Brazilian Journal of Probability and Statistics

Stochastic volatility in mean models with heavy-tailed distributions

Carlos A. Abanto-Valle, Helio S. Migon, and Victor H. Lachos

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A stochastic volatility in mean (SVM) model using the class of symmetric scale mixtures of normal (SMN) distributions is introduced in this article. The SMN distributions form a class of symmetric thick-tailed distributions that includes the normal one as a special case, providing a robust alternative to estimation in SVM models in the absence of normality. A Bayesian method via Markov-chain Monte Carlo (MCMC) techniques is used to estimate parameters. The deviance information criterion (DIC) and the Bayesian predictive information criteria (BPIC) are calculated to compare the fit of distributions. The method is illustrated by analyzing daily stock return data from the São Paulo Stock, Mercantile & Futures Exchange index (IBOVESPA). According to both model selection criteria as well as out-of-sample forecasting, we found that the SVM model with slash distribution provides a significant improvement in model fit as well as prediction for the IBOVESPA data over the usual normal model.

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Braz. J. Probab. Stat., Volume 26, Number 4 (2012), 402-422.

First available in Project Euclid: 3 July 2012

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Feedback effect Markov chain Monte Carlo non-Gaussian and nonlinear state space models scale mixture of normal distributions stochastic volatility in mean


Abanto-Valle, Carlos A.; Migon, Helio S.; Lachos, Victor H. Stochastic volatility in mean models with heavy-tailed distributions. Braz. J. Probab. Stat. 26 (2012), no. 4, 402--422. doi:10.1214/11-BJPS169.

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