tawn, Jonathan Angus (2012) The extremal index for GARCH(1,1) processes. Extremes, 15 (4). pp. 511-529. ISSN 1386-1999

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Abstract

Generalised autoregressive conditional heteroskedastic (GARCH) processes have wide application in financial modelling. To characterise the extreme values of this process the extremal index is required. Existing results, which derive the analytical expression for the extremal index for the squared GARCH(1, 1) process, cannot be used to obtain the extremal index for the GARCH(1, 1) process. For the squared GARCH(1, 1) process with symmetric innovations with continuous density function and satisfying a finite moment condition, we derive an alternative analytical expression for the extremal index and new results for the limiting distribution of the size of clusters of extremes. Using these results we obtain an analytical expression for the extremal index of the GARCH(1, 1) process and an algorithm for the evaluation of properties of other cluster functionals and risk measures. We tabulate the extremal index of the GARCH(1, 1) process when the innovations are Student-t and Gaussian distributed.

Item Type:
Journal Article
Journal or Publication Title:
Extremes
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2613
Subjects:
ID Code:
76761
Deposited By:
Deposited On:
23 Nov 2015 11:08
Refereed?:
Yes
Published?:
Published
Last Modified:
24 Mar 2020 04:32