Quantile forecasts made across multiple horizons have become an important output of many financial institutions, central banks and international organisations. This paper proposes misspecification tests for such quantile forecasts that assess optimality over a set of multiple forecast horizons and/or quantiles. The tests build on multiple Mincer-Zarnowitz quantile regressions cast in a moment equality framework. Our main test is for the null hypothesis of autocalibration, a concept which assesses optimality with respect to the information contained in the forecasts themselves. We provide an extension that allows to test for optimality with respect to larger information sets and a multivariate extension. Importantly, our tests do not just inform about general violations of optimality, but may also provide useful insights into specific forms of sub-optimality. A simulation study investigates the finite sample performance of our tests, and two empirical applications to financial returns and U.S. macroeconomic series illustrate that our tests can yield interesting insights into quantile forecast sub-optimality and its causes.

翻译：跨多个预测期的分位数预测已成为许多金融机构、中央银行和国际组织的重要产出。本文针对此类分位数预测提出了误设定检验，用于评估多个预测期和/或分位数集上的最优性。该检验基于在矩等式框架下构建的多元Mincer-Zarnowitz分位数回归。我们的主要检验针对自动校准这一原假设，该概念评估相对于预测本身所含信息的最优性。我们提供了一个扩展版本，可检验相对于更大信息集的最优性，并提供了多元扩展版本。重要的是，我们的检验不仅揭示最优性的一般违反情况，还能提供关于特定次优形式的深刻见解。模拟研究考察了检验的有限样本表现，两项针对金融收益率和美国宏观经济序列的实证应用表明，我们的检验能够为分位数预测的次优性及其成因提供有价值的启示。