Ratio tests for change point detection

TL;DR

This paper introduces ratio-based CUSUM tests for change point detection in time series, avoiding complex scale estimation, and demonstrates their effectiveness on AR(1) and GARCH(1,1) models.

Contribution

The paper proposes novel ratio tests for change point detection that eliminate the need for scale parameter estimation, simplifying analysis for dependent data.

Findings

Effective detection of mean change in AR(1) sequences

Applicable to GARCH(1,1) error models

Avoids complex scale estimation procedures

Abstract

We propose new tests to detect a change in the mean of a time series. Like many existing tests, the new ones are based on the CUSUM process. Existing CUSUM tests require an estimator of a scale parameter to make them asymptotically distribution free under the no change null hypothesis. Even if the observations are independent, the estimation of the scale parameter is not simple since the estimator for the scale parameter should be at least consistent under the null as well as under the alternative. The situation is much more complicated in case of dependent data, where the empirical spectral density at 0 is used to scale the CUSUM process. To circumvent these difficulties, new tests are proposed which are ratios of CUSUM functionals. We demonstrate the applicability of our method to detect a change in the mean when the errors are AR(1) and GARCH(1,1) sequences.