Comparing and Evaluating Bayesian Predictive Distributions of Asset Returns

John Geweke and Gianni Amisano
CQER Working Paper 09-04
October 2009

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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 1972 through 2005. The comparison exercise uses predictive likelihoods and is inherently Bayesian. The evaluation exercise uses the probability integral transform and is inherently frequentist. The illustration shows that the two approaches can be complementary, each identifying strengths and weaknesses in models that are not evident using the other.

JEL classification: C11, C53

Key words: forecasting, GARCH, inverse probability transform, Markov-mixture, predictive likelihood, S&P 500 returns, stochastic volatility

The authors gratefully acknowledge financial support from NSF grant SBR-0720547. The views expressed here are the authors' and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors' responsibility.

Please address questions regarding content to John Geweke, Departments of Statistics and Economics, W210 Pappajohn Business Bldg., University of Iowa, Iowa City, IA 52242-1000,, and Gianni Amisano, University of Brescia and European Central Bank,

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