论文标题
强大的多尺度估计时间平均差异的时间序列分段
Robust multiscale estimation of time-average variance for time series segmentation
论文作者
论文摘要
为了检测多个均值移位的规范变更点问题而开发了几种方法，这些方法在多个尺度上寻找数据的变化。在这种方法中，通常需要对噪声水平进行估计，以区分真正的变化与由于噪声引起的随机波动。当存在串行依赖性时，使用噪声水平的单个估计器可能不合适。取而代之的是，提议采用依赖比例的时间平均方差常数，该方差取决于考虑数据部分的长度，以评估其噪声的水平。因此，开发了对多个均值偏移存在的强大估计器。提出的估计器的一致性在允许重尾的一般假设下显示，并讨论了两种广泛采用的数据分割算法，即移动总和和野生二进制分割程序。通过广泛的仿真研究以及对房屋价格指数和空气质量数据集的应用来说明拟议估计器的性能。
There exist several methods developed for the canonical change point problem of detecting multiple mean shifts, which search for changes over sections of the data at multiple scales. In such methods, estimation of the noise level is often required in order to distinguish genuine changes from random fluctuations due to the noise. When serial dependence is present, using a single estimator of the noise level may not be appropriate. Instead, it is proposed to adopt a scale-dependent time-average variance constant that depends on the length of the data section in consideration, to gauge the level of the noise therein. Accordingly, an estimator that is robust to the presence of multiple mean shifts is developed. The consistency of the proposed estimator is shown under general assumptions permitting heavy-tailedness, and its use with two widely adopted data segmentation algorithms, the moving sum and the wild binary segmentation procedures, is discussed. The performance of the proposed estimator is illustrated through extensive simulation studies and on applications to the house price index and air quality data sets.
