Properties of moments of a family of GARCH processes
AbstractThis 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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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 92 (1999)
Issue (Month): 1 (September)
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Other versions of this item:
- He, Changli & TerÃ¤svirta, Timo, 1997. "Properties of Moments of a Family of GARCH Processes," Working Paper Series in Economics and Finance 198, Stockholm School of Economics.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
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