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

TL;DR

This paper introduces a robust, scale-dependent estimator for the noise level in time series segmentation, improving change point detection accuracy in the presence of serial dependence and multiple mean shifts.

Contribution

It proposes a novel scale-dependent time-average variance estimator that is consistent under heavy-tailed distributions and enhances existing segmentation algorithms.

Findings

Estimator performs well in simulations with heavy-tailed data.

Improves change point detection in real-world house price and air quality data.

Robust to multiple mean shifts and serial dependence.

Abstract

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.