Variance and skewness in density forecasts: assessing world GDP growth

This paper introduces a novel methodology, Bayesian cross-entropy forecasting (BCEF), for predicting the variance and skewness of density forecasts. BCEF evaluates the first-order effects of risk factors on the variability and asymmetry of predictive distributions, enabling a clear assessment of a forecasted variable’s upside and downside risks. A key innovation of BCEF lies in its ability to decompose variance and skewness within density forecasts, providing a robust framework for uncertainty analysis. By leveraging the two-piece normal distribution, BCEF generates asymmetric density forecasts incorporating forward-looking information from expectation surveys and statistical outputs of predictive models. The methodology's effectiveness is demonstrated through its application to world GDP growth forecasts using data from October 2005 to August 2015. The results, evaluated using the continuous-ranked probability score, show that BCEF fan charts are more accurate and consistently outperform standard symmetric and calibrated asymmetric density forecast benchmarks.