A Formal Test of Density Forecast Evaluation - BERA, Anil K. (Institutional Knowledge at Singapore Management University, 2003)
Recent econometricians have shifted their attention from point and interval forecasts of the probability density functions (PDF) of various market variables. One of the main problems in this area has been evaluation of the density forecasts. In this papers, we propose a formal test for density forecast evaluation using Neyman (1937) smooth test procedure. Apart from giving indications of acceptance or rejection of the tested model, this approach provides specific sources (such as the mean, variance, skewness and kurtosis or the location, scale and shape of the distribution) or rejections, thereby helping in deciding possible modifications of the assumed model. Our applications to value weighted S&P returns indicated that introduction of a conditional heteroscedelasticity model significantly improved the model over a model with constant conditional variance.