Estimation of the location and exponent of the spectral singularity of a long memory process
Résumé
We consider the estimation of the location of the pole and memory parameter $\omega_0$ and $d$ of a covariance stationary process with spectral density $f(x) = |1-e^{i(x-\omega_0)}|^{-d} |1-e^{i(x+\omega_0)}|^{-d}f^*(x)$. We investigate optimal rates of convergence for the estimators of $\omega_0$ and $d$, and the consequence that the lack of knowledge of $\omega_0$ has on the estimation of the memory parameter $d$. We present estimators which achieve the optimal rates.
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