一阶自回归模型参数变点的假设检验

本文讨论一阶自回归模型自回归参数$phi$的变点问题. 对于一阶自回归模型, 在模型的白噪声序列的方差$sigma^2$已知和未知的条件下, 利用最大似然方法, 我们分别讨论了模型自回归参数$phi$的Abrupt Change-Point 和Gradual Change-Point的检测问题.

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 timeseries 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.