Scaling and measurement error sensitivity of scoring rules for distribution forecasts
研究了数据缩放和测量误差对分布预测评分规则的影响，发现常用评分规则对缩放稳健，而连续排序概率评分比对数评分对严重测量误差更不敏感，并通过GDP和金融波动模拟及实证验证。
Summary This paper examines the impact of data rescaling and measurement error on scoring rules for distribution forecast. First, I show that all commonly used scoring rules for distribution forecasts are robust to rescaling the data. Second, the forecast ranking based on the continuous ranked probability score is less sensitive to gross measurement error than the ranking based on the log score. The theoretical results are complemented by a simulation study aligned with frequently revised quarterly US gross domestic product (GDP) growth data, a simulation study aligned with financial market volatility, and an empirical application forecasting realized variances of S&P 100 constituents.