An analytical formula is derived to approximate the finite sample bias of the ordinary least-squares (OLS) estimator of the autoregressive parameter when the underlying process has a unit root. It is found that the bias is expressible in terms of parabolic cylinder functions which are easy to...

It was recently shown (Abadir, 1993b) that nonstationarity causes the limiting distributions of the Wald (<italic>W</italic>) and Lagrange multiplier (<italic>LM</italic>) statistics to become different from each other. This paper demonstrates that such a divergence between the two distributions can be used as an indicator of...

Closed forms for the distribution of some conventional statistics are given as a prelude to deriving their asymptotic power functions as unit root tests. In the process, an important distinction is drawn between two classes of statistics: one which relies on deterministic normalizations and the...

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...