He, Changli () (Dept. of Economic Statistics, Stockholm School of Economics) Teräsvirta, Timo () (Dept. of Economic Statistics, Stockholm School of Economics)
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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.
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Length: 35 pages Date of creation: 26 Sep 1997 Date of revision: Publication status: Published in Journal of Econometrics, 1999, pages 173-192. Handle: RePEc:hhs:hastef:0198
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Find related papers by JEL classification: C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
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