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

  • He, Changli

    ()

    (Dept. of Economic Statistics, Stockholm School of Economics)

  • Teräsvirta, Timo

    ()

    (Dept. of Economic Statistics, Stockholm School of Economics)

  • Malmsten, Hans

    ()

    (Dept. of Economic Statistics, Stockholm School of Economics)

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 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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Paper provided by Stockholm School of Economics in its series SSE/EFI Working Paper Series in Economics and Finance with number 345.

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Length: 24 pages
Date of creation: 19 Nov 1999
Date of revision:
Publication status: Published in Econometric Theory, 2002, pages 868-885.
Handle: RePEc:hhs:hastef:0345
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