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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