Asset Pricing with Neural Networks : A Variable Significant Test

To facilitate crossing from the "black box" to "glass box" in the application of neural networks (NNs), we develop a variable significant test for the multi-layer perceptrons. To derive the test statistic and its asymptotic distribution, we provide the consistency of the multi-layer perceptrons via the method of sieves. We apply the proposed test to identify the most significant predictors in forecasting equity risk premium. The main results show the superiority of NN relative to the linear regression for forecasting excess returns benchmarking against naive zero forecasts. Furthermore, the most significant predictors are inflation, percent equity issuing, and default return spread