We consider a parametric spectral density with power-law behavior
about a fractional pole at the unknown frequency $\omega$. The case of known
$\omega$, especially $\omega =0$, is standard in the long memory literature.
When $omega$ is unknown, asymptotic distribution theory for estimates of
parameters, including the (long) memory parameter, is significantly harder. We
study a form of Gaussian estimate. We establish $n$-consistency of the estimate
of $\omega$, and discuss its (non-standard) limiting distributional behavior.
For the remaining parameter estimates,we establish $\sqrt{n}$-consistency and
asymptotic normality.