论文标题
通过应用于COVID-19的大流行数据，用于测试和监测结构变化的后退cusum
Backward CUSUM for Testing and Monitoring Structural Change with an Application to COVID-19 Pandemic Data
论文作者
论文摘要
众所周知，常规累积总和（CUSUM）测试患有低功率和大检测延迟。为了提高测试的能力，我们提出了两个替代统计数据。向后的cusum探测器以相反的时间顺序考虑递归残差，而堆叠的后cusum检测器依次累积了一个向后累积的残留物的三角形阵列。给出了递归残差部分的多元不变性原则，并在局部替代方案下得出了测试统计数据的限制分布。在回顾性背景下，如果在样品的中间或结束时发生断裂，则证明测试的局部功率大大高于常规库司测试的局部力量。当应用于监视方案时，发现堆叠后的cusum的检测延迟比常规监测的库司程序短得多。此外，我们根据向后的cusum检测器提出了一个断裂日期的估计器，并表明在监视练习中，该估计器倾向于优于通常的最大似然估计器。最后，提出了该方法对COVID-19数据的应用。
It is well known that the conventional cumulative sum (CUSUM) test suffers from low power and large detection delay. In order to improve the power of the test, we propose two alternative statistics. The backward CUSUM detector considers the recursive residuals in reverse chronological order, whereas the stacked backward CUSUM detector sequentially cumulates a triangular array of backwardly cumulated residuals. A multivariate invariance principle for partial sums of recursive residuals is given, and the limiting distributions of the test statistics are derived under local alternatives. In the retrospective context, the local power of the tests is shown to be substantially higher than that of the conventional CUSUM test if a break occurs in the middle or at the end of the sample. When applied to monitoring schemes, the detection delay of the stacked backward CUSUM is found to be much shorter than that of the conventional monitoring CUSUM procedure. Furthermore, we propose an estimator of the break date based on the backward CUSUM detector and show that in monitoring exercises this estimator tends to outperform the usual maximum likelihood estimator. Finally, an application of the methodology to COVID-19 data is presented.
