Bayesian inference of multivariate rotated GARCH models with skew returns

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Bayesian inference is proposed for volatility models, targeting financial returns, which exhibit high kurtosis and slight skewness. Rotated GARCH models are considered which can accommodate the multivariate standard normal, Student t, generalized error distributions and their skewed versions. Inference on the model parameters and prediction of future volatilities and cross-correlations are addressed by Markov chain Monte Carlo inference. Bivariate simulated data is used to assess the performance of the method, while two sets of real data are used for illustration: the first is a trivariate data set of financial stock indices and the second is a higher dimensional data set for which a portfolio allocation is performed.