Robust multiscale estimation of time-average variance for time series segmentation

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, we propose 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, and propose an estimator that is robust to the presence of multiple change points. We show the consistency of the proposed estimator under general assumptions permitting heavy-tailedness, and discuss its use with two widely adopted data segmentation algorithms, the moving sum and the wild binary segmentation procedures. We illustrate the good performance of the proposed estimator through extensive simulation studies and on applications to the house price index and air quality data sets.