论文标题
由长记忆高斯噪声驱动的AR（1）模型的第二钟估计器
Second Moment Estimator for An AR(1) Model Driven by A Long Memory Gaussian Noise
论文作者
论文摘要
在本文中，我们考虑了由长的记忆固定的高斯过程驱动的一阶自回归过程的推论问题。假设噪声的协方差函数可以表示为$ \ abs {k}^{2H-2} $ timple timers一个函数在无穷大处缓慢变化。分数高斯噪声和分数Arima模型以及其他一些高斯噪声是满足此假设的特殊示例。我们提出了第二钟估计器，并证明了强大的一致性并给出了渐近分布。此外，当极限分布是高斯时，我们给出了第四刻定理限制的上部浆果 - 埃塞恩。
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-Esséen bound by means of Fourth moment theorem.
