Estimation of the location and exponent of the spectral singularity of a long memory process

We consider the estimation of the location of the pole and memory parameter ω0 and d of a covariance stationary process with spectral density. We investigate optimal rates of convergence for the estimators of ω0 and d, and the consequence that the lack of knowledge of ω0 has on the estimation of the memory parameter d. We present estimators which achieve the optimal rates. A small Monte-Carlo study is included to illustrate the finite sample performance of our estimators.