Limit theory for the sample autocorrelations and extremes of a GARCH (1,1) process

@article{Mikosch2000LimitTF,
  title={Limit theory for the sample autocorrelations and extremes of a GARCH (1,1) process},
  author={Thomas Mikosch and Cătălin Stărică},
  journal={Annals of Statistics},
  year={2000},
  volume={28},
  pages={1427-1451}
}
The asymptotic theory for the sample autocorrelations and extremes of a GARCH(I, 1) process is provided. Special attention is given to the case when the sum of the ARCH and GARCH parameters is close to 1, that is, when one is close to an infinite Variance marginal distribution. This situation has been observed for various financial log-return series and led to the introduction of the IGARCH model. In such a situation, the sample autocorrelations are unreliable estimators of their deterministic… Expand

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