This paper proposes a novel technique for the prediction of solar-terrestrial data sets that contain a significant proportion of missing data points. A nonlinear interpolation technique is employed to assign values to gaps in a time series. It interpolates each missing point such that the error introduced into any specific predictive function is minimised. Radial basis function (RBF) neural networks (NN) are adopted for the purpose of prediction, and their advantages over their multi-layer perceptron (MLP) counterparts are outlined. This technique has general application in any instance where the effects of interpolation upon a given analysis process need to be minimised or a complete time series needs to be constructed from non-contiguous data. (5 pages)