Multiscale and multilevel technique for consistent segmentation of nonstationary time series

TL;DR

This paper introduces a fast, consistent segmentation method for nonstationary time series using wavelet-based analysis, capable of accurately detecting multiple change points across scales.

Contribution

It presents a novel binary segmentation approach with a theoretically justified test criterion for wavelet periodograms, improving detection of breakpoints in nonstationary time series.

Findings

Method achieves accurate breakpoint detection in simulations

Performs well across different scales and locations

Demonstrates robustness and efficiency in practice

Abstract

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.