ON THE THIRD‐ORDER MOMENT STRUCTURE AND BISPECTRAL ANALYSIS OF SOME BILINEAR TIME SERIES

Abstract

Abstract For the bilinear time series model X t =βX t‐k e t‐t + e t , k > l, k = l and k < l formulae for the third‐order theoretical moments and an expression for the bispectral density function are obtained. These results can be used to distinguish between bilinear models and white noise and, in general, linear models. Furthermore, they give an indication of the type combination ( k, l ) in the above model. The modulus of the bispectral density function of the above bilinear time series model for different combinations of ( k, l ) and values of β are computed and the properties are studied.