Forecasting volatility with neural regression: a contribution to model adequacy.

Neural nets' usefulness for forecasting is limited by problems of overfitting and the lack of rigorous procedures for model identification, selection and adequacy testing. This paper describes a methodology for neural model misspecification testing. We introduce a generalization of the Durbin-Watson statistic for neural regression and discuss the general issues of misspecification testing using residual analysis. We derive a generalized influence matrix for neural estimators which enables us to evaluate the distribution of the statistic. We deploy Monte Carlo simulation to compare the power of the test for neural and linear regressors. While residual testing is not a sufficient condition for model adequacy, it is nevertheless a necessary condition to demonstrate that the model is a good approximation to the data generating process, particularly as neural-network estimation procedures are susceptible to partial convergence. The work is also an important step toward developing rigorous procedures for neural model identification, selection and adequacy testing which have started to appear in the literature. We demonstrate its applicability in the nontrivial problem of forecasting implied volatility innovations using high-frequency stock index options. Each step of the model building process is validated using statistical tests to verify variable significance and model adequacy with the results confirming the presence of nonlinear relationships in implied volatility innovations.

Neural networks in financial engineering: a study in methodology.

Neural networks have shown considerable successes in modeling financial data series. However, a major weakness of neural modeling is the lack of established procedures for performing tests for misspecified models, and tests of statistical significance for the various parameters that have been estimated. This is a serious disadvantage in applications where there is a strong culture for testing not only the predictive power of a model or the sensitivity of the dependent variable to changes in the inputs but also the statistical significance of the finding at a specified level of confidence. Rarely is this more important than in the case of financial engineering, where the data generating processes are dominantly stochastic and only partially deterministic. Partly a tutorial, partly a review, this paper describes a collection of typical applications in options pricing, cointegration, the term structure of interest rates and models of investor behavior which highlight these weaknesses and propose and evaluate a number of solutions. We describe a number of alternative ways to deal with the problem of variable selection, show how to use model misspecification tests, we deploy a novel way based on cointegration to deal with the problem of nonstationarity, and generally describe approaches to predictive neural modeling which are more in tune with the requirements for modeling financial data series.