A Simple Cointegration Test Robust to Serial Correlation

This paper presents a novel test of cointegration that is robust to general forms of weak dependence in the innovation sequences and is simple to implement. In contrast to existing procedures, this is achieved without applying corrections to the test statistic for removing the effect of serial dependence; the choice of suitable estimators of nuisance parameters affecting the test distribution or the application of modified information criteria to select the truncation lag in residual-based tests. In the scalar case our test is two sided and does not require pre-estimation of the cointegration relationship. Under cointegration, the test converges to zero for beta>0, and four, for beta<0, with beta the cointegrating parameter. Under the null hypothesis of no cointegration, the test statistic converges to the asymptotic distribution of the parameter estimator of a spurious regression. Critical values are tabulated without the need of estimating nuisance parameters, and provide reliable finite-sample performance under general forms of weak dependence in the stationary sequence. For multiple time series, the cointegration vector needs to be estimated and has an effect on the asymptotic distribution of the test that is, nevertheless, free of nuisance parameters. Critical values are tabulated, conditional on the number of unit roots in the system. A Monte-Carlo simulation exercise shows the excellent size and power properties of the proposed test for a wide variety of ARMA(1,1) models