Testing for Change-Point of the First-Order Autoregressive Time Series Models

In this paper, we consider the change point problem with the autocorrelated coefficient \phi in the first-order autoregressive time series models when the variance \sigma^2 is known and unknown. Using maximum likelihood method, we respectively discuss the abrupt change point and the gradual change point problems for the autocorrelated coefficient in first-order autoregressive time series models. With several situations, we propose some test statistics detecting the change point of the first-order autoregressive time series models and give the methods for detecting abrupt change point and gradual change point.