“…The model (1.1) has been studied by Bibi et al { [5,7,8,9,10,11]}, more precisely, with respect to the probabilistic properties, Bibi [5], beside the motivations proposed to introduce the class of bilinear models with time-dependent coefficients, he also studied the L 2 −structure and some empirical properties of such models. In particular, with periodic coefficients, Bibi and Lessak [9] have established some sufficient conditions for the existence of causal, periodically correlated (P C) and β−mixing of the solution process for some specifications of (1.2) (see the subsection 2.2 for a definition of P C processes).…”