Neural networks in nonlinear time series: a subsampling model selection procedure

In this chapter, the problem of model selection in neural networks for nonlinear time series data is addressed. A systematic review and an appraisal of previously published research on the topic are presented and discussed with emphasis on a complete strategy to select the topology of the model. The procedure attempts to explain the black box structure of a neural network by providing information on the complex structure of the relationship between a set of inputs and the output. The procedure combines a set of graphical and inferential statistical tools and allows to choose the number and the type of inputs, considered as explanatory variables, by using a formal test procedure based on relevance measures and to identify the hidden layer size by looking at the predictive performance of the neural network model. To obtain an approximation of the involved statistics, the approach heavily uses the subsampling technique, a computer-intensive statistical methodology. The results on simulated data show the good performance of the overall procedure.