Power of Weighted Test Statistics for Structural Change in Time Series

TL;DR

This paper analyzes how weighted test statistics for change-point detection in time series perform depending on the change-point location, highlighting their strengths and weaknesses in different scenarios.

Contribution

It introduces a framework to evaluate the power of weighted change-point tests, including CUSUM and Wilcoxon, as functions of change-point position and magnitude.

Findings

Weighted tests are more powerful near the interval's edges.

They lose power when the change occurs in the middle.

The study quantifies the effectiveness of different weighting schemes.

Abstract

We investigate the power of some common change-point tests as a function of the location of the change-point. The test statistics are maxima of weighted U-statistics, with the CUSUM test and the Wilcoxon change-point test as special examples. We study the power under local alternatives, where we vary both the location of the change-point and the magnitude of the change. We quantify in which way weighted versions of the tests are more powerful when the change occurs near the beginning or the end of the time interval, while losing power against changes in the center.