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<p>We derive some log-likelihood ratio-based tests for <i>weak change</i> detection in the conditional mean of a class of parametric conditional heteroscedastic nonlinear models. The weak convergence of the log-likelihood process is studied under the null hypothesis of no change and under a sequence of local alternatives of a weak change. For the study of the latter, we make use of the LAN property previously established. We first investigate the case where all the parameters involved are known. Next, we treat the case where only the shift parameter is known, and finally the case where this parameter is unknown. For the last case, a Bayesian technique is used for the construction of the test statistic. Numerical simulations show that, compared to the usual CUSUM test, ours has a more larger power. The method is also applied to three sets of real-world data.</p>

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On testing for weak change in the conditional mean of a class of nonlinear heteroscedastic models

  • 期刊论文

  • 发表日期：

    2025年11月23日

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  • Fatma Aouissaoui,
  • Joseph Ngatchou-Wandji,
  • Hamdi Fathallah

摘要

We derive some log-likelihood ratio-based tests for weak change detection in the conditional mean of a class of parametric conditional heteroscedastic nonlinear models. The weak convergence of the log-likelihood process is studied under the null hypothesis of no change and under a sequence of local alternatives of a weak change. For the study of the latter, we make use of the LAN property previously established. We first investigate the case where all the parameters involved are known. Next, we treat the case where only the shift parameter is known, and finally the case where this parameter is unknown. For the last case, a Bayesian technique is used for the construction of the test statistic. Numerical simulations show that, compared to the usual CUSUM test, ours has a more larger power. The method is also applied to three sets of real-world data.