  Spectral singularities at non-zero frequencies play an important role in
investigating cyclic or seasonal time series. The publication [2] introduced
the generalized filtered method-of-moments approach to simultaneously estimate
singularity location and long-memory parameters. This paper continues studies
of these simultaneous estimators. A wide class of Gegenbauer-type
semi-parametric models is considered. Asymptotic normality of several
statistics of the cyclic and long-memory parameters is proved. New adjusted
estimates are proposed and investigated. The theoretical findings are
illustrated by numerical results. The methodology includes wavelet
transformations as a particular case.
