Neural Network approaches to time series prediction are briefly discussed, and the need to specify an appropriately sized input window identified. Relevant theoretical results from dynamic systems theory are briefly introduced, and heuristics for finding the correct embedding dimension, and thence window size, are discussed. The method is applied to two time series and the resulting generalization performance of the trained feed-forward neural network predictors is analyzed. It is shown that the heuristics can provide useful information in defining the appropriate network architecture.