An application of three bivariate time-varying volatility models (Q2722298)

The phenomenon of ``volatility clustering'' is often encountered in financial time series such as stock returns and exchange rates. The autoregressive conditional heteroskedasticity (ARCH) model and the stochastic volatility model are the most popular modelling approaches to capture this data structure. This paper is focused on bivariate models. It deals with the GARCH model with constant conditional correlation, a version of the ARCH model, and the unobserved ARCH model which can be classified as a stochastic volatility model. The parameters of these models are estimated using Bayesian techniques and, in particular, Markov chain Monte Carlo (MCMC). The paper is also concerned with the comparison of multivariate ARCH-GARCH and stochastic volatility models by using predictive distributions. Using the output of the MCMC algorithms these models are compared using their predictive ability following the criteria proposed by \textit{A. E. Gelfand, D. K. Dey} and \textit{H. Chang} [Bayesian Statistics, Vol. 4, Oxford University Press: Oxford, 147-167 (1992)]. For their comparative illustration the authors generalize slightly one of the models analysed by them in the previous work [Technical Report 86, Dept. of Stat., Athens Univ. of Economics and Business (1999)] by including a correlation term for the ARCH model.