Stationarity of stable power-GARCH processes

We present conditions for strict stationarity of power-GARCH processes whose innovations are described by a heavy-tailed and possibly asymmetric stable Paretian distribution. The results generalize those of Bougerol and Picard (J. Econom. 52 (1992) 115), who derived analogous conditions for standard, i.e., power-two, GARCH processes with finite-variance innovations.