Testing Quantile Forecast Optimality
提出检验多期分位数预测最优性的方法，基于Mincer-Zarnowitz分位数回归构建矩条件框架，可识别预测偏差的具体形式，适用于金融和宏观经济数据。
Quantile forecasts made across multiple horizons have become an important output of many financial institutions, central banks and international organizations. This article 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.