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Robust Bayesian analysis of heavy-tailed stochastic volatility models using scale mixtures of normal distributions. (English) Zbl 1284.91579
Summary: A Bayesian analysis of stochastic volatility (SV) models using the class of symmetric scale mixtures of normal (SMN) distributions is considered. In the face of non-normality, this provides an appealing robust alternative to the routine use of the normal distribution. Specific distributions examined include the normal, student-\(t\), slash and the variance gamma distributions. Using a Bayesian paradigm, an efficient Markov chain Monte Carlo (MCMC) algorithm is introduced for parameter estimation. Moreover, the mixing parameters obtained as a by-product of the scale mixture representation can be used to identify outliers. The methods developed are applied to analyze daily stock returns data on S&P500 index. Bayesian model selection criteria as well as out-of-sample forecasting results reveal that the SV models based on heavy-tailed SMN distributions provide significant improvement in model fit as well as prediction to the S&P500 index data over the usual normal model.

MSC:
91G70 Statistical methods; risk measures
62F35 Robustness and adaptive procedures (parametric inference)
62F15 Bayesian inference
91B70 Stochastic models in economics
Software:
Scythe
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