We propose a location-adaptive self-normalization (SN) based test for change points in time series. The SN technique has been extensively used in change-point detection for its capability to avoid direct estimation of nuisance parameters. However, we find that the power of the SN-based test is susceptible to the location of the break and may suffer from a severe power loss, especially when the change occurs at the early or late stage of the sequence. This phenomenon is essentially caused by the unbalance of the data used before and after the change point when one is building a test statistic based on the cumulative sum (CUSUM) process. Hence, we consider leaving out the samples far away from the potential locations of change points and propose an optimal data selection scheme. Based on this scheme, a new SN-based test statistic adaptive to the locations of breaks is established. The new test can significantly improve the power of the existing SN-based tests while maintaining a satisfactory size. It is a unified treatment that can be readily extended to tests for general quantities of interest, such as the median and the model parameters. The derived optimal subsample selection strategy is not specific to the SN-based tests but is applicable to any method that relies on the CUSUM process, which may provide new insights in the area for future research.
翻译:我们建议对时间序列的变化点进行基于位置的自适应自我正常化(SN)测试。SN技术在变化点检测中广泛应用,以获得避免直接估计干扰参数的能力。然而,我们发现,基于SN测试的力量很容易受到断裂地点的影响,并可能遭受严重的功率损失,特别是当变化发生在序列的早期阶段或后期时,特别是当变化发生在顺序的早期阶段或后期时。这一现象主要是由于在变化点之前和之后使用的数据的不平衡造成的。当一个人正在根据累积总和(CUSUUM)进程建立测试统计时。因此,我们考虑将样本远离潜在变化点的位置,并提出最佳的数据选择方案。根据这个办法,将基于SNN测试的新测试数据用于调整断裂地点。新的测试可以大大提高现有基于SN的测试的力量,同时保持令人满意的尺寸。这是一种统一的处理方法,可以很容易扩展为一般利益量的测试,例如中位值和模型参数。因此,我们考虑将样品从可能的变异点中抽出最佳的子选择战略远离潜在的变异点,根据SNUM的任何区域进行特定的深入研究。新的研究方法,这种选择战略可能以SNUF的任何区域为SNUU的精确方法。