Test for the null hypothesis of cointegration with reduced size distortion

This paper considers a single equation cointegrating model and proposes the locally best invariant and unbiased (LBIU) test for the null hypothesis of cointegration. We derive the asymptotic local power functions and compare them with the standard residualbased test, and we show that the LBIU test is more powerful in a wide range of local alternatives. Then, we conduct a Monte Carlo simulation to investigate the nite sample properties of the tests and show that the LBIU test outperforms the residual-based test in terms of both size and power. The advantage of the LBIU test is particularly patent when the error is highly autocorrelated. Further, we point out that nite sample performance of existing tests is largely affected by the initial value condition while our tests are immune to it. We propose a simple transformation of data that resolves the problem in the existing tests.