Abstract We consider testing for the presence of a change in mean, at an unknown point in the sample, in data that are possibly fractionally integrated, and of unknown order. This testing problem has recently been considered in a number of papers, most notably Shao (2011, “A Simple Test of Changes in Mean in the Possible Presence of Long-Range Dependence.” Journal of Time Series Analysis 32:598–606) and Iacone, Leybourne, and Taylor (2013b, “A Fixed-b Test for a Break in Level at an Unknown Time under Fractional Integration.” Journal of Time Series Analysis 35:40–54) who employ Wald-type statistics based on OLS estimation and rely on a self-normalization to overcome the fact that the standard Wald statistic does not have a well-defined limiting distribution across different values of the memory parameter. Here, we consider an alternative approach that uses the standard Wald statistic but is based on quasi-GLS estimation to control for the effect of the memory parameter. We show that this approach leads to significant improvements in asymptotic local power.

中文翻译：

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在分数积分下测试均值的变化

摘要我们考虑在样本中一个未知点，可能是部分积分且阶次未知的数据中测试均值变化的存在。最近在许多论文中都考虑到了这个测试问题，最著名的是Shao（2011年，“对可能存在的远程依赖项进行均值变化的简单测试。”时间序列分析杂志32：598-606）和Iacone，Leybourne和Taylor（2013b，“分数积分下未知时间的水平破损的固定b检验”。时间序列分析杂志35：40–54），他们使用基于OLS估计的Wald型统计数据并依靠自我归一化来克服以下事实：标准Wald统计量在内存参数的不同值之间没有明确定义的极限分布。这里，我们考虑使用标准Wald统计量但基于准GLS估计来控制内存参数影响的替代方法。我们表明，这种方法可以显着改善渐近局部功率。