Neural networks have had considerable success in a variety of disciplines including engineering, control, and financial modelling. However a major weakness is the lack of established procedures for testing mis-specified models and the statistical significance of the various parameters which have been estimated. This is particularly important in the majority of financial applications where the data generating processes are dominantly shastic and only partially deterministic. Based on the latest, most significant developments in estimation theory, model selection and the theory of mis-specified models, this volume develops neural networks into an advanced financial econometrics tool for non-parametric modelling. It provides the theoretical framework required, and displays the efficient use of neural networks for modelling complex financial phenomena. Unlike most other books in this area, this one treats neural networks as statistical devices for non-linear, non-parametric regression analysis.