Survey density forecast comparison in small samples

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.