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

  • F. Laurini
  • J. A. Tawn

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    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.

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    Paper provided by Department of Economics, Parma University (Italy) in its series Economics Department Working Papers with number 2006-SE01.

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    Length: 23 pages
    Date of creation: 2006
    Date of revision:
    Handle: RePEc:par:dipeco:2006-se01
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    Web page: http://economia.unipr.it/de
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    1. 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.
    2. 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.
    3. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
    4. Paola Bortot & Stuart Coles, 2003. "Extremes of Markov chains with tail switching potential," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(4), pages 851-867.
    5. Christopher A. T. Ferro & Johan Segers, 2003. "Inference for clusters of extreme values," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 545-556.
    6. Borkovec, Milan, 2000. "Extremal behavior of the autoregressive process with ARCH(1) errors," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 189-207, February.
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