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. (C) 2017 Elsevier B.V. All rights reserved.