Abstract
We derive the limit theory of the Gaussian QMLE in a non-stationary Asymmetric GARCH(1,1) model when the squared innovation process lies in the domain of attraction of a stable law. When the stability parameter lies in 1,2, we find regularly varying rates and stable limits for the QMLE of the asymmetry and GARCH parameters. When it is less than one we derive total inconsistency.
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