Accurate future prediction of wave fields can be used to optimize the performance of wave energy converters as well as various offshore operations. A highly efficient model using single, fixed-probe measurements for predicting unidirectional wave fields of up to second-order nonlinearity has been developed. The fundamental problem with the use of the Fast Fourier Transform (FFT) in forward prediction is the inherent assumption of periodicity of the finite-length record beyond its ends. The main aim here is to enhance the performance of the FFT algorithm during prediction of linear wave fields while retaining its computational efficiency. Given a finite-duration wave record up to the present time at a location upwave, it is observed that introducing a smooth transition of the record down to zero at both ends by adding half of a NewWave-type wave group improves the prediction at the point of interest dramatically compared to just using the raw record. These extensions can in turn serve as predictions for cases requiring future knowledge without the use of upwave measurements. These schemes are tested on their capability to predict synthetic wave fields at locations downwave and into the future. Comparisons are made by computing the numerical error within a theoretical predictable zone which is also estimated in this work. A second validation is done on weakly nonlinear sea states that include both sum and difference bound wave components calculated using exact second-order theory. A simulation method that initially linearizes the signal, then advances it in both space and time, and finally re-inserts estimated bound-harmonics based on a narrow-banded approximation proves to be very effective, yielding substantial improvements compared to assuming the signal is completely linear. The narrow-banded linearization/re-insertion is a very fast time-domain operation, hence the additional computational cost is very little. The nonlinear model is validated using synthetic wave records for waves in intermediate-depth water.