Stable limits for the Gaussian QMLE in the non-stationary GARCH(1,1) model

We derive the limit theory of the Gaussian QMLE in the non-stationary GARCH(1,1) model when the squared innovation process lies in the domain of attraction of a stable law. Analogously to the stationary case, when the stability parameter lies in 1,2, we find regularly varying rates and stable limits for the QMLE of the ARCH and GARCH parameters.