一阶自回归模型参数变点的假设检验

摘要

本文讨论一阶自回归模型自归参数φ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σ2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φ的Abrupt Change-Point 和Gradual Change-Point的检测问题.%In this paper,we consider the change point problem with the autocorrelated coefficient φ in the first-order autoregressive time series models when the variance σ2 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.