Bootstrapping confidence intervals for the change-point of time series

TL;DR

This paper develops a bootstrap-based method to construct confidence intervals for the unknown change-point in time series with abrupt mean changes and dependent errors, demonstrating improved accuracy over asymptotic intervals.

Contribution

It introduces a block bootstrap approach for estimating confidence intervals of change-points in dependent time series, accounting for dependence and providing more accurate interval estimation.

Findings

Bootstrap confidence intervals are closer to target levels.

Resampled intervals are generally smaller than asymptotic ones.

Method performs well in simulation studies.

Abstract

We study an AMOC time series model with an abrupt change in the mean and dependent errors that fulfill certain mixing conditions. We obtain confidence intervals for the unknown change-point via bootstrapping methods. Precisely we use a block bootstrap of the estimated centered error sequence. Then we reconstruct a sequence with a change in the mean using the same estimators as before. The difference between the change-point estimator of the resampled sequence and the one for the original sequence can be use as an approximation of the difference between the real change-point and its estimator. This enables us to construct confidence intervals using the empirical distribution of the resampled time series. A simulation study shows that the resampled confidence intervals are usually closer to their target levels and at the same time smaller than the asymptotic intervals.