Bayesian estimation of stochastic volatility models based on OU processes with marginal Gamma laws

This paper discusses practical Bayesian estimation of stochastic volatility
models based on OU processes with marginal Gamma laws. Estimation is based on
a parameterization which is derived from the Rosi´nski representation, and has the
advantage of being a non-centered parameterization. The parameterization is based
on a marked point process, living on the positive real line, with uniformly distributed
marks. We define a Markov chain Monte Carlo (MCMC) scheme which enables
multiple updates of the latent point process, and generalizes single updating algorithm
used earlier. At each MCMC draw more than one point is added or deleted
from the latent point process. This is particularly useful for high intensity processes.
Furthermore, the article deals with superposition models, where it discuss how the
identifiability problem inherent in the superposition model may be avoided by the use
of aMarkov prior. Finally, applications to simulated data as well as exchange rate data
are discussed