this presentation contributes to the theoretical background for a new quadratic prediction method for time series. we develop a theory of polyspectral factorization, providing new mathematical results for polyspectral densities. new bijections between a restricted space of higher-dimensional cepstral coefficients (where the restrictions are induced by the symmetries of the polyspectra) and the auto-cumulants are derived. applications to modeling are developed; in particular, it is shown that semi-parametric nonlinear time series modeling can be accomplished by approximation of the cepstral representation of polyspectra.