Robust cointegration testing in the presence of weak trends,with an application to the human origin of global warming

Standard tests for the rank of cointegration of a vector autoregressive process present distributions that are affected by the presence of deterministic trends. We consider the recent approach of Demetrescu et al. (2009 Demetrescu, M., Lütkepohl, H., Saikkonen, P. (2009). Testing for the cointegrating rank of a vector autoregressive process with an uncertain deterministic trend term. Econometrics Journal 12:414–35.Crossref], Web of Science ®] , Google Scholar]) who recommend testing a composite null. We assess this methodology in the presence of trends (linear or broken) whose magnitude is small enough not to be always detectable at conventional significance levels. We model them using local asymptotics and derive the properties of the test statistics. We show that whether the trend is orthogonal to the cointegrating vector has a major impact on the distributions but that the test combination approach remains valid. We apply of the methodology to the study of cointegration properties between global temperatures and the radiative forcing of human gas emissions. We find new evidence of Granger Causality.