A Cramér–von Mises test for a class of mean time dependent CHARN models with application to change-point detection

We derive a Cramér–von Mises test for testing a class of time dependent coefficients Coditional Heteroscedastic AutoRegressive Non Linear (CHARN) models. The test statistic is based on the log-likelihood ratio process whose weak convergence in a suitable Fréchet space is studied under the null hypot...

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Bibliographic Details
Published in:Statistical inference for stochastic processes : an international journal devoted to time series analysis and the statistics of continuous time processes and dynamic systems 2024-04, Vol.27 (1), p.25-61
Main Authors: Ngatchou-Wandji, Joseph, Ltaifa, Marwa
Format: Article
Language:English
Subjects:
Asymptotic properties
Empirical analysis
Likelihood ratio
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Statistical Theory and Methods
Time dependence
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Summary:We derive a Cramér–von Mises test for testing a class of time dependent coefficients Coditional Heteroscedastic AutoRegressive Non Linear (CHARN) models. The test statistic is based on the log-likelihood ratio process whose weak convergence in a suitable Fréchet space is studied under the null hypothesis and under the sequence of local alternatives considered. This study makes use of the locally asymptotically normal (LAN) result previously established. Using the Karhunen–Loève expansion of the limiting process of the log-likelihood ratio process, the asymptotic null distribution and the power of the test statistic are accurately approximated. These results are applied to change-point analysis. An empirical study is done for evaluating the performance of the methodology proposed.
ISSN:1387-0874
1572-9311
DOI:10.1007/s11203-023-09295-x