The extremal index for GARCH(1,1) processes with t-distributed innovations
AbstractGeneralised 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.
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Bibliographic InfoPaper provided by Department of Economics, Parma University (Italy) in its series Economics Department Working Papers with number 2006-SE01.
Length: 23 pages
Date of creation: 2006
Date of revision:
clusters; extreme value theory; extremal index; finance; GARCH; multivariate regular variation;
Find related papers by JEL classification:
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
- C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-10-21 (All new papers)
- NEP-ECM-2006-10-21 (Econometrics)
- NEP-ETS-2006-10-21 (Econometric Time Series)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ferro, Christopher A. T., 2003. "Inference for clusters of extreme values," Open Access publications from UniversitÃ© catholique de Louvain info:hdl:2078/114575, Université catholique de Louvain.
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- Basrak, Bojan & Davis, Richard A. & Mikosch, Thomas, 2002. "Regular variation of GARCH processes," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 95-115, May.
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- Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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