Testing for Correct Specification of Path Density Forecasts

Abstract

We propose a correct specification test for path density forecasts. In comparison with the usual evaluation of forecasts’ calibration at each horizon, our test does not over-reject under the null as we account for the multiple horizons when setting the critical values. A simulation exercise shows our bootstrap method leads to good size and power properties in comparison with alternatives. The application of our test procedure to the Bank of England fan charts shows how useful our approach is to evaluate the calibration of density forecasts.