Testing for Cointegrating Relationships with Near-Integrated Data

Abstract

Testing theories about political change requires analysts to make assumptions about the memory of their time series. Applied analyses are often based on inferences that time series are integrated and cointegrated. Typically analyses rest on Dickey—Fuller pretests for unit roots and a test for cointegration based on the Engle—Granger two-step method. We argue that this approach is not a good one and use Monte Carlo analysis to show that these tests can lead analysts to conclude falsely that the data are cointegrated (or nearly cointegrated) when the data are near-integrated and not cointegrating. Further, analysts are likely to conclude falsely that the relationship is not cointegrated when it is. We show how inferences are highly sensitive to sample size and the signal-to-noise ratio in the data. We suggest three things. First, analysts should use the single equation error correction test for cointegrating relationships; second, caution is in order in all cases where near-integration is a reasonable alternative to unit roots; and third, analysts should drop the language of cointegration in many cases and adopt single-equation error correction models when the theory of error correction is relevant.