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Estimation of tail thickness parameters from GJR-GARCH models

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  • Emma M. Iglesias

    ()

  • Oliver Linton

    ()

Abstract

We propose a method of estimating the Pareto tail thickness parameter of the unconditional distribution of a financial time series by exploiting the implications of a GJR-GARCH volatility model. The method is based on some recent work on the extremes of GARCH-type processes and extends the method proposed by Berkes, Horváth and Kokoszka (2003). We show that the estimator of tail thickness is consistent and converges at rate ?T to a normal distribution (where T is the sample size), provided the model for conditional variance is correctly specified as a GJR-GARCH. This is much faster than the convergence rate of the Hill estimator, since that procedure only uses a vanishing fraction of the sample. We also develop new specification tests based on this method and propose new alternative estimates of unconditional value at risk. We show in Monte Carlo simulations the advantages of our procedure in finite samples; and finally an application concludes the paper

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Bibliographic Info

Paper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we094726.

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Date of creation: Jun 2009
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Handle: RePEc:cte:werepe:we094726

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Keywords: Pareto tail thickness parameter; GARCH-type models; Value-at-Risk; Extreme value theory; Heavy tails;

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References

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Cited by:
  1. Beran, Jan & Schell, Dieter, 2012. "On robust tail index estimation," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 56(11), pages 3430-3443.
  2. Stavros Degiannakis & Christos Floros & Alexandra Livada, 2012. "Evaluating value-at-risk models before and after the financial crisis of 2008: International evidence," Managerial Finance, Emerald Group Publishing, Emerald Group Publishing, vol. 38(3), pages 436-452, March.

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