On the autocorrelation structure and identification of some bilinear time series

For the bilinear time series Xt=βX(t-k)e(t-l)+e(v1)k≥l, formulas for the first k-1 autocorrelations of X2t are obtained. These results fill in a gap in Granger and Andersen (1978). Simulation experiments are used to study the applicability of theoretical results and to investigate some more general situations. It is found that if ß is not too small, k and l may be identified using the autocorrelations of X2r. Application to more general situations is also briefly discussed