Second-order properties for multiple-bilinear models (Q751717)

This paper deals with multiple bilinear time series models in the frequency domain; it uses the Wiener-Itô spectral representation to describe the second order properties. The author gives a necessary and sufficient condition for the second order stationarity of multiple bilinear models in terms of the spectral radius of a matrix involving the coefficients of the model. The exact form of the spectral density function shows that there is no way one can discriminate between a linear (non Gaussian) and a bilinear model based on the second order properties of the process.