Functional Sieve Bootstrap for the Partial Sum Process with Application to Change-Point Detection

TL;DR

This paper develops a functional sieve bootstrap method to accurately estimate the distribution of partial sum processes in functional time series, enabling reliable change-point detection with theoretical guarantees and demonstrated finite sample effectiveness.

Contribution

It introduces a consistent functional sieve bootstrap approach for change-point detection in functional time series, with theoretical validation and practical simulation results.

Findings

FSB accurately estimates critical values for CUSUM tests

The method is consistent under weak assumptions

Finite sample simulations show good performance

Abstract

This paper applies the functional sieve bootstrap (FSB) to estimate the distribution of the partial sum process for time series stemming from a weakly stationary functional process. Consistency of the FSB procedure under weak assumptions on the underlying functional process is established. This result allows for the application of the FSB procedure to testing for a change-point in the mean of a functional time series using the CUSUM-statistic. We show that the FSB asymptotically correctly estimates critical values of the CUSUM-based test under the null-hypothesis. Consistency of the FSB-based test under local alternatives also is proven. The finite sample performance of the procedure is studied via simulations.