Nonparametric and Parametric Methods for Change-Point Detection in Parametric Models

We consider a posteriori and a priori change-point models. The parametric regression functions of the each phase can be nonlinear or linear, and moreover, in the linear case, the number of the explanatory variables could be large. Theoretical results and simulations are presented for each model. For a posteriori change-point nonlinear model, the results obtained by two estimation techniques are given in the case when the change-point number is known. So, the quantile and empirical likelihood nonparametric methods are considered. If the number of the change-points is unknown, a consistent criterion is proposed. When the change-point model is linear with a large number of explanatory variables, it would make the automatic selection of variables. The adaptive LASSO quantile method is then proposed and studied. On the other hand, we propose a nonparametric test based on the empirical likelihood, in order to test if the model changes. For detecting in real time a change in model, we consider two cases, nonlinear and linear models. For a nonlinear model, a hypothesis test based on CUSUM of LS residuals is constructed. For a linear model with large number of explanatory variables, we propose a CUSUM test statistic based on adaptive LASSO residuals.