The behavioral approach to system theory provides a parameter-free framework for the study of the general problem of linear exact modeling and recursive modeling. The main contribution of this paper is the solution of the (continuous-time) polynomial-exponential time series modeling problem. Both recursive and nonrecursive solutions are provided and classified according to properties like complexity and controllability. It is shown in particular, that recursive modeling corresponds to updating by means of a cascade interconnection of systems. As a special case the solution of several other problems, like rational interpolation, realization, modeling of arbitrary discrete-time time series, is obtained.