We introduce an estimation method for the scaled skewness coefficient of the sample mean of short and long memory linear processes. This method can be extended to estimate higher moments such as curtosis coefficient of the sample mean. Also a general result on computing all asymptotic moments of partial sums is obtained, allowing in particular a much easier derivation of some existing central limit theorems for linear processes. The introduced skewness estimator provides a tool to empirically examine the error of the central limit theorem for long and short memory linear processes. We also show that, for both short and long memory linear processes, the skewness coefficient of the sample mean converges to zero at the same rate as in the i.i.d. case.

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相关数据部分和的偏度的一致估计量

我们介绍了一种对短记忆线性过程和长记忆线性过程的样本均值的缩放偏度系数的估计方法。这种方法可以扩展到估计更高的矩，例如样本均值的屈曲系数。还获得了计算部分和的所有渐近矩的一般结果，特别是允许更容易地推导出一些现有的线性过程的中心极限定理。引入的偏度估计器提供了一种工具，可以根据经验检查长短记忆线性过程的中心极限定理的误差。我们还表明，对于短期和长期记忆线性过程，样本均值的偏度系数以与 iid 情况相同的速率收敛到零。