Stationarity domains for δδ-power Garch process with heavy tails

We show that the characterization of the strict stationarity domain for a δδ-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 δδ-moments. We prove some general properties of these domains and analyze some cases particularly relevant in applications