Robust multiscale estimation of time-average variance for time series segmentation
针对时间序列分割中多尺度噪声水平估计问题，提出一种对多重均值偏移稳健的尺度依赖时间平均方差估计器，并证明其一致性，适用于移动和与野生二元分割算法。
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.