Before revision:  Our main result is a classification of such models in the spirit of Filipovic's maximal degree theorem for exponential polynomial models  .
After revision:  Our main result is a classification of such models in the spirit of Filipovic's maximal degree theorem for exponential polynomial models , as well as an explicit characterisation of the set of feasible parameters in the case when the factor process is bounded. Extensions to time-inhomogeneous and multi-factor polynomial models are also considered .