The Periodogram of Spurious Long-Memory Processes

We derive the properties of the periodogram local to the zero frequency for a large class of spurious long-memory processes. The periodogram is of crucial importance in this context, since it forms the basis for most commonly used estimation methods for the memory parameter. The class considered nests a wide range of processes such as deterministic or stochastic structural breaks and smooth trends as special cases. Several previous results on these special cases are generalized and extended. All of the spurious long-memory processes considered share the property that their impact on the periodogram at the Fourier frequencies local to the origin is different than that of true long-memory processes. Both types of processes therefore exhibit clearly distinct empirical features.