On detecting weak changes in the mean of CHARN models

TL;DR

This paper develops an asymptotically optimal likelihood ratio test for detecting weak mean changes in CHARN models, providing explicit power calculations, detection strategies, and demonstrating effectiveness through simulations and real data applications.

Contribution

It introduces a new likelihood ratio test for weak change detection in CHARN models, with explicit power analysis and practical detection strategies.

Findings

Test is asymptotically optimal under LAN structure.

Detection strategies based on local power estimates.

Simulation and real data show superior performance.

Abstract

We study a likelihood ratio test for detecting multiple {\it weak} changes in the mean of a class of CHARN models. The locally asymptotically normal (LAN) structure of the family of likelihoods under study is established. It results that the test is asymptotically optimal, and an explicit form of its asymptotic local power is given as a function of candidates change locations and changes magnitudes. Strategies for weak change-points detection and their locations estimates are described. The estimates are obtained as the time indices maximizing an estimate of the local power. A simulation study shows the good performance of our methods compared to some existing approaches. Our results are also applied to three sets of real data.