A semiparametric Bayesian approach to the analysis of financial time series with applications to value at risk estimation

• We develop a Bayesian semiparametric approach to GARCH-type models.
• The innovations follow the class of scale mixtures of Gaussian distributions with a Dirichlet process prior in the mixing distribution.
• It is also shown how to undertake Bayesian prediction of the Value at Risk (VaR).
• We have obtained significant differences in the predictive distribution of the returns, especially in the tails.
• We have observed different results in the VaR estimation with different specifications.

GARCH models are commonly used for describing, estimating and predicting the dynamics of financial returns. Here, we relax the usual parametric distributional assumptions of GARCH models and develop a Bayesian semiparametric approach based on modeling the innovations using the class of scale mixtures of Gaussian distributions with a Dirichlet process prior on the mixing distribution. The proposed specification allows for greater flexibility in capturing the usual patterns observed in financial returns. It is also shown how to undertake Bayesian prediction of the Value at Risk (VaR). The performance of the proposed semiparametric method is illustrated using simulated and real data from the Hang Seng Index (HSI) and Bombay Stock Exchange index (BSE30).