  In this paper, we consider an inference problem for the first order
autoregressive process with non-zero mean driven by a long memory stationary
Gaussian process. Suppose that the covariance function of the noise can be
expressed as $|k|^{2H-2}$ times a positive constant when $k$ tends to infinity,
and the fractional Gaussian noise and the fractional ARIMA model are special
examples that satisfy this assumption. We propose moment estimators and prove
the strong consistency, the asymptotic normality and joint asymptotic
normality.
