Multivariate arma models with generalized autoregressive linear innovation

In this paper we develop, in a multivariate framework, an alternative approach to the classical non linear analysis of time series. The proposed class of stochastic processes, of which the bilinear model is a special case, is based on a generalized autoregressive modelling of linear innovations. The probability structure is analyzed under quite general conditions. Moreover an important subclass of bilinear processes is studied in greater details. Finally, the usefulness of the results is illustrated via a numerical study.