Variable selection in neural network regression models with dependent data: a subsampling approach

The problem of variable selection in neural network regression models with dependent data is considered. In this framework, a test procedure based on the introduction of a measure for the variable relevance to the model is discussed. The main difficulty in using this procedure is related to the asymptotic distribution of the test statistic which is not one of the familiar tabulated distributions. Moreover, it depends on matrices which are very difficult to estimate because of their complex structure. To overcome these analytical issues and to get a consistent approximation for the sampling distribution of the statistic involved, a subsampling scheme is proposed. The procedure, which takes explicitly into account the dependence structure of the data, will be justified from an asymptotic point of view and evaluated in finite samples by a small Monte Carlo study.