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

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Author Info
F. Laurini
J. A. Tawn ()
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.

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Publisher Info
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
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Handle: RePEc:par:dipeco:2006-se01

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Related research
Keywords: 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: General - - - Statistical Simulation Methods
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions
C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Other Model Applications

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References listed on IDEAS
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.:
  1. 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. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
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