Tests of the Null of Cointegration Using Integrated and Modified OLS Residuals

This study investigates the asymptotic and finite-sample properties of KPSS-type cointegra-tion tests that use residuals from integrated and modified ordinary least squares estimations.The test statistic, denoted by KPSS^Fb is shown to provide a consistent test against the al-ternative of no cointegration under traditional small-b asymptotics, and has a pivotal null limitdistribution under fixed-b asymptotics. This study further analyzes the performance of thistest when the Andrews' AR(1) plug-in data-dependent bandwidth is employed. The estimatedAR(1) coefficient for the IMOLS residual is shown to not converge to 1 under the alternative ofno cointegration, which leads to a non-degenerate power in the limit. Simulation experimentsevaluate the performance of the test with various bandwidth rules being used, characterizingthe advantages and limitations of the test. To provide a partial remedy to some limitationsof the test, some modified IMOLS residuals are considered to obtain alternative data-drivenbandwidths