Empirical likelihood for change point detection in autoregressive models

Change point analysis has become an important research topic in many fields of applications. Several research work have been carried out to detect changes and its locations in time series data. In this paper, a nonparametric method based on the empirical likelihood is proposed to detect structural changes in the parameters of autoregressive (AR) models . Under certain conditions, the asymptotic null distribution of the empirical likelihood ratio test statistic is proved to be Gumbel type. Further, the consistency of the test statistic is verified. Simulations are carried out to show that the power of the proposed test statistic is significant. The proposed method is applied to monthly average soybean sales data to further illustrate the testing procedure.