  In this paper, we consider an inference problem for the first order
autoregressive process driven by a long memory stationary Gaussian process.
Suppose that the covariance function of the noise can be expressed as
$\abs{k}^{2H-2}$ times a function slowly varying at infinity. The fractional
Gaussian noise and the fractional ARIMA model and some others Gaussian noise
are special examples that satisfy this assumption. We propose a second moment
estimator and prove the strong consistency and give the asymptotic
distribution. Moreover, when the limit distribution is Gaussian, we give the
upper Berry-Ess\'een bound by means of Fourth moment theorem.
