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Moments and the Autocorrelation Structure of the Exponential GARCH(p,q) Process


  • He, Changli

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


In this paper the autocorrelation structure of the Exponential GARCH(p,q) process of Nelson (1991) is considered. Conditions for the existence of any arbitrary unconditional moment are given. Furthermore, the expressions for the kurtosis and the autocorrelations of squared observations are derived. The properties of the autocorrelation structure are discussed and compared to those of the standard GARCH(p,q) process. In particular, it is seen that, the EGARCH(p,q) model has a richer autocorrelation structure than the standard GARCH(p,q) one. The statistical theory is further illustrated by a few special cases such as the symmetric and the asymmetric EGARCH(2,2) models under the assumption of normal errors or non-normal errors. The autocorrelations computed from an estimated EGARCH(2,1) model of Nelson (1991) are highlighted.

Suggested Citation

  • He, Changli, 2000. "Moments and the Autocorrelation Structure of the Exponential GARCH(p,q) Process," SSE/EFI Working Paper Series in Economics and Finance 359, Stockholm School of Economics.
  • Handle: RePEc:hhs:hastef:0359

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    Cited by:

    1. Antonis Demos, 2002. "Moments and dynamic structure of a time-varying parameter stochastic volatility in mean model," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 345-357, June.

    More about this item


    autocorrelation function of squared observations; conditional variance model; GARCH; time series; volatility;

    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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