Mixed signals among tests for cointegration

This paper illustrates that, under the null hypothesis of no cointegration, the correlation of p ‐values from a single‐equation residual‐based test (i.e., ADF or $\widehat{Z}_{\alpha}$ ) with a system‐based test (trace or maximum eigenvalue) is very low even as the sample size gets large. 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. As a practical matter, we also conduct tests for cointegration on 132 data sets from 34 studies appearing in this Journal and find substantial differences in p ‐values for the same data set. Copyright © 2004 John Wiley & Sons, Ltd.