The mixing property of bilinear and generalised random coefficient autoregressive models

The paper gives sufficient conditions for the absolute regularity of bilinear models. Our approach is based on their Markovian representation. The above property is a direct consequence of the geometric ergodicity of the Markovian process in this representation. The latter process belongs to what we call the generalised random coefficients autoregressive models. Conditions for the geometric ergodicity and also for the existence of moments for this model are given. Our results generalise that of Feigin and Tweedie.