We consider the near-integrated autoregressive model where and the sequence of errors u_t 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 K_T(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.