Limit results for $L^p$ functionals of weighted CUSUM processes

TL;DR

This paper characterizes the asymptotic distribution of $L^p$ functionals of weighted CUSUM processes in time series, providing theoretical insights for change point detection methods.

Contribution

It offers a comprehensive description of the asymptotic behavior of $L^p$ functionals of weighted CUSUM processes under general conditions, advancing change point analysis theory.

Findings

Asymptotic distribution formulas derived for $L^p$ functionals.

Applicable to a wide class of time series models.

Enhances understanding of change point detection methods.

Abstract

The cumulative sum (CUSUM) process is often used in change point analysis to detect changes in the mean of sequentially observed data. We provide a full description of the asymptotic distribution of $L^p, 1\leq p <\infty$, functionals of the weighted CUSUM process for time series under general conditions.