Approximations to some exact distributions in the rrasr orderautoregressive model with dependenterrors
研究了带相关误差的近单位根自回归模型中最小二乘估计量的分布，提出一种基于样本量依赖核的近似方法，改进了现有局部渐近框架，适用于边界参数情形。
We consider the near-integrated autoregressive model where and the sequence of errors ut is allowed to be an MA(l) process process or an AR(1) process . We study the distribution of α the least-squares estimator of α. We suggest modifications to the local asymptotic framework analyzed by Nabeya and Perron (1992) which provide excellent approximations for all cases where θ or ρ are close to their relevant boundaries. The idea behind this new approximation is based on the “Fredholm determinant approach” where instead of approximating, for example, the finite sample distribution by, say where K(s,t,x) is a suitable limiting kernel (independent of the sample size T), we use a kernel KT(s,t,x), say, that depends on the sample size. By a judicious choice of the dependence of the kernel on Twe are able to 0 btain approximations that are not only excellent but also relatively easy to evaluate using straightforward numerical integration techniques. Our results are very encouraging and show the approach to be worthy of further investigations and applications in more complex models.