The speech production can be modeled by linear and nonlinear systems. In this contribution a time variable nonlinear Volterra system is used to model the fluctuations of the voiced excitation while a linear system models the resonances of the speech production system. The estimation of the Volterra system is performed by a prediction algorithm. This is enabled by a description of the prediction problem as an approximation by a series expansion. Speech examples show that the use of a time variable Volterra system improves the naturalness of the synthetic speech.