Neural network models for empirical finance

This paper presents an overview of the procedures that are involved in prediction with machine learning models with special emphasis on deep learning. We study suitable objective functions for prediction in high-dimensional settings and discuss the role of regularization methods in order to alleviate the problem of overfitting. We also review other features of machine learning methods, such as the selection of hyperparameters, the role of the architecture of a deep neural network for model prediction, or the importance of using different optimization routines for model selection. The review also considers the issue of model uncertainty and presents state-of-the-art methods for constructing prediction intervals using ensemble methods, such as bootstrap and Monte Carlo dropout. These methods are illustrated in an out-of-sample empirical forecasting exercise that compares the performance of machine learning methods against conventional time series models for different financial indices. These results are confirmed in an asset allocation context.