Origins of Spurious Long Memory

We consider a large class of structural change processes that generate spurious long memory. Among others, this class encompasses structural breaks as well as random level shift processes and smooth trends. The properties of these processes are studied based on a simple representation of their discrete Fourier transform. We find, that under very general conditions all of the models nested in this class generate poles in the periodogram at the zero frequency. These are of order $O(T)$, instead of the usual $O(T^2d)$ for long memory processes and $O(T^2)$ for a random walk. This order arises whenever both the mean changes and sample fractions at which they occur are non-degenerate, asymptotically.