Neural Networks and Bootstrap Methods for Regression Models with Dependent Errors

This chapter introduces the use of the bootstrap in a nonlinear, nonparametric regression framework with dependent errors. The aim is to construct approximate confidence intervals for the regression function which is estimated by using a single hidden layer feedforward neural network. In this framework, the use of a standard residual bootstrap scheme is not appropriate and it may lead to results that are not consistent. As an alternative solution, we investigate the AR-Sieve bootstrap and the Moving Block bootstrap, which are used to generate bootstrap replicates with a proper dependence structure. Both approaches are nonparametric bootstrap schemes, a consistent choice when dealing with neural network models which are often used as an accurate nonparametric estimation and prediction tool. In this context, both procedures may lead to satisfactory results but the AR sieve bootstrap seems to outperform the moving block bootstrap delivering confidence intervals with coverages closer to the nominal levels.