Empirical Likelihood for Change Point Detection in Autoregressive Models

TL;DR

This paper introduces a nonparametric empirical likelihood method for detecting change points in autoregressive models, providing theoretical guarantees and demonstrating effectiveness through simulations and real data applications.

Contribution

It proposes a novel empirical likelihood-based change point detection method for AR models with proven asymptotic distribution and consistency, advancing nonparametric change point analysis.

Findings

Asymptotic null distribution is the extreme value distribution.

The test statistic is consistent.

Simulation results show high power of the proposed test.

Abstract

Change point analysis has become an important research topic in many fields of applications. Several research work has 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 the structural changes of the parameters in autoregressive (AR) models . Under certain conditions, the asymptotic null distribution of the empirical likelihood ratio test statistic is proved to be the extreme value distribution. Further, the consistency of the test statistic has been proved. Simulations have been carried out to show that the power of the proposed test statistic is significant. The proposed method is applied to real world data set to further illustrate the testing procedure.