**4. Conclusion**

In financial applications, modelling the correlation structures of the returns is important because empirical analyses show that there is time-varying relation among return-on-assets. In this context, factor-MSVOL models have been preferred. Thanks to these models, volatility dynamics of financial and economic time series can be modelled with few latent factors.

In this study, parameter estimations concerning additive factor-MSVOL models were modelled with normal distribution assigned on the error, Student-t distribution, and Slash distribution in the frame of Bayesian analysis. Normal, Student-t and Slash distributions were assigned as prior distribution to the error distributions and full conditioned posterior distributions were obtained by a kind of MCMC method-Gibbs sampling. Among the criteria of model choosing, DIC is used for comparison and it showed that Student-t and Slash distributions can be used as alternative of normal AFactor-MSVOL models. Provided that the analysis results are evaluated in respect of DIC criteria and model complexity, it is seen that AFactor-MSVOL-Sl model in which the errors are scaled with Slash distribution is better than the other models. In case the error terms are modelled with Slash distribution, analysis of financial return series, which involves deviated and extreme observations, will provide more correct results. Both Student-t and Slash distributions are robust distributions. Both of the distributions better adapted to the data compared to normal distribution. Student-t distribution allows kurtosis in a larger interval for high degrees of freedom but it is possible to say that Slash distribution is more robust as it gives better parameter estimations in case there are more unusual

*Bayesian Analysis of Additive Factor Volatility Models with Heavy-Tailed Distributions… DOI: http://dx.doi.org/10.5772/intechopen.93685*

points. Therefore; it is seen that Student-t and Slash distributions are applicable as an alternative of normal distribution in the analysis of financial return series. Moreover, it is possible to say that heavy-tailed distributions can substitute normal distribution in case deviated observation values are not present.
