Smooth Test for Density Forecast Evaluation

Abstract

Recently econometricians have shifted their attention from point and interval forecasts to density forecasts because at the heart of market risk measurement is the forecast of the probability density functions of various financial variables. In this paper, we propose a formal test for density forecast evaluation based on Neyman's smooth test procedure. Apart from accepting or rejecting the tested model, this approach provides specific sources (such as the location, scale and shape of the distribution) of rejection, thereby helping in deciding possible modifications of the assumed model. Our applications to S&P 500 returns indicate capturing time-varying volatility and non-gaussianity significantly improve the performance of the model.

Keywords: Score test, probability integral transform, model selection, GARCH model, simulation based method, sample size selection

JEL Classification: C12, C52, C53