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Fourth Moment Structure of a Family of First-Order Exponential GARCH Models

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  • C. He
  • Timo Terasvirta
  • H. Malmsten

Abstract

In this paper we consider the fourth moment structure of a class of first-order Exponential GARCH models. This class contains as special cases both the standard Exponential GARCH model and the symmetric and asymmetric Logarithmic GARCH one. Conditions for the existence of any arbitrary moment are given. Furthermore, the expressions for the kurtosis and the autocorrelations of squared observations are derived. The properties of the autocorrelations of squared observations are derived. The properties of the autocorrelation structure are discussed and compared to those of the standard first-order GARCH process. In particular, it is seen that, contrary to the standard GARCH case, the decay rate of the autocorrelations is not constant and that the rate can be quite rapid in the beginning, depending on the parameters of the model.

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Bibliographic Info

Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 29.

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Date of creation: 01 Dec 1999
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Handle: RePEc:uts:rpaper:29

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Keywords: autocorrelation function of squared observations; conditional variance model; heavy tails; exponential GARCH; logarithmic GARCH;

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Cited by:
  1. Fernandes, Marcelo & Grammig, Joachim, 2002. "A Family of Autoregressive Conditional Duration Models," Economics Working Papers (Ensaios Economicos da EPGE) 440, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  2. M. Angeles Carnero & Daniel Peña & Esther Ruiz, 2001. "Outliers And Conditional Autoregressive Heteroscedasticity In Time Series," Statistics and Econometrics Working Papers ws010704, Universidad Carlos III, Departamento de Estadística y Econometría.

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