Properties of Moments of a Family of GARCH Processes

Working Paper Series in Economics and Finance No 198

Posted: 16 Jan 1998

See all articles by Changli He

Changli He

Stockholm School of Economics - Department of Economic Statistics

Timo Teräsvirta

Stockholm School of Economics - Department of Economics

Date Written: September 1997

Abstract

This paper considers the moments of a family of first-order GARCH processes. First, a general condition of the existence of any integer moment of the absolute values of the observations is given. Second, a general expression for this moment as a function of lower-order moments is derived. Third, the kurtosis and the autocorrelation function of the squared and absolute-valued observations are derived. The results apply to a host of different GARCH parameterizations. Finally, the existence, or the lack thereof, of a theoretical counterpart to the so-called Taylor effect for some members of this GARCH family is discussed. Possibilities of extending some of the results to higher-order GARCH processes are indicated and potential applications of the statistical theory proposed.

JEL Classification: C22

Suggested Citation

He, Changli and Teräsvirta, Timo, Properties of Moments of a Family of GARCH Processes (September 1997). Working Paper Series in Economics and Finance No 198, Available at SSRN: https://ssrn.com/abstract=53366

Changli He (Contact Author)

Stockholm School of Economics - Department of Economic Statistics ( email )

P.O. Box 6501
S-113 83 Stockholm
Sweden
+46 8 736 9236 (Phone)

Timo Teräsvirta

Stockholm School of Economics - Department of Economics ( email )

P.O. Box 6501
Sveavagen 65
S-113 83 Stockholm
Sweden

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