Conflicts Among Tests For Cointegration

This note illustrates that, under the null hypothesis of no cointegration, the correlation of p-values from a single-equation residual-based test (i.e. ADF, Zt, or Zx) with a system-based test (trace or maximum eigenvalue) is very low. With data generating processes under the null or 'near' it, the two types of tests can yield virtually any combination of p-values regardless of sample size.