Properties of Moments of a Family of GARCH Processes
Working Paper Series in Economics and Finance No 198
Posted: 16 Jan 1998
Date Written: September 1997
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: Suggested Citation