  The generalized filtered method of moments was developed in the recent papers
by Alomari et al., 2020, and Ayache et al., 2022. It used functional data
obtained from continuously sampled cyclic long-memory stochastic processes to
simultaneously estimate their parameters. However, the majority of applications
deal with discretely sampled processes or time series. This paper extends the
approach to accommodate discrete-time scenarios. It proves that the new
discrete estimates exhibit analogous properties to the continuous case and are
strongly consistent with the same rates of convergence. The numerical study
results are presented to illustrate the theoretical findings and to indicate
the sampling rates and resolution levels required for accurate estimates.
