Inference for mean change-point in infinite variance AR(p) process

In this paper a weighted least square method is proposed to infer the change-point in AR(p) process with infinite variance, and a weighted cumulative sum statistic (CUSUM) is obtained. Based on the weighted CUSUM statistic the distribution of the test statistic is derived. The consistency and the rate of convergence for the weighted CUSUM estimator are also established. The simulation results support the validity of such a weighted CUSUM estimator.