Calibration tests based on the probability integral transform (PIT) are routinely used to assess the quality of univariate distributional forecasts. However, PIT-based calibration tests for multivariate distributional forecasts face various challenges. We propose two new types of tests based on proper scoring rules, which overcome these challenges. They arise from a general framework for calibration testing in the multivariate case, introduced in this work. The new tests have good size and power properties in simulations and solve various problems of existing tests. We apply the tests to forecast distributions for macroeconomic and financial time series data.

翻译：基于概率积分变换（PIT）的校准检验通常用于评估单变量分布预测的质量。然而，针对多元分布预测的PIT校准检验面临诸多挑战。我们提出两类基于适当评分规则的新型检验方法，这些方法克服了上述挑战。它们源于本文引入的多元校准检验通用框架。在模拟实验中，新提出的检验方法具有良好的检验水平和检验功效，并解决了现有检验方法的多种问题。我们将这些检验方法应用于宏观经济与金融时间序列数据的预测分布评估。