Some Recent Developments in Markov Chain Monte Carlo for Cointegrated Time Series

We consider multivariate time series that exhibit reduced rank cointegration, which means a lower dimensional linear projection of the process becomes stationary. We will review recent suitable Markov Chain Monte Carlo approaches for Bayesian inference such as the Gibbs sampler and the Geodesic Hamiltonian Monte Carlo method. Then we will propose extensions that can allow the ideas in both methods to be applied for cointegrated time series with non-Gaussian noise. We illustrate the efficiency and accuracy of these extensions using appropriate numerical experiments