英文文献：Measurement Errors and Outliers in Seasonal Unit Root Testing-季节单位根检验中的测量误差和异常值
英文文献作者：Niels Haldrup,Antonio Montanés,Andreu Sanso
英文文献摘要：
Frequently, seasonal and non-seasonal data (especially macro time series) are observed with noise. For instance, the time series can have irregular abrupt changes and interruptions following as a result of additive or temporary change outliers caused by external circumstances which are irrelevant for the series of interest. Equally, the time series can have measurement errors. In this paper we analyse the above types of data irregularities on the behaviour of seasonal unit root tests. It occurs that in most cases outliers and measurement errors can seriously affect inference towards the rejection of seasonal unit roots. It is shown how the distortion of the tests will depend upon the frequency, magnitude, and persistence of the outliers as well as on the signal to noise ratio associated with measurement errors. Some solutions to the implied inference problems are suggested.

季节和非季节数据(特别是宏观时间序列)经常是用噪声观测的。例如，由于与感兴趣的序列无关的外部环境造成的附加或临时变化异常值，时间序列可能会出现不规则的突变和中断。同样，时间序列也会有测量误差。在本文中，我们分析了上述类型的数据不规则性对季节单位根检验行为的影响。在大多数情况下，异常值和测量误差会严重影响对季节单位根拒绝的推断。它显示了测试的失真将如何依赖于频率、幅度和异常值的持久性以及与测量误差相关的信噪比。提出了一些隐含推理问题的解决方法。