Trend adjustment prior to testing for the cointegrating rank of a VAR process

Testing the cointegrating rank of a vector autoregressive process which may have a deterministic linear trend is considered. Previous proposals for dealing with such a situation are either to allow for a deterministic trend term in computing a suitable test statistic or else remove the linear trend first and then derive the test statistic from the trend-adjusted data. In this study the latter approach is considered and a new, simple method for trend removal is proposed which is based on estimating the trend parameters under the null hypothesis. LR (likelihood ratio) and LM (Lagrange multiplier) type test statistics are derived on the basis of the trend-adjusted data and their asymptotic distributions are considered under the null hypothesis and under local alternatives. A simulation comparison with other proposals is performed which demonstrates the potentially superior small sample performance of the new tests.