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Properties of moments of a family of GARCH processes

  • He, Changli
  • Terasvirta, Timo

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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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 92 (1999)
Issue (Month): 1 (September)
Pages: 173-192

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Handle: RePEc:eee:econom:v:92:y:1999:i:1:p:173-192
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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