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 of [41] and the Geodesic Hamiltonian Monte Carlo method of [3]. 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.