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

Abstract.  We consider the estimation of the location of the pole and memory parameter ω ₀ and d of a covariance stationary process with spectral density
We investigate optimal rates of convergence for the estimators of ω ₀ and d , and the consequence that the lack of knowledge of ω ₀ 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.