A Smooth Test for Density Forecast Evaluation

Recently financial econometricians have shifted their attention from point and interval forecasts to density forecasts mainly to address the issue of the huge loss of information that results from depicting portfolio risk by a measure of dispersion alone. One of the major problems in this area has been the evaluation of the quality of different density forecasts. In this paper I propose an analytical test for density forecast evaluation using the Smooth Test procedure for both independent and serially dependent data. Apart from indicating the acceptance or rejection of the hypothesized model, this approach provides specific sources (such as the mean, variance, skewness and kurtosis or the location, scale and shape of the distribution or types of dependence) of departure, thereby helping in deciding possible modifications of the assumed forecast model. I also address the issue of where to split the sample into in-sample (estimation sample) and out-of-sample (testing sample) observations in order to evaluate the “goodness-of-fit� of the forecasting model both analytically, as well as through simulation exercises. Monte Carlo studies revealed that the proposed test has good size and power properties. I also further investigate applications to value weighted S&P 500 returns that initially indicates that introduction of a conditional heteroscedasticity model significantly improve the model over one with constant conditional variance. The simplicity of the proposed “parametric� test based on the classical score test should also appeal the practitioners