Scandinavian Working Papers in Economics

SSE/EFI Working Paper Series in Economics and Finance,
Stockholm School of Economics

No 345: Fourth Moment Structure of a Family of First-Order Exponential GARCH Models

Changli He (), Timo Teräsvirta () and Hans Malmsten ()
Additional contact information
Changli He: Dept. of Economic Statistics, Stockholm School of Economics, Postal: Stockholm School of Economics, P.O. Box 6501, S-113 83 Stockholm, Sweden
Timo Teräsvirta: Dept. of Economic Statistics, Stockholm School of Economics, Postal: Stockholm School of Economics, P.O. Box 6501, S-113 83 Stockholm, Sweden
Hans Malmsten: Dept. of Economic Statistics, Stockholm School of Economics, Postal: Stockholm School of Economics, P.O. Box 6501, S-113 83 Stockholm, Sweden

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 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.

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

JEL-codes: C22

24 pages, November 19, 1999

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