DIFFERENT REPRESENTATIONS FOR BILINEAR MODELS

Abstract. In this paper, we investigate different representations of bilinear models introduced by Granger and Andersen (1978). We consider first the decomposition of these models on the chaos of Wiener, then we give for the subdiagonal models a l -Markovian representation, generalizing a result obtained by Pham Dinh (1985) in the case of the superdiagonal models. Thus we consider the polynomial state affine representation. For these representations, we are interested in the existence and the uniqueness of the decomposition and the expression of the different moments of the models.