Polyspectral factorization: necessary and sufficient condition for finite extent cumulant sequences

The authors provide necessary and sufficient conditions for bispectral and trispectral factorization for processes with finite-extent cumulant sequences. These conditions are derived entirely in terms of the cumulant sequences. They use the fact that for a finite-extent cumulant sequence factorability is equivalent to finding a finite-order moving-average process with an identical cumulant sequence. In principle the results can be extended to polyspectra of even higher orders. An interesting result of the investigation is that there exist processes generated by nonlinear mechanisms that are factorable