Estimation in the First Order Moving Average Model Based on Sample Autocorrelations
基于样本自相关的一阶移动平均模型估计
For the first order moving average we consider a proposal by Walker (Biometrika, 1961) to use $k$ sample autocorrelations $(1 < k < T, T$ sample size), to estimate the first autocorrelation of the model, and hence its basic parameter. When $k = k_T \rightarrow \infty$ as $T \rightarrow \infty$, the estimator is proved consistent and asymptotically normal and efficient, the latter provided $k_T$ dominates $\log T$ and is dominated by $T^\frac{1}{2}$. An alternative form of…