Detecting Change Points in Segmented Linear Regression Heteroscedastic Models by Empirical Likelihood Methods

There have been increasingly keen interests in recent years in detecting change points under a segmented linear regression model with a series of observations. Central to the problem is how to detect the change point. For example, in econometrics it is an important and yet difficult problem how to determine as early as possible the starting and the ending points of a suspected ongoing recession. Existing detection procedures are mostly constructed under the assumption of homo-scedasticity in parametric models or via classic rank-test statistics in nonparametric models. The inference based on these procedures is sometimes invalidated by hetero-scedasticity. Another problem in the existing procedures is that the covariate values xi's are not used efficiently to construct a detection procedure. In this paper, we propose a new empirical likelihood approach to tackle these problems. The new method is an improvement over the procedure recently proposed by [5]. Empirical likelihood is a nonparametric technique for inference on functional population characteristics such as means and medians. One of the most appealing features of empirical likelihood methods is that it has large sampling properties similar to its counterpart likelihood-based parametric methods and enjoys both the robustness from its nonparametric nature and the efficiency from its likelihood construction. A bootstrap method is proposed to approximate the p-values of the new change point detection procedure. Simulation results show that the new procedure performs well with great improvement over [5]'s procedure.