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Properties of moments of a family of GARCH processes
Dalarna University, School of Technology and Business Studies, Statistics.
1999 (English)In: Journal of Econometrics, ISSN 0304-4076, E-ISSN 1872-6895, Vol. 92, no 1, 173-192 p.Article in journal (Refereed) Published
Abstract [en]

This paper considers the moments of a family of first-order GARCH processes. First, a general condition for 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 number of different GARCH parameterizations. Finally, the existence, or lack thereof, of the theoretical counterpart to the so-called Taylor effect in some members of this GARCH family is discussed. Possibilities of extending the results to higher-order GARCH processes are indicated and potential applications of the statistical theory proposed.

Place, publisher, year, edition, pages
Elsevier Science S.A. , 1999. Vol. 92, no 1, 173-192 p.
Keyword [en]
variance; Heteroskedasticity; Second-order dependence; Stochastic volatility; Time series
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:du-6098DOI: 10.1016/S0304-4076(98)00089-XOAI: oai:dalea.du.se:6098DiVA: diva2:520499
Available from: 2011-11-29 Created: 2011-11-29 Last updated: 2013-05-21Bibliographically approved

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CiteExportLink to record
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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
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Language
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  • nn-NO
  • nn-NB
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  • asciidoc
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