Evaluating the Predictive Distributions of Bayesian Models of Asset Returns
19 Pages Posted: 4 Jul 2008
Date Written: June 30, 2008
Abstract
Bayesian time series models provide exact, out-of-sample predictive distributions. This paper examines two approaches to the comparison and evaluation of these distributions and illustrates them using five alternative models of asset returns applied to the daily S&P 500 index from 1976 through 2005. It is shown that the first approach, using predictive likelihoods, is intimately related to Bayes factors. The illustration shows how analysis of predictive likelihoods provides insight into the relative strengths and weaknesses of alternative prediction models. The second approach, using the probability integral transform, provides absolute standards in the evaluation of the quality of predictive distributions. The illustration shows that the two approaches can be complementary, each identifying strengths and weaknesses in the model that are not evident using the other. For the S&P 500 data, the predictive distributions of the hierarchical Markov normal mixture model prove superior to those of a stochastic volatility model and several models in the ARCH family.
Keywords: forecasting, GARCH, inverse probability transform, Markov mixture, predictive likelihood, S&P 500 returns, stochastic volatility
JEL Classification: C53, G12, C11
Suggested Citation: Suggested Citation
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