Density forecast revisions and forecast efficiency

We explain that revisions to successive density forecasts of the same outcome, as measured by the Kullback-Leibler Information Criterion, need not be unpredictable, unlike those to conditional mean forecasts, even when the forecaster uses information efficiently. However one can still test the efficiency of fixed-event conditional density forecasts, similarly to conditional mean forecasts, by testing the independence of revisions to an event forecast extracted from the density forecast. In an application we thereby test the efficiency of the fixed-event density forecasts of U.S. inflation and GDP growth supplied by the Survey of Professional Forecasters. ∗Address for correspondence: James Mitchell, National Institute of Economic and Social Research, 2 Dean Trench Street, Smith Square, London, SW1P 3HE, U.K. Tel: +44 (0) 207 654 1926. Fax: +44 (0) 207 654 1900. E-Mail: [email protected]. Mitchell gratefully acknowledges financial support from the ESRC (Award Reference: RES-000-22-1512). Thanks to Stephen Hall, Martin Weale and seminar participants at Warwick for helpful conversations. Particular thanks to Ken Wallis for written comments.