In recent years an impressive array of publications has appeared claiming considerable successes of neural networks in modelling ®nancial data but sceptical practitioners and statisticians are still raising the question of whether neural networks really are a major breakthrough or just a passing fad'. A major reason for this is the lack of procedures for performing tests for misspeci®ed models, and tests of statistical signi®cance for the various parameters that have been estimated, which makes it dicult to assess the model's signi®cance and the possibility that any short-term successes that are reported might be due to data mining'. In this paper we describe a methodology for neural model identi®cation which facilitates hypothesis testing at two levels: model adequacy and variable signi®cance. The methodology includes a model selection procedure to produce consistent estimators, a variable selection procedure based on statistical signi®cance and a model adequacy procedure based on residuals analysis. We propose a novel, computationally ecient scheme for estimating sampling variability of arbitrarily complex statistics for neural models and apply it to variable selection. The approach is based on sampling from the asymptotic distribution of the neural model's parameters (`parametric sampling'). Controlled simulations are used for the analysis and evaluation of our model ident-i®cation methodology. A case study in tactical asset allocation is used to demonstrate how the methodology can be applied to real-life problems in a way analogous to stepwise forward regression analysis. Neural models are contrasted to multiple linear regression. The results indicate the presence of non-linear relationships in modelling the equity premium.