DISTRIBUTION OF THE LEAST SQUARES ESTIMATOR IN A FIRST-ORDER AUTOREGRESSIVE MODEL
研究了一阶自回归模型中最小平方法估计量的有限样本分布，给出了适用于平稳和非平稳情况的统一渐近展开式，并验证了其高精度，优于现有近似方法。
This paper investigates the finite sample distribution of the least squares estimator of the autoregressive parameter in a first-order autoregressive model. A uniform asymptotic expansion for the distribution applicable to both stationary and nonstationary cases is obtained. Accuracy of the approximation to the distribution by a first few terms of this expansion is then investigated. It is found that the leading term of this expansion approximates well the distribution. The approximation is, in almost all cases, accurate to the second decimal place throughout the distribution. In the literature, there exist a number of approximations to this distribution which are specifically designed to apply in some special cases of this model. The present approximation compares favorably with those approximations and in fact, its accuracy is, with almost no exception, as good as or better than these other approximations. Convenience of numerical computations seems also to favor the present approximations over the others. An application of the finding is illustrated with examples.