Forecasting Value-at-Risk Using Deep Neural Network Quantile Regression*

In this article, we use a deep quantile estimator, based on neural networks and their universal approximation property to examine a non-linear association between the conditional quantiles of a dependent variable and predictors. This methodology is versatile and allows both the use of different penalty functions, as well as high dimensional covariates. We present a Monte Carlo exercise where we examine the finite sample properties of the deep quantile estimator and show that it delivers good finite sample performance. We use the deep quantile estimator to forecast value-at-risk and find significant gains over linear quantile regression alternatives and other models, which are supported by various testing schemes. Further, we consider also an alternative architecture that allows the use of mixed frequency data in neural networks. This article also contributes to the interpretability of neural network output by making comparisons between the commonly used Shapley Additive Explanation values and an alternative method based on partial derivatives.