This paper investigates the large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. The authors propose an estimator for the unknown parameter vector θ and show that it is consistent and asymptotically normal under appropriate conditions. These conditions are satisfied by fractional Gaussian noise and fractional ARMA processes, which are examples of strongly dependent sequences. The paper begins by introducing the concept of strongly dependent sequences, which have spectral densities that decay slowly near zero. These sequences are important in the study of self-similar stochastic processes. The authors then describe two examples of such sequences: fractional Gaussian noise and fractional ARMA processes. The paper then presents the theoretical properties of the proposed estimator. It shows that the estimator is consistent and asymptotically normal under conditions that are satisfied by fractional Gaussian noise and fractional ARMA processes. The conditions include the differentiability of the spectral density and its inverse, as well as the continuity of their derivatives. The paper also discusses the application of the results to fractional Gaussian noise and fractional ARMA processes. It shows that the estimator is consistent and asymptotically normal for these processes. The paper concludes with a discussion of the implications of the results for the estimation of parameters in strongly dependent stationary Gaussian time series.This paper investigates the large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. The authors propose an estimator for the unknown parameter vector θ and show that it is consistent and asymptotically normal under appropriate conditions. These conditions are satisfied by fractional Gaussian noise and fractional ARMA processes, which are examples of strongly dependent sequences. The paper begins by introducing the concept of strongly dependent sequences, which have spectral densities that decay slowly near zero. These sequences are important in the study of self-similar stochastic processes. The authors then describe two examples of such sequences: fractional Gaussian noise and fractional ARMA processes. The paper then presents the theoretical properties of the proposed estimator. It shows that the estimator is consistent and asymptotically normal under conditions that are satisfied by fractional Gaussian noise and fractional ARMA processes. The conditions include the differentiability of the spectral density and its inverse, as well as the continuity of their derivatives. The paper also discusses the application of the results to fractional Gaussian noise and fractional ARMA processes. It shows that the estimator is consistent and asymptotically normal for these processes. The paper concludes with a discussion of the implications of the results for the estimation of parameters in strongly dependent stationary Gaussian time series.