Density Forecasting with Time Varying Higher Moments – A Model Confidence Set Approach

Density forecasts contain a complete description of the uncertainty associated with a point forecast and are therefore important measures of financial risk. This paper aims to examine if the new more complicated models for financial returns that allow for time variation in higher moments lead to better out-of-sample density forecasts. Using two decades of daily Standard and Poor's 500 index returns I find that a model with time varying conditional variance, skewness and kurtosis produces significantly better density forecasts than the competing models.