Neural networks are one of a variety of machine learning models which are beginning to be widely used in economic forecasting applications. Despite this, there is relatively little understanding of the conditions in which neural networks provide accurate forecasts, the uncertainty bounds which can be put on such forecasts, and the most suitable network types and parameters for forecasting in the relatively small-sample settings encountered within economics. This thesis fits into a growing body of literature which aims to answer some of these questions. In Chapter 1, we present a detailed study of the accuracy of neural networks for forecasting financial volatility, and present a novel adaptation of networks for time series data. In Chapter 2, we present an adaptation to the output layer of neural networks which allows the generation of prediction intervals for forecasts, and present variants to the architecture which improve the accuracy of these prediction intervals. In Chapter 3, we focus on confidence intervals, and present the first simulation study of the suitability of bootstrapping for neural networks for generating confidence intervals with correct coverage. Finally, in Chapter 4, we focus on an alternate application of neural networks in forecasting; that of converting free-form text data into indices, and present a novel neural network architecture for improving the recognition of named entities (companies, people etc.) in text, a necessary first step in such forecasting.