# Multiscale and multilevel technique for consistent segmentation of nonstationary time series

arXiv: https://arxiv.org/abs/1611.09727 · HTML: https://mlsanity.com/paper/1611.09727/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2016.

## Built on by (most cited first, 5 of 5)

- [Testing Stationarity and Change Point Detection in Reinforcement Learning](https://mlsanity.com/paper/2203.01707/) (2022)
- [Long Short-term Cognitive Networks](https://mlsanity.com/paper/2106.16233/) (2021)
- [Multi-scale Anomaly Detection for Big Time Series of Industrial Sensors](https://mlsanity.com/paper/2204.08159/) (2022)
- [Monitoring the risk of a tailings dam collapse through spectral analysis of satellite InSAR time-series data](https://mlsanity.com/paper/2302.00781/) (2023)
- [Change Point Detection with Conceptors](https://mlsanity.com/paper/2308.06213/) (2023)

## Abstract (arXiv)

In this paper, we propose a fast, well-performing, and consistent method for segmenting a piecewise-stationary, linear time series with an unknown number of breakpoints. The time series model we use is the nonparametric Locally Stationary Wavelet model, in which a complete description of the piecewise-stationary second-order structure is provided by wavelet periodograms computed at multiple scales and locations. The initial stage of our method is a new binary segmentation procedure, with a theoretically justified and rapidly computable test criterion that detects breakpoints in wavelet periodograms separately at each scale. This is followed by within-scale and across-scales post-processing steps, leading to consistent estimation of the number and locations of breakpoints in the second-order structure of the original process. An extensive simulation study demonstrates good performance of our method.