We study asymptotic properties of nonparametric coherence estimator at the zero frequency in the presence of over-differenced time series. It is found that when one series is over-differenced, the coherences at the origin decay to zero, regardless of the bandwidths for kernel estimation. On the other hand, when both series are over differenced, coherences at the zero frequency grow with the bandwidths, which lead to misleading interpretation of non-existent long-run relationships. Our simulation studies confirm the theoretical conjecture.