Low-frequency Robust Cointegration Testing

Standard inference in cointegrating models is fragile for two distinct reasons. First, even though cointegration concerns low-frequency variability, inference relies on higher frequency variability in the data; second, inference assumes an I(1) model for the common trends which may not accurately describe the data’s persistence. This paper discusses efficient inference about the cointegrating vector in a bivariate model that is robust to both sources of misspecification. A small of number of weighted averages are used to summarize the data’s low-frequency variability. These weighted averages have an asymptotic multivariate normal distribution, and cointegration imposes restrictions on the associated covariance matrix. Under the null hypothesis, the common trend is modeled by a flexible limiting Gaussian process that includes the I(1), local-to-unity, and fractional model as special cases. The flexibility in the trend process introduces a large number of nuisance parameters. An upper bound on power for tests is pre-sented, and this upper bound is computed for tests that control size for the flexible trend specification, and several special cases. A simple test motivated by the analysis in Wright (2000) almost achieves the power bound under the flexible common trend specification, so the test is approximately optimal