Bootstrapping the likelihood ratio cointegration test in error correction models with unknown lag order

The finite-sample size and power properties of bootstrapped likelihood ratio systems cointegration tests are investigated via Monte Carlo simulations when the true lag order of the data generating process is unknown. Recursive bootstrap schemes are employed which differ in the way the lag order is chosen. The order is estimated by minimizing different information criteria and by combining the corresponding order estimates. In comparison to the standard asymptotic likelihood ratio test based on an estimated lag order, it is found that bootstrapping can lead to improvements in small samples even when the true lag order is unknown while the power loss is moderate.