Abstract
This paper presents a semi-parametric approach to estimate the kurtosis in a GARCH process using quasi-maximum likelihood estimation. The proposed estimator performs better than the sample kurtosis in terms of tracking the true parameter. In addition, contrary to maximum likelihood estimator, the proposed method does not require any assumption on the innovation and hence is robust to misspecification. Furthermore, our simulation study shows that a GARCH process produces smaller sample kurtosis than the theoretical value, which suggests matching sample kurtosis is not necessary when determining the innovation distribution for the GARCH process.
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