Data-driven semi-parametric detection of multiple changes in long-range dependent processes

TL;DR

This paper introduces a data-driven semi-parametric method for detecting multiple change points in long-range dependent processes, providing consistent estimators and improved accuracy through a penalized local Whittle contrast.

Contribution

It proposes a novel semi-parametric approach with a penalized local Whittle contrast for multiple change detection in long-range dependence processes, including a data-driven penalty selection.

Findings

Estimators are consistent with known convergence rates.

Monte-Carlo experiments confirm high accuracy of the estimators.

Data-driven penalty improves change point estimation accuracy.

Abstract

This paper is devoted to the offline multiple changes detection for long-range dependence processes. The observations are supposed to satisfy a semi-parametric long-range dependence assumption with distinct memory parameters on each stage. A penalized local Whittle contrast is considered for estimating all the parameters, notably the number of changes. The consistency as well as convergence rates are obtained. Monte-Carlo experiments exhibit the accuracy of the estimators. They also show that the estimation of the number of breaks is improved by using a data-driven slope heuristic procedure of choice of the penalization parameter.