On the identification of some bilinear time series models

In their book on bilinear time series models Granger and Andersen (1978, p. 43) dismiss the use of third order moments for identifying models on the grounds that for some bilinear models they will all be zero and hence are of no use in discriminating between true white noise and some bilinear models. However, in this paper it is shown that some of the third order moments do not vanish for some superdiagonal and diagonal bilinear models and the pattern of non zero moments can be used to discriminate between true white noise and these bilinear models and also between different bilinear models. Simulation experiments are used to study the applicability of theoretical results.