On the problem of model selection in bilinear time series analyses

One of the problems in bilinear time series (BLTS) analysis is that of identification. Unlike linear models, the identification in BLTS modelling is not always based on the autocorrelation function (or spectrum) since it is sometimes misleading, The authors, therefore., derive in this note the autocorrelation function of a function of a bilinear process which can be used for identification as well as for testing the linearity.