SSE/EFI Working Paper Series in Economics and Finance
Properties of Moments of a Family of GARCH Processes
() and Timo Teräsvirta
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.
Keywords: Conditional variance; heteroskedasticity; second-order dependence; stochastic volatility; time series; (follow links to similar papers)
JEL-Codes: C22; (follow links to similar papers)
35 pages, September 26, 1997
- This paper is published as:
He, Changli and Timo Teräsvirta, (1999), 'Properties of Moments of a Family of GARCH Processes', Journal of Econometrics, Vol. 92, pages 173-192
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