Fourth Moment Structure of a Family of First-Order Exponential GARCH Models
AbstractIn 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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Bibliographic InfoPaper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 345.
Length: 24 pages
Date of creation: 19 Nov 1999
Date of revision:
Publication status: Published in Econometric Theory, 2002, pages 868-885.
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autocorrelation function of squared observations; conditional variance model; heavy tails; exponential GARCH; logarithmic GARCH;
Other versions of this item:
- C. He & Timo Terasvirta & H. Malmsten, 1999. "Fourth Moment Structure of a Family of First-Order Exponential GARCH Models," Research Paper Series 29, Quantitative Finance Research Centre, University of Technology, Sydney.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2000-01-24 (All new papers)
- NEP-ECM-2000-01-24 (Econometrics)
- NEP-ETS-2000-01-24 (Econometric Time Series)
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