Unfolded Skewness and Kurtosis Timings in Out-of-Sample Density Forecasts of Financial Returns

This paper assesses both statistical significance and economic relevance of distributional timing in out-of-sample density forecasts. A comprehensive set of model specifications incorporating dynamic higher moments is estimated, and a wide range of statistical tests is conducted. The results consistently indicate that modeling time-varying skewness and kurtosis significantly enhances the adequacy and accuracy of density forecasts. In utility-based evaluations, transitioning from portfolios based on constant higher moments to those incorporating time-varying skewness and kurtosis generates average annual gains of 265 and 439 basis points, respectively. Furthermore, an investor would be willing to pay approximately 170 basis points per year to obtain information on skewness and kurtosis beyond volatility. Among the competing models, the unfolded GARCH model—which decomposes returns into the product of their absolute values and signs—not only demonstrates the strongest statistical significance for capturing the left tail of financial returns, but also yields the highest average gains of approximately 9.4% and 11.9% for investors who unfold skewness and kurtosis timing in their decision-making.