Finding cointegration rank in high dimensional systems using the Johansen test: An illustration using data based Monte Carlo simulations

We examine the ability of the Johansen (1991) test to estimate the number of unit roots in high dimensional systems. We use data based Monte Carlo methods as a simple means of evaluating the validity of inference using asymptotic critical values. These simulations for a typical annual post WW2 dataset illustrate how the estimated number of unit roots change in a nonmonotone fashion with the dimension of the system, and with the number of lags in the VAR representation. We find that overparametrization in high dimensions is as bad as underparametrization. The BIC outperforms the AIC in our setup.