On the Autocorrelation Structure and Identification of Some Bilinear Time Series

Abstract.For the bilinear time seriesXt=βXt‐ket‐l+ev,k≥l, formulas for the firstk‐1 autocorrelations ofX2tare 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,kandlmay be identified using the autocorrelations ofX2t. Application to more general situations is also briefly discussed.