Testing a Class of Piece-Wise CHARN Models with Application to Change-Point Study

We study a likelihood ratio test for testing the conditional mean of a class of piece-wise stationary CHARN models. We establish the locally asymptotically normal (LAN) structure of the family of likelihoods under study. We prove that the test is asymptotically optimal, and we give an explicit form...

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Bibliographic Details
Published in:Mathematics (Basel) 2024-07, Vol.12 (13), p.2092
Main Authors: Salman, Youssef, Ngatchou-Wandji, Joseph, Khraibani, Zaher
Format: Article
Language:English
Subjects:
Algorithms
Asymptotic methods
change points
CHARN models
Generalized linear models
Generalized method of moments
LAN
Likelihood ratio
likelihood ratio tests
Mathematical functions
Mathematics
Optimization
Signal processing
Statistics
Stochastic models
Time series
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Summary:We study a likelihood ratio test for testing the conditional mean of a class of piece-wise stationary CHARN models. We establish the locally asymptotically normal (LAN) structure of the family of likelihoods under study. We prove that the test is asymptotically optimal, and we give an explicit form of its asymptotic local power. We describe an algorithm for detecting change points and estimating their locations. The estimates are obtained as time indices, maximizing the estimate of the local power. The simulation study we conduct shows the good performance of our method on the examples considered. This method is also applied to a set of financial data.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12132092