  Vector Error Correction Model (VECM) is a classic method to analyse
cointegration relationships amongst multivariate non-stationary time series. In
this paper, we focus on high dimensional setting and seek for
sample-size-efficient methodology to determine the level of cointegration. Our
investigation centres at a Bayesian approach to analyse the cointegration
matrix, henceforth determining the cointegration rank. We design two algorithms
and implement them on simulated examples, yielding promising results
particularly when dealing with high number of variables and relatively low
number of observations. Furthermore, we extend this methodology to empirically
investigate the constituents of the S&P 500 index, where low-volatility
portfolios can be found during both in-sample training and out-of-sample
testing periods.
