Stationarity domains for [delta]-power Garch process with heavy tails

We show that the characterization of the strict stationarity domain for a [delta]-power stable Garch model obtained in Mittnik et al. [2002. Stationarity of stable power-GARCH processes. J. Econometrics 106, 97-107] can be extended to general innovations, regardless of the existence of their [delta]-moments. We prove some general properties of these domains and analyze some cases particularly relevant in applicationsPower Garch models Strict and weak stationarity [alpha]-stable distributions Heavy tails distributions