Estimation of tail thickness parameters from GJR-GARCH models

Emma Iglesias and Oliver Linton

UC3M Working papers. Economics from Universidad Carlos III de Madrid. Departamento de Economía

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

Keywords: Pareto; tail; thickness; parameter; GARCH-type; models; Value-at-Risk; Extreme; value; theory; Heavy; tails (search for similar items in EconPapers)
JEL-codes: C12 C13 C22 G11 G32 (search for similar items in EconPapers)
Date: 2009-06-12
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:cte:werepe:we094726

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