On the structure of nonlinear polynomial models: higher order correlation functions, spectra, and term clusters

A framework is established which relates the structure of nonlinear polynomial models to the dynamical properties of the estimation data. Such a framework uses the concepts of term clusters, higher order correlation functions and higher order spectra. The results discussed offer a new way of understanding and interpreting term clusters in structure selection problems for nonlinear polynomial models. A numerical example which uses real data is included to illustrate the new results.