Asset pricing with neural networks: Significance tests

Abstract

This study proposes a novel hypothesis test for evaluating the statistical significance of input variables in multi-layer perceptron (MLP) regression models. Theoretical foundations are established through consistency results and estimation rate analysis using the sieves method. To validate the test's performance in complex and realistic settings, an extensive Monte Carlo simulation is conducted. Results of the simulation reveal that the test has a high power and low rate of false positives, making it a powerful tool for detecting true effects in data. The test is further applied to identify the most influential predictors of equity risk premiums, with results indicating that only a small number of characteristics have statistical significance and all macroeconomic predictors are insignificant at the 1% level. These findings are consistent across a variety of neural network architectures.

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