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 InfoPaper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 198.
Length: 35 pages
Date of creation: 26 Sep 1997
Date of revision:
Publication status: Published in Journal of Econometrics, 1999, pages 173-192.
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Conditional variance; heteroskedasticity; second-order dependence; stochastic volatility; time series;
Other versions of this item:
- He, Changli & Terasvirta, Timo, 1999. "Properties of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 92(1), pages 173-192, September.
- 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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