We apply fixed-$b$ and fixed-$m$ asymptotics to tests of equal predictive accuracy and of encompassing for survey density forecasts. We verify in an original Monte Carlo design that fixed-smoothing asymptotics delivers correctly sized tests in this framework, even when only a small number of out of sample observations is available. We use the proposed density forecast comparison tests with fixed-smoothing asymptotics to assess the predictive ability of density forecasts from the European Central Bank’s Survey of Professional Forecasters (ECB SPF). We find an improvement in the relative predictive ability of the ECB SPF since 2010, suggesting a change in the forecasting practice after the financial crisis.

我们应用固定-$乙$和固定-$米$渐近测试同等预测准确性和包含调查密度预测的测试。我们在原始的蒙特卡洛设计中验证了固定平滑渐进在这个框架中提供了正确大小的测试，即使只有少量的样本外观察可用。我们使用所提出的密度预测比较检验与固定平滑渐近法来评估欧洲央行专业预测员调查 (ECB SPF) 的密度预测的预测能力。我们发现自 2010 年以来欧洲央行 SPF 的相对预测能力有所提高，这表明金融危机后预测实践发生了变化。