Empirical likelihood test in a posteriori change-point nonlinear model

Abstract

In this paper, in order to test whether changes have occurred in a nonlinear parametric regression, we propose a nonparametric method based on the empirical likelihood. Firstly, we test the null hypothesis of no-change against the alternative of one change in the regression parameters. Under null hypothesis, the consistency and the convergence rate of the regression parameter estimators are proved. The asymptotic distribution of the test statistic under the null hypothesis is obtained, which allows to find the asymptotic critical value. On the other hand, we prove that the proposed test statistic has the asymptotic power equal to 1. These theoretical results allows find a simple test statistic, very useful for applications. The epidemic model, a particular model with two change-points under the alternative hypothesis, is also studied. Numerical studies by Monte-Carlo simulations show the performance of the proposed test statistic, compared to an existing method in literature.

Change‐Point Detection in Autoregressive Models with no Moment Assumptions

“…We do not put any restriction between the parameters before and after the change under the alternative. Thus our approach differs from a part of the literature, which considers the statistic where (see Chuang and Chan, , or Ciuperca and Salloum, ). In other words, we work with a more general alternative that yields substantial computational advantages because the calculation of the supremum in the denominator of corresponds to a (2 p +2)‐dimensional optimization problem, which has to be solved for each k .…”

“…Baragona et al () used this concept to construct a test for change points and showed that in the case where the location of the break points is known, the limiting distribution of the corresponding test oxstatistic is a chi‐square distribution. Ciuperca and Salloum () considered the change‐point problem in a nonlinear model with independent data without assuming any knowledge of its location and derived an extreme value distribution as the limit distribution of the empirical likelihood ratio (ELR) test statistic. These findings are similar in spirit to the classical results in Csörgö and Horváth (), who considered the likelihood ratio test.…”

“…Convex hull of the set {g 1 ( 1 ), g 2 ( 1 ), g 3 ( 1 )} (gray region) (see Chuang andChan, 2002, or Ciuperca andSalloum, 2015). In other words, we work with a more general alternative that yields substantial computational advantages because the calculation of the supremum in the denominator of ( 2.9) corresponds to a (2p + 2)-dimensional optimization problem, which has to be solved for each k. Moreover, we demonstrate in Section 4 that this approach has a good finite-sample performance.…”

“…that in the case where the location of the break points is known, the limiting distribution of the corresponding test statistic is a chi-square distribution. Ciuperca and Salloum (2015) considered the change-point problem in a nonlinear model with independent data without assuming any knowledge of its location and derived an extreme value distribution as the limit distribution of the empirical likelihood ratio (ELR) test statistic. These findings are similar in spirit to the classical results in Csörgö and Horváth (1997), who considered the likelihood ratio test.The purpose of this paper is to investigate an EL test for a change in the parameters of an AR process with infinite variance (more precisely we do not assume the existence of any moments).…”

Parameter change test for location‐scale time series models with heteroscedasticity based on bootstrap

“…However, this test also has a drawback when dealing with conditional mean change. As such, the score vector‐based CUSUM test obtained from log‐likelihood functions has been used as an alternative . In fact, the estimates‐based CUSUM test behaves asymptotically similar to the score vector‐based CUSUM (hereafter, S‐CUSUM) test.…”