Finite Inference Of Autoregressive Coefficient In AR (1) Model

This paper discusses thoroughly the problem of finite sample statistical inference for autoregressive coefficient in AR(1) model. There are two parts in this paper. In the front part, for first order autoregressive model with normal white noise, this paper constructs the exact confidence region of autoregressive coefficient in the model firstly(no matter the mean of AR(1) series is or not known), and some simple test questions about autoregressive coefficient is research on it. Then, the asymptotic confidence region is established by likelihood ratio test. This two kinds of confidence region is compared in coverage probability sense at last(by Monte Carlo method). The result shows that, in finite sample situation, the exact confidence region proposed in this paper is better than the asymptotic confidence region based on likelihood ratio test.In another part behind, the paper is devoted to the study of existence and uniqueness of maximum likelihood estimates of unknown parameters in AR(1) model with normal white noise. The results are provided the present: no matter the mean of AR(1) series is or not known, the maximum likelihood estimates of unknown parameters in AR(1) model exist and unique with probability one. And the distribution of maximum likelihood estimation of autoregressive coefficient only rely on itself. The method that used can give analytical expressions of distribution function of maximum likelihood estimation of autoregressive coefficient, bases on this, the figure can be drawn by using Monte Carlo method.