Comparing and evaluating Bayesian predictive distributions of asset returns

Bayesian inference in a time series model provides exact out-of-sample predictive distributions that fully and coherently incorporate parameter uncertainty. This study compares and evaluates Bayesian predictive distributions from alternative models, using as an illustration five alternative models of asset returns applied to daily S&P 500 returns from the period 1976 through 2005. The comparison exercise uses predictive likelihoods and is inherently Bayesian. The evaluation exercise uses the probability integral transformation and is inherently frequentist. The illustration shows that the two approaches can be complementary, with each identifying strengths and weaknesses in models that are not evident using the other.