标题： Murphy图：预期损失的预报评估 显示英文标题

标题： Murphy Diagrams: Forecast Evaluation of Expected Shortfall

摘要： 受巴塞尔3号监管规定的影响，最近的研究考虑了风险价值和预期损失的联合预测。 在这一背景下，可以使用一大类评分函数来评估预测性能。 然而，目前缺乏直观或实证的指导，这使得在实践中选择评分函数变得困难。 因此，我们开发了图形检查（Murphy图），以判断在相关评分函数类别下，一种预测方法是否优于另一种，并提出了相关的假设检验。 我们通过模拟示例和对标准普尔500指数和DAX指数收益的实证分析来说明这些工具。 显示英文摘要

摘要： Motivated by the Basel 3 regulations, recent studies have considered joint forecasts of Value-at-Risk and Expected Shortfall. A large family of scoring functions can be used to evaluate forecast performance in this context. However, little intuitive or empirical guidance is currently available, which renders the choice of scoring function awkward in practice. We therefore develop graphical checks (Murphy diagrams) of whether one forecast method dominates another under a relevant class of scoring functions, and propose an associated hypothesis test. We illustrate these tools with simulation examples and an empirical analysis of S&P 500 and DAX returns.