Bayesian analysis of the unobserved ARCH model

The Unobserved ARCH model is a good description of the phenomenon of changing volatility that is commonly appeared in the financial time series. We study this model adopting Bayesian inference via Markov Chain Monte Carlo (MCMC). In order to provide an easy to implement MCMC algorithm we adopt some suitable non-linear transformations of the parameter space such that the resulting MCMC algorithm is based only on Gibbs sampling steps. We illustrate our methodology with data from real world. The Unobserved ARCH is shown to be a good description of the exchange rate movements. Numerical comparisons between competing MCMC algorithms are also presented.