Asymptotic distributions of some test statistics in near-integrated AR processes are studied. Some exact formulas for the distribution functions are given as well as approximative results obtained by saddlepoint approximation techniques.

Let (<italic>X</italic>₁) be a discrete multivariate Gaussian autoregressive process of order 1. The paper derives the exact finite-sample joint moment generating function (m.g.f.) of the three quadratic forms constituting the sufficient statistic of the process. The formula is then specialized to some cases of...