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.

翻译：在本文中,我们考虑了第一个顺序自动递减过程的推论问题,第一个顺序是非零平均值,由长期记忆固定的高斯进程驱动。假设噪音的共变函数可以以美元表示为正常数乘以美元,当美元倾向于无穷的时候,当美元时,美元是正常数,分数高斯噪音和分数ARIMA模型是满足这一假设的特殊例子。 我们提出片刻估计并证明强烈的连贯性、无药可治的正常性和联合无药可治的正常性。