Notes on the Effects of Over-Differencing on the Long-Run Relationship between Two Time Series Processes
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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.
Abstract
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.