Density Forecast Evaluations via a Simulation-Based Dynamic Probability Integral Transformation*

This paper presents simulation-based density forecast evaluation methods using particle filters. The simulation-based dynamic probability integral transformation or log-likelihood evaluation method is combined with the existing density forecast evaluation methods. This methodology is applicable to various density forecast models, such as log stochastic volatility models and affine jump diffusion (AJD) models, for which the probability integral transform or likelihood computation is difficult due to the presence of latent stochastic volatilities. This methodology is applied to the daily S&P 500 stock index. The empirical results show that the AJD models with jumps perform the best for out-of-sample evaluations.