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Properties of Moments of a Family of GARCH Processes

Author

Listed:
  • He, Changli

    (Dept. of Economic Statistics, Stockholm School of Economics)

  • Teräsvirta, Timo

    (Dept. of Economic Statistics, Stockholm School of Economics)

Abstract

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.

Suggested Citation

  • He, Changli & Teräsvirta, Timo, 1997. "Properties of Moments of a Family of GARCH Processes," SSE/EFI Working Paper Series in Economics and Finance 198, Stockholm School of Economics.
    • Handle: RePEc:hhs:hastef:0198
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Conditional variance; heteroskedasticity; second-order dependence; stochastic volatility; time series;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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