Low-frequency robust cointegration testing

Standard inference in cointegrating models is fragile because it relies on an assumption of an I ( 1 ) model for the common stochastic trends, which may not accurately describe the data’s persistence. This paper considers low-frequency tests about cointegrating vectors under a range of restrictions on the common stochastic trends. We quantify how much power can potentially be gained by exploiting correct restrictions, as well as the magnitude of size distortions if such restrictions are imposed erroneously. A simple test motivated by the analysis in Wright (2000) is developed and shown to be approximately optimal for inference about a single cointegrating vector in the unrestricted stochastic trend model.