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.

中文翻译：

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使用深度神经网络分位数回归预测风险值

在本文中，我们使用基于神经网络及其通用逼近特性的深度分位数估计器来检查因变量的条件分位数与预测变量之间的非线性关联。这种方法是通用的，允许使用不同的惩罚函数，以及高维协变量。我们提出了一个蒙特卡罗练习，其中我们检查了深度分位数估计器的有限样本属性，并表明它提供了良好的有限样本性能。我们使用深度分位数估计器来预测风险价值，并发现优于线性分位数回归替代方案和其他模型的显着收益，这些模型得到各种测试方案的支持。此外，我们还考虑了一种允许在神经网络中使用混合频率数据的替代架构。