Weak Dependence Beyond Mixing for Infinite ARCH-type Bilinear Models

Weak dependence properties of ARCH-type bilinear models as introduced by Doukhanand Louhichi (1999) is investigated here. Those models are usually considered for their longrange dependence properties, see Giraitis and Surgailis (2002). Decay of the weak dependencecoefficient sequence are established under different specifications of the model’s coefficients.This implies various limit theorems and asymptotics for statistical procedures.We also derivejoint densities for such models in case of regular inputs.