Stationarity in fourth order and the marginal bispectrum for bilinear models with Gaussian residuals

The paper concerns the bilinear stochastic models generated by Gaussian white noise processes. The bilinear process is considered as a stationary series of -functionals of a Gaussian white noise series. The Wiener-Ito spectral representation is used to derive the necessary and sufficient condition for the second and fourth order stationarity. It is shown that the spectrum characterizes only the linear part of the process. The exact form of the bispectrum points to the bilinear properties.