The extremal index for GARCH(1,1) processes with t-distributed innovations

F. Laurini and J. A. Tawn ()

No 2006-SE01, Economics Department Working Papers from Department of Economics, Parma University (Italy)

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. Mikosch and Starica (2000) derive the extremal index for the squared GARCH(1,1) process. Here we propose an algorithm for the evaluation of the extremal index and for the limiting distribution of the size of clusters of extremes for GARCH(1,1) processes with t-distributed innovations, and tabulate values of these characteristics for a range of parameters of the GARCH(1,1) process. This algorithm also enables properties of other cluster functionals to be evaluated.

Keywords: clusters; extreme value theory; extremal index; finance; GARCH; multivariate regular variation (search for similar items in EconPapers)
JEL-codes: C15 C32 C53 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-ets
Date: 2006
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